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<title>DISCRETE FORMULATION</title> |
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<o:Author>Physical Oceanography</o:Author> |
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<o:LastAuthor>Chris Hill</o:LastAuthor> |
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<o:Revision>2</o:Revision> |
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<o:TotalTime>349</o:TotalTime> |
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<o:LastPrinted>1997-12-19T16:44:00Z</o:LastPrinted> |
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<o:Created>2001-05-21T01:59:00Z</o:Created> |
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<o:Company>MIT</o:Company> |
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margin-left:90.0pt; |
| 434 |
text-indent:-18.0pt;} |
| 435 |
@list l1 |
| 436 |
{mso-list-id:-131; |
| 437 |
mso-list-type:simple; |
| 438 |
mso-list-template-ids:1943580580;} |
| 439 |
@list l1:level1 |
| 440 |
{mso-level-tab-stop:72.0pt; |
| 441 |
mso-level-number-position:left; |
| 442 |
margin-left:72.0pt; |
| 443 |
text-indent:-18.0pt;} |
| 444 |
@list l2 |
| 445 |
{mso-list-id:-130; |
| 446 |
mso-list-type:simple; |
| 447 |
mso-list-template-ids:201997080;} |
| 448 |
@list l2:level1 |
| 449 |
{mso-level-tab-stop:54.0pt; |
| 450 |
mso-level-number-position:left; |
| 451 |
margin-left:54.0pt; |
| 452 |
text-indent:-18.0pt;} |
| 453 |
@list l3 |
| 454 |
{mso-list-id:-129; |
| 455 |
mso-list-type:simple; |
| 456 |
mso-list-template-ids:734058442;} |
| 457 |
@list l3:level1 |
| 458 |
{mso-level-tab-stop:36.0pt; |
| 459 |
mso-level-number-position:left; |
| 460 |
text-indent:-18.0pt;} |
| 461 |
@list l4 |
| 462 |
{mso-list-id:-128; |
| 463 |
mso-list-type:simple; |
| 464 |
mso-list-template-ids:-2121900762;} |
| 465 |
@list l4:level1 |
| 466 |
{mso-level-number-format:bullet; |
| 467 |
mso-level-text:\F0B7; |
| 468 |
mso-level-tab-stop:90.0pt; |
| 469 |
mso-level-number-position:left; |
| 470 |
margin-left:90.0pt; |
| 471 |
text-indent:-18.0pt; |
| 472 |
font-family:Symbol;} |
| 473 |
@list l5 |
| 474 |
{mso-list-id:-127; |
| 475 |
mso-list-type:simple; |
| 476 |
mso-list-template-ids:-117900590;} |
| 477 |
@list l5:level1 |
| 478 |
{mso-level-number-format:bullet; |
| 479 |
mso-level-text:\F0B7; |
| 480 |
mso-level-tab-stop:72.0pt; |
| 481 |
mso-level-number-position:left; |
| 482 |
margin-left:72.0pt; |
| 483 |
text-indent:-18.0pt; |
| 484 |
font-family:Symbol;} |
| 485 |
@list l6 |
| 486 |
{mso-list-id:-126; |
| 487 |
mso-list-type:simple; |
| 488 |
mso-list-template-ids:264658678;} |
| 489 |
@list l6:level1 |
| 490 |
{mso-level-number-format:bullet; |
| 491 |
mso-level-text:\F0B7; |
| 492 |
mso-level-tab-stop:54.0pt; |
| 493 |
mso-level-number-position:left; |
| 494 |
margin-left:54.0pt; |
| 495 |
text-indent:-18.0pt; |
| 496 |
font-family:Symbol;} |
| 497 |
@list l7 |
| 498 |
{mso-list-id:-125; |
| 499 |
mso-list-type:simple; |
| 500 |
mso-list-template-ids:1012666270;} |
| 501 |
@list l7:level1 |
| 502 |
{mso-level-number-format:bullet; |
| 503 |
mso-level-text:\F0B7; |
| 504 |
mso-level-tab-stop:36.0pt; |
| 505 |
mso-level-number-position:left; |
| 506 |
text-indent:-18.0pt; |
| 507 |
font-family:Symbol;} |
| 508 |
@list l8 |
| 509 |
{mso-list-id:-120; |
| 510 |
mso-list-type:simple; |
| 511 |
mso-list-template-ids:228515806;} |
| 512 |
@list l8:level1 |
| 513 |
{mso-level-tab-stop:18.0pt; |
| 514 |
mso-level-number-position:left; |
| 515 |
margin-left:18.0pt; |
| 516 |
text-indent:-18.0pt;} |
| 517 |
@list l9 |
| 518 |
{mso-list-id:-119; |
| 519 |
mso-list-type:simple; |
| 520 |
mso-list-template-ids:412366024;} |
| 521 |
@list l9:level1 |
| 522 |
{mso-level-number-format:bullet; |
| 523 |
mso-level-text:\F0B7; |
| 524 |
mso-level-tab-stop:18.0pt; |
| 525 |
mso-level-number-position:left; |
| 526 |
margin-left:18.0pt; |
| 527 |
text-indent:-18.0pt; |
| 528 |
font-family:Symbol;} |
| 529 |
@list l10 |
| 530 |
{mso-list-id:34432912; |
| 531 |
mso-list-template-ids:-1574938486;} |
| 532 |
@list l10:level1 |
| 533 |
{mso-level-text:%1; |
| 534 |
mso-level-tab-stop:20.25pt; |
| 535 |
mso-level-number-position:left; |
| 536 |
margin-left:20.25pt; |
| 537 |
text-indent:-20.25pt;} |
| 538 |
@list l10:level2 |
| 539 |
{mso-level-start-at:2; |
| 540 |
mso-level-text:"%1\.%2"; |
| 541 |
mso-level-tab-stop:36.0pt; |
| 542 |
mso-level-number-position:left; |
| 543 |
margin-left:36.0pt; |
| 544 |
text-indent:-36.0pt;} |
| 545 |
@list l10:level3 |
| 546 |
{mso-level-text:"%1\.%2\.%3"; |
| 547 |
mso-level-tab-stop:36.0pt; |
| 548 |
mso-level-number-position:left; |
| 549 |
margin-left:36.0pt; |
| 550 |
text-indent:-36.0pt;} |
| 551 |
@list l10:level4 |
| 552 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 553 |
mso-level-tab-stop:54.0pt; |
| 554 |
mso-level-number-position:left; |
| 555 |
margin-left:54.0pt; |
| 556 |
text-indent:-54.0pt;} |
| 557 |
@list l10:level5 |
| 558 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 559 |
mso-level-tab-stop:72.0pt; |
| 560 |
mso-level-number-position:left; |
| 561 |
margin-left:72.0pt; |
| 562 |
text-indent:-72.0pt;} |
| 563 |
@list l10:level6 |
| 564 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 565 |
mso-level-tab-stop:72.0pt; |
| 566 |
mso-level-number-position:left; |
| 567 |
margin-left:72.0pt; |
| 568 |
text-indent:-72.0pt;} |
| 569 |
@list l10:level7 |
| 570 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 571 |
mso-level-tab-stop:90.0pt; |
| 572 |
mso-level-number-position:left; |
| 573 |
margin-left:90.0pt; |
| 574 |
text-indent:-90.0pt;} |
| 575 |
@list l10:level8 |
| 576 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 577 |
mso-level-tab-stop:90.0pt; |
| 578 |
mso-level-number-position:left; |
| 579 |
margin-left:90.0pt; |
| 580 |
text-indent:-90.0pt;} |
| 581 |
@list l10:level9 |
| 582 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 583 |
mso-level-tab-stop:108.0pt; |
| 584 |
mso-level-number-position:left; |
| 585 |
margin-left:108.0pt; |
| 586 |
text-indent:-108.0pt;} |
| 587 |
@list l11 |
| 588 |
{mso-list-id:219946188; |
| 589 |
mso-list-type:simple; |
| 590 |
mso-list-template-ids:67698703;} |
| 591 |
@list l11:level1 |
| 592 |
{mso-level-tab-stop:18.0pt; |
| 593 |
mso-level-number-position:left; |
| 594 |
margin-left:18.0pt; |
| 595 |
text-indent:-18.0pt;} |
| 596 |
@list l12 |
| 597 |
{mso-list-id:271713038; |
| 598 |
mso-list-template-ids:-1131771434;} |
| 599 |
@list l12:level1 |
| 600 |
{mso-level-start-at:4; |
| 601 |
mso-level-text:%1; |
| 602 |
mso-level-tab-stop:26.25pt; |
| 603 |
mso-level-number-position:left; |
| 604 |
margin-left:26.25pt; |
| 605 |
text-indent:-26.25pt;} |
| 606 |
@list l12:level2 |
| 607 |
{mso-level-start-at:2; |
| 608 |
mso-level-text:"%1\.%2"; |
| 609 |
mso-level-tab-stop:26.25pt; |
| 610 |
mso-level-number-position:left; |
| 611 |
margin-left:26.25pt; |
| 612 |
text-indent:-26.25pt;} |
| 613 |
@list l12:level3 |
| 614 |
{mso-level-start-at:2; |
| 615 |
mso-level-text:"%1\.%2\.%3"; |
| 616 |
mso-level-tab-stop:36.0pt; |
| 617 |
mso-level-number-position:left; |
| 618 |
margin-left:36.0pt; |
| 619 |
text-indent:-36.0pt;} |
| 620 |
@list l12:level4 |
| 621 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 622 |
mso-level-tab-stop:54.0pt; |
| 623 |
mso-level-number-position:left; |
| 624 |
margin-left:54.0pt; |
| 625 |
text-indent:-54.0pt;} |
| 626 |
@list l12:level5 |
| 627 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 628 |
mso-level-tab-stop:54.0pt; |
| 629 |
mso-level-number-position:left; |
| 630 |
margin-left:54.0pt; |
| 631 |
text-indent:-54.0pt;} |
| 632 |
@list l12:level6 |
| 633 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 634 |
mso-level-tab-stop:72.0pt; |
| 635 |
mso-level-number-position:left; |
| 636 |
margin-left:72.0pt; |
| 637 |
text-indent:-72.0pt;} |
| 638 |
@list l12:level7 |
| 639 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 640 |
mso-level-tab-stop:72.0pt; |
| 641 |
mso-level-number-position:left; |
| 642 |
margin-left:72.0pt; |
| 643 |
text-indent:-72.0pt;} |
| 644 |
@list l12:level8 |
| 645 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 646 |
mso-level-tab-stop:90.0pt; |
| 647 |
mso-level-number-position:left; |
| 648 |
margin-left:90.0pt; |
| 649 |
text-indent:-90.0pt;} |
| 650 |
@list l12:level9 |
| 651 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 652 |
mso-level-tab-stop:90.0pt; |
| 653 |
mso-level-number-position:left; |
| 654 |
margin-left:90.0pt; |
| 655 |
text-indent:-90.0pt;} |
| 656 |
@list l13 |
| 657 |
{mso-list-id:277765196; |
| 658 |
mso-list-type:simple; |
| 659 |
mso-list-template-ids:67698705;} |
| 660 |
@list l13:level1 |
| 661 |
{mso-level-text:"%1\)"; |
| 662 |
mso-level-tab-stop:18.0pt; |
| 663 |
mso-level-number-position:left; |
| 664 |
margin-left:18.0pt; |
| 665 |
text-indent:-18.0pt;} |
| 666 |
@list l14 |
| 667 |
{mso-list-id:348529515; |
| 668 |
mso-list-type:simple; |
| 669 |
mso-list-template-ids:67698689;} |
| 670 |
@list l14:level1 |
| 671 |
{mso-level-number-format:bullet; |
| 672 |
mso-level-text:\F0B7; |
| 673 |
mso-level-tab-stop:18.0pt; |
| 674 |
mso-level-number-position:left; |
| 675 |
margin-left:18.0pt; |
| 676 |
text-indent:-18.0pt; |
| 677 |
font-family:Symbol;} |
| 678 |
@list l15 |
| 679 |
{mso-list-id:357661414; |
| 680 |
mso-list-template-ids:827492610;} |
| 681 |
@list l15:level1 |
| 682 |
{mso-level-start-at:4; |
| 683 |
mso-level-text:%1; |
| 684 |
mso-level-tab-stop:26.25pt; |
| 685 |
mso-level-number-position:left; |
| 686 |
margin-left:26.25pt; |
| 687 |
text-indent:-26.25pt;} |
| 688 |
@list l15:level2 |
| 689 |
{mso-level-start-at:2; |
| 690 |
mso-level-text:"%1\.%2"; |
| 691 |
mso-level-tab-stop:26.25pt; |
| 692 |
mso-level-number-position:left; |
| 693 |
margin-left:26.25pt; |
| 694 |
text-indent:-26.25pt;} |
| 695 |
@list l15:level3 |
| 696 |
{mso-level-start-at:3; |
| 697 |
mso-level-text:"%1\.%2\.%3"; |
| 698 |
mso-level-tab-stop:36.0pt; |
| 699 |
mso-level-number-position:left; |
| 700 |
margin-left:36.0pt; |
| 701 |
text-indent:-36.0pt;} |
| 702 |
@list l15:level4 |
| 703 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 704 |
mso-level-tab-stop:54.0pt; |
| 705 |
mso-level-number-position:left; |
| 706 |
margin-left:54.0pt; |
| 707 |
text-indent:-54.0pt;} |
| 708 |
@list l15:level5 |
| 709 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 710 |
mso-level-tab-stop:54.0pt; |
| 711 |
mso-level-number-position:left; |
| 712 |
margin-left:54.0pt; |
| 713 |
text-indent:-54.0pt;} |
| 714 |
@list l15:level6 |
| 715 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 716 |
mso-level-tab-stop:72.0pt; |
| 717 |
mso-level-number-position:left; |
| 718 |
margin-left:72.0pt; |
| 719 |
text-indent:-72.0pt;} |
| 720 |
@list l15:level7 |
| 721 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 722 |
mso-level-tab-stop:72.0pt; |
| 723 |
mso-level-number-position:left; |
| 724 |
margin-left:72.0pt; |
| 725 |
text-indent:-72.0pt;} |
| 726 |
@list l15:level8 |
| 727 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 728 |
mso-level-tab-stop:90.0pt; |
| 729 |
mso-level-number-position:left; |
| 730 |
margin-left:90.0pt; |
| 731 |
text-indent:-90.0pt;} |
| 732 |
@list l15:level9 |
| 733 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 734 |
mso-level-tab-stop:90.0pt; |
| 735 |
mso-level-number-position:left; |
| 736 |
margin-left:90.0pt; |
| 737 |
text-indent:-90.0pt;} |
| 738 |
@list l16 |
| 739 |
{mso-list-id:402534437; |
| 740 |
mso-list-type:simple; |
| 741 |
mso-list-template-ids:67698689;} |
| 742 |
@list l16:level1 |
| 743 |
{mso-level-number-format:bullet; |
| 744 |
mso-level-text:\F0B7; |
| 745 |
mso-level-tab-stop:18.0pt; |
| 746 |
mso-level-number-position:left; |
| 747 |
margin-left:18.0pt; |
| 748 |
text-indent:-18.0pt; |
| 749 |
font-family:Symbol;} |
| 750 |
@list l17 |
| 751 |
{mso-list-id:437454622; |
| 752 |
mso-list-template-ids:1548257524;} |
| 753 |
@list l17:level1 |
| 754 |
{mso-level-text:%1; |
| 755 |
mso-level-tab-stop:19.5pt; |
| 756 |
mso-level-number-position:left; |
| 757 |
margin-left:19.5pt; |
| 758 |
text-indent:-19.5pt;} |
| 759 |
@list l17:level2 |
| 760 |
{mso-level-text:"%1\.%2"; |
| 761 |
mso-level-tab-stop:37.5pt; |
| 762 |
mso-level-number-position:left; |
| 763 |
margin-left:37.5pt; |
| 764 |
text-indent:-19.5pt;} |
| 765 |
@list l17:level3 |
| 766 |
{mso-level-text:"%1\.%2\.%3"; |
| 767 |
mso-level-tab-stop:72.0pt; |
| 768 |
mso-level-number-position:left; |
| 769 |
margin-left:72.0pt; |
| 770 |
text-indent:-36.0pt;} |
| 771 |
@list l17:level4 |
| 772 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 773 |
mso-level-tab-stop:108.0pt; |
| 774 |
mso-level-number-position:left; |
| 775 |
margin-left:108.0pt; |
| 776 |
text-indent:-54.0pt;} |
| 777 |
@list l17:level5 |
| 778 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 779 |
mso-level-tab-stop:126.0pt; |
| 780 |
mso-level-number-position:left; |
| 781 |
margin-left:126.0pt; |
| 782 |
text-indent:-54.0pt;} |
| 783 |
@list l17:level6 |
| 784 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 785 |
mso-level-tab-stop:162.0pt; |
| 786 |
mso-level-number-position:left; |
| 787 |
margin-left:162.0pt; |
| 788 |
text-indent:-72.0pt;} |
| 789 |
@list l17:level7 |
| 790 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 791 |
mso-level-tab-stop:180.0pt; |
| 792 |
mso-level-number-position:left; |
| 793 |
margin-left:180.0pt; |
| 794 |
text-indent:-72.0pt;} |
| 795 |
@list l17:level8 |
| 796 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 797 |
mso-level-tab-stop:216.0pt; |
| 798 |
mso-level-number-position:left; |
| 799 |
margin-left:216.0pt; |
| 800 |
text-indent:-90.0pt;} |
| 801 |
@list l17:level9 |
| 802 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 803 |
mso-level-tab-stop:234.0pt; |
| 804 |
mso-level-number-position:left; |
| 805 |
margin-left:234.0pt; |
| 806 |
text-indent:-90.0pt;} |
| 807 |
@list l18 |
| 808 |
{mso-list-id:540287448; |
| 809 |
mso-list-template-ids:1179308946;} |
| 810 |
@list l18:level1 |
| 811 |
{mso-level-start-at:4; |
| 812 |
mso-level-text:%1; |
| 813 |
mso-level-tab-stop:26.25pt; |
| 814 |
mso-level-number-position:left; |
| 815 |
margin-left:26.25pt; |
| 816 |
text-indent:-26.25pt;} |
| 817 |
@list l18:level2 |
| 818 |
{mso-level-start-at:2; |
| 819 |
mso-level-text:"%1\.%2"; |
| 820 |
mso-level-tab-stop:26.25pt; |
| 821 |
mso-level-number-position:left; |
| 822 |
margin-left:26.25pt; |
| 823 |
text-indent:-26.25pt;} |
| 824 |
@list l18:level3 |
| 825 |
{mso-level-start-at:3; |
| 826 |
mso-level-text:"%1\.%2\.%3"; |
| 827 |
mso-level-tab-stop:36.0pt; |
| 828 |
mso-level-number-position:left; |
| 829 |
margin-left:36.0pt; |
| 830 |
text-indent:-36.0pt;} |
| 831 |
@list l18:level4 |
| 832 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 833 |
mso-level-tab-stop:54.0pt; |
| 834 |
mso-level-number-position:left; |
| 835 |
margin-left:54.0pt; |
| 836 |
text-indent:-54.0pt;} |
| 837 |
@list l18:level5 |
| 838 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 839 |
mso-level-tab-stop:54.0pt; |
| 840 |
mso-level-number-position:left; |
| 841 |
margin-left:54.0pt; |
| 842 |
text-indent:-54.0pt;} |
| 843 |
@list l18:level6 |
| 844 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 845 |
mso-level-tab-stop:72.0pt; |
| 846 |
mso-level-number-position:left; |
| 847 |
margin-left:72.0pt; |
| 848 |
text-indent:-72.0pt;} |
| 849 |
@list l18:level7 |
| 850 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 851 |
mso-level-tab-stop:72.0pt; |
| 852 |
mso-level-number-position:left; |
| 853 |
margin-left:72.0pt; |
| 854 |
text-indent:-72.0pt;} |
| 855 |
@list l18:level8 |
| 856 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 857 |
mso-level-tab-stop:90.0pt; |
| 858 |
mso-level-number-position:left; |
| 859 |
margin-left:90.0pt; |
| 860 |
text-indent:-90.0pt;} |
| 861 |
@list l18:level9 |
| 862 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 863 |
mso-level-tab-stop:90.0pt; |
| 864 |
mso-level-number-position:left; |
| 865 |
margin-left:90.0pt; |
| 866 |
text-indent:-90.0pt;} |
| 867 |
@list l19 |
| 868 |
{mso-list-id:594679853; |
| 869 |
mso-list-type:simple; |
| 870 |
mso-list-template-ids:1239063504;} |
| 871 |
@list l19:level1 |
| 872 |
{mso-level-start-at:5; |
| 873 |
mso-level-number-format:bullet; |
| 874 |
mso-level-text:-; |
| 875 |
mso-level-tab-stop:18.0pt; |
| 876 |
mso-level-number-position:left; |
| 877 |
margin-left:18.0pt; |
| 878 |
text-indent:-18.0pt; |
| 879 |
font-family:"Times New Roman";} |
| 880 |
@list l20 |
| 881 |
{mso-list-id:607203342; |
| 882 |
mso-list-type:simple; |
| 883 |
mso-list-template-ids:1239063504;} |
| 884 |
@list l20:level1 |
| 885 |
{mso-level-start-at:5; |
| 886 |
mso-level-number-format:bullet; |
| 887 |
mso-level-text:-; |
| 888 |
mso-level-tab-stop:18.0pt; |
| 889 |
mso-level-number-position:left; |
| 890 |
margin-left:18.0pt; |
| 891 |
text-indent:-18.0pt; |
| 892 |
font-family:"Times New Roman";} |
| 893 |
@list l21 |
| 894 |
{mso-list-id:631406463; |
| 895 |
mso-list-type:simple; |
| 896 |
mso-list-template-ids:67698697;} |
| 897 |
@list l21:level1 |
| 898 |
{mso-level-number-format:bullet; |
| 899 |
mso-level-text:\F076; |
| 900 |
mso-level-tab-stop:18.0pt; |
| 901 |
mso-level-number-position:left; |
| 902 |
margin-left:18.0pt; |
| 903 |
text-indent:-18.0pt; |
| 904 |
font-family:Wingdings;} |
| 905 |
@list l22 |
| 906 |
{mso-list-id:649332976; |
| 907 |
mso-list-type:simple; |
| 908 |
mso-list-template-ids:-1203462186;} |
| 909 |
@list l22:level1 |
| 910 |
{mso-level-number-format:roman-lower; |
| 911 |
mso-level-text:"\(%1\)"; |
| 912 |
mso-level-tab-stop:72.0pt; |
| 913 |
mso-level-number-position:left; |
| 914 |
margin-left:72.0pt; |
| 915 |
text-indent:-36.0pt;} |
| 916 |
@list l23 |
| 917 |
{mso-list-id:708070908; |
| 918 |
mso-list-type:simple; |
| 919 |
mso-list-template-ids:67698697;} |
| 920 |
@list l23:level1 |
| 921 |
{mso-level-number-format:bullet; |
| 922 |
mso-level-text:\F076; |
| 923 |
mso-level-tab-stop:18.0pt; |
| 924 |
mso-level-number-position:left; |
| 925 |
margin-left:18.0pt; |
| 926 |
text-indent:-18.0pt; |
| 927 |
font-family:Wingdings;} |
| 928 |
@list l24 |
| 929 |
{mso-list-id:712925444; |
| 930 |
mso-list-type:simple; |
| 931 |
mso-list-template-ids:67698689;} |
| 932 |
@list l24:level1 |
| 933 |
{mso-level-number-format:bullet; |
| 934 |
mso-level-text:\F0B7; |
| 935 |
mso-level-tab-stop:18.0pt; |
| 936 |
mso-level-number-position:left; |
| 937 |
margin-left:18.0pt; |
| 938 |
text-indent:-18.0pt; |
| 939 |
font-family:Symbol;} |
| 940 |
@list l25 |
| 941 |
{mso-list-id:936060930; |
| 942 |
mso-list-type:simple; |
| 943 |
mso-list-template-ids:67698689;} |
| 944 |
@list l25:level1 |
| 945 |
{mso-level-number-format:bullet; |
| 946 |
mso-level-text:\F0B7; |
| 947 |
mso-level-tab-stop:18.0pt; |
| 948 |
mso-level-number-position:left; |
| 949 |
margin-left:18.0pt; |
| 950 |
text-indent:-18.0pt; |
| 951 |
font-family:Symbol;} |
| 952 |
@list l26 |
| 953 |
{mso-list-id:995962217; |
| 954 |
mso-list-template-ids:-1447678044;} |
| 955 |
@list l26:level1 |
| 956 |
{mso-level-start-at:4; |
| 957 |
mso-level-text:%1; |
| 958 |
mso-level-tab-stop:26.25pt; |
| 959 |
mso-level-number-position:left; |
| 960 |
margin-left:26.25pt; |
| 961 |
text-indent:-26.25pt;} |
| 962 |
@list l26:level2 |
| 963 |
{mso-level-start-at:2; |
| 964 |
mso-level-text:"%1\.%2"; |
| 965 |
mso-level-tab-stop:26.25pt; |
| 966 |
mso-level-number-position:left; |
| 967 |
margin-left:26.25pt; |
| 968 |
text-indent:-26.25pt;} |
| 969 |
@list l26:level3 |
| 970 |
{mso-level-start-at:3; |
| 971 |
mso-level-text:"%1\.%2\.%3"; |
| 972 |
mso-level-tab-stop:36.0pt; |
| 973 |
mso-level-number-position:left; |
| 974 |
margin-left:36.0pt; |
| 975 |
text-indent:-36.0pt;} |
| 976 |
@list l26:level4 |
| 977 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 978 |
mso-level-tab-stop:54.0pt; |
| 979 |
mso-level-number-position:left; |
| 980 |
margin-left:54.0pt; |
| 981 |
text-indent:-54.0pt;} |
| 982 |
@list l26:level5 |
| 983 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 984 |
mso-level-tab-stop:54.0pt; |
| 985 |
mso-level-number-position:left; |
| 986 |
margin-left:54.0pt; |
| 987 |
text-indent:-54.0pt;} |
| 988 |
@list l26:level6 |
| 989 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 990 |
mso-level-tab-stop:72.0pt; |
| 991 |
mso-level-number-position:left; |
| 992 |
margin-left:72.0pt; |
| 993 |
text-indent:-72.0pt;} |
| 994 |
@list l26:level7 |
| 995 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 996 |
mso-level-tab-stop:72.0pt; |
| 997 |
mso-level-number-position:left; |
| 998 |
margin-left:72.0pt; |
| 999 |
text-indent:-72.0pt;} |
| 1000 |
@list l26:level8 |
| 1001 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 1002 |
mso-level-tab-stop:90.0pt; |
| 1003 |
mso-level-number-position:left; |
| 1004 |
margin-left:90.0pt; |
| 1005 |
text-indent:-90.0pt;} |
| 1006 |
@list l26:level9 |
| 1007 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 1008 |
mso-level-tab-stop:90.0pt; |
| 1009 |
mso-level-number-position:left; |
| 1010 |
margin-left:90.0pt; |
| 1011 |
text-indent:-90.0pt;} |
| 1012 |
@list l27 |
| 1013 |
{mso-list-id:1033920558; |
| 1014 |
mso-list-type:simple; |
| 1015 |
mso-list-template-ids:67698705;} |
| 1016 |
@list l27:level1 |
| 1017 |
{mso-level-text:"%1\)"; |
| 1018 |
mso-level-tab-stop:18.0pt; |
| 1019 |
mso-level-number-position:left; |
| 1020 |
margin-left:18.0pt; |
| 1021 |
text-indent:-18.0pt;} |
| 1022 |
@list l28 |
| 1023 |
{mso-list-id:1107194941; |
| 1024 |
mso-list-type:simple; |
| 1025 |
mso-list-template-ids:67698703;} |
| 1026 |
@list l28:level1 |
| 1027 |
{mso-level-tab-stop:18.0pt; |
| 1028 |
mso-level-number-position:left; |
| 1029 |
margin-left:18.0pt; |
| 1030 |
text-indent:-18.0pt;} |
| 1031 |
@list l29 |
| 1032 |
{mso-list-id:1112672709; |
| 1033 |
mso-list-type:simple; |
| 1034 |
mso-list-template-ids:67698697;} |
| 1035 |
@list l29:level1 |
| 1036 |
{mso-level-number-format:bullet; |
| 1037 |
mso-level-text:\F076; |
| 1038 |
mso-level-tab-stop:18.0pt; |
| 1039 |
mso-level-number-position:left; |
| 1040 |
margin-left:18.0pt; |
| 1041 |
text-indent:-18.0pt; |
| 1042 |
font-family:Wingdings;} |
| 1043 |
@list l30 |
| 1044 |
{mso-list-id:1128937926; |
| 1045 |
mso-list-template-ids:1251396830;} |
| 1046 |
@list l30:level1 |
| 1047 |
{mso-level-text:%1; |
| 1048 |
mso-level-tab-stop:20.25pt; |
| 1049 |
mso-level-number-position:left; |
| 1050 |
margin-left:20.25pt; |
| 1051 |
text-indent:-20.25pt;} |
| 1052 |
@list l30:level2 |
| 1053 |
{mso-level-text:"%1\.%2"; |
| 1054 |
mso-level-tab-stop:36.0pt; |
| 1055 |
mso-level-number-position:left; |
| 1056 |
margin-left:36.0pt; |
| 1057 |
text-indent:-36.0pt;} |
| 1058 |
@list l30:level3 |
| 1059 |
{mso-level-text:"%1\.%2\.%3"; |
| 1060 |
mso-level-tab-stop:36.0pt; |
| 1061 |
mso-level-number-position:left; |
| 1062 |
margin-left:36.0pt; |
| 1063 |
text-indent:-36.0pt;} |
| 1064 |
@list l30:level4 |
| 1065 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 1066 |
mso-level-tab-stop:54.0pt; |
| 1067 |
mso-level-number-position:left; |
| 1068 |
margin-left:54.0pt; |
| 1069 |
text-indent:-54.0pt;} |
| 1070 |
@list l30:level5 |
| 1071 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 1072 |
mso-level-tab-stop:72.0pt; |
| 1073 |
mso-level-number-position:left; |
| 1074 |
margin-left:72.0pt; |
| 1075 |
text-indent:-72.0pt;} |
| 1076 |
@list l30:level6 |
| 1077 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 1078 |
mso-level-tab-stop:72.0pt; |
| 1079 |
mso-level-number-position:left; |
| 1080 |
margin-left:72.0pt; |
| 1081 |
text-indent:-72.0pt;} |
| 1082 |
@list l30:level7 |
| 1083 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 1084 |
mso-level-tab-stop:90.0pt; |
| 1085 |
mso-level-number-position:left; |
| 1086 |
margin-left:90.0pt; |
| 1087 |
text-indent:-90.0pt;} |
| 1088 |
@list l30:level8 |
| 1089 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 1090 |
mso-level-tab-stop:90.0pt; |
| 1091 |
mso-level-number-position:left; |
| 1092 |
margin-left:90.0pt; |
| 1093 |
text-indent:-90.0pt;} |
| 1094 |
@list l30:level9 |
| 1095 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 1096 |
mso-level-tab-stop:108.0pt; |
| 1097 |
mso-level-number-position:left; |
| 1098 |
margin-left:108.0pt; |
| 1099 |
text-indent:-108.0pt;} |
| 1100 |
@list l31 |
| 1101 |
{mso-list-id:1421371121; |
| 1102 |
mso-list-template-ids:-1242003894;} |
| 1103 |
@list l31:level1 |
| 1104 |
{mso-level-start-at:4; |
| 1105 |
mso-level-text:%1; |
| 1106 |
mso-level-tab-stop:26.25pt; |
| 1107 |
mso-level-number-position:left; |
| 1108 |
margin-left:26.25pt; |
| 1109 |
text-indent:-26.25pt;} |
| 1110 |
@list l31:level2 |
| 1111 |
{mso-level-start-at:2; |
| 1112 |
mso-level-text:"%1\.%2"; |
| 1113 |
mso-level-tab-stop:26.25pt; |
| 1114 |
mso-level-number-position:left; |
| 1115 |
margin-left:26.25pt; |
| 1116 |
text-indent:-26.25pt;} |
| 1117 |
@list l31:level3 |
| 1118 |
{mso-level-start-at:3; |
| 1119 |
mso-level-text:"%1\.%2\.%3"; |
| 1120 |
mso-level-tab-stop:36.0pt; |
| 1121 |
mso-level-number-position:left; |
| 1122 |
margin-left:36.0pt; |
| 1123 |
text-indent:-36.0pt;} |
| 1124 |
@list l31:level4 |
| 1125 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 1126 |
mso-level-tab-stop:54.0pt; |
| 1127 |
mso-level-number-position:left; |
| 1128 |
margin-left:54.0pt; |
| 1129 |
text-indent:-54.0pt;} |
| 1130 |
@list l31:level5 |
| 1131 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 1132 |
mso-level-tab-stop:54.0pt; |
| 1133 |
mso-level-number-position:left; |
| 1134 |
margin-left:54.0pt; |
| 1135 |
text-indent:-54.0pt;} |
| 1136 |
@list l31:level6 |
| 1137 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 1138 |
mso-level-tab-stop:72.0pt; |
| 1139 |
mso-level-number-position:left; |
| 1140 |
margin-left:72.0pt; |
| 1141 |
text-indent:-72.0pt;} |
| 1142 |
@list l31:level7 |
| 1143 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 1144 |
mso-level-tab-stop:72.0pt; |
| 1145 |
mso-level-number-position:left; |
| 1146 |
margin-left:72.0pt; |
| 1147 |
text-indent:-72.0pt;} |
| 1148 |
@list l31:level8 |
| 1149 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 1150 |
mso-level-tab-stop:90.0pt; |
| 1151 |
mso-level-number-position:left; |
| 1152 |
margin-left:90.0pt; |
| 1153 |
text-indent:-90.0pt;} |
| 1154 |
@list l31:level9 |
| 1155 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 1156 |
mso-level-tab-stop:90.0pt; |
| 1157 |
mso-level-number-position:left; |
| 1158 |
margin-left:90.0pt; |
| 1159 |
text-indent:-90.0pt;} |
| 1160 |
@list l32 |
| 1161 |
{mso-list-id:1454595286; |
| 1162 |
mso-list-type:simple; |
| 1163 |
mso-list-template-ids:1239063504;} |
| 1164 |
@list l32:level1 |
| 1165 |
{mso-level-start-at:5; |
| 1166 |
mso-level-number-format:bullet; |
| 1167 |
mso-level-text:-; |
| 1168 |
mso-level-tab-stop:18.0pt; |
| 1169 |
mso-level-number-position:left; |
| 1170 |
margin-left:18.0pt; |
| 1171 |
text-indent:-18.0pt; |
| 1172 |
font-family:"Times New Roman";} |
| 1173 |
@list l33 |
| 1174 |
{mso-list-id:1479226569; |
| 1175 |
mso-list-type:simple; |
| 1176 |
mso-list-template-ids:67698689;} |
| 1177 |
@list l33:level1 |
| 1178 |
{mso-level-number-format:bullet; |
| 1179 |
mso-level-text:\F0B7; |
| 1180 |
mso-level-tab-stop:18.0pt; |
| 1181 |
mso-level-number-position:left; |
| 1182 |
margin-left:18.0pt; |
| 1183 |
text-indent:-18.0pt; |
| 1184 |
font-family:Symbol;} |
| 1185 |
@list l34 |
| 1186 |
{mso-list-id:1501846478; |
| 1187 |
mso-list-type:simple; |
| 1188 |
mso-list-template-ids:67698697;} |
| 1189 |
@list l34:level1 |
| 1190 |
{mso-level-number-format:bullet; |
| 1191 |
mso-level-text:\F076; |
| 1192 |
mso-level-tab-stop:18.0pt; |
| 1193 |
mso-level-number-position:left; |
| 1194 |
margin-left:18.0pt; |
| 1195 |
text-indent:-18.0pt; |
| 1196 |
font-family:Wingdings;} |
| 1197 |
@list l35 |
| 1198 |
{mso-list-id:1672175972; |
| 1199 |
mso-list-type:simple; |
| 1200 |
mso-list-template-ids:67698697;} |
| 1201 |
@list l35:level1 |
| 1202 |
{mso-level-number-format:bullet; |
| 1203 |
mso-level-text:\F076; |
| 1204 |
mso-level-tab-stop:18.0pt; |
| 1205 |
mso-level-number-position:left; |
| 1206 |
margin-left:18.0pt; |
| 1207 |
text-indent:-18.0pt; |
| 1208 |
font-family:Wingdings;} |
| 1209 |
@list l36 |
| 1210 |
{mso-list-id:1683387560; |
| 1211 |
mso-list-type:simple; |
| 1212 |
mso-list-template-ids:1239063504;} |
| 1213 |
@list l36:level1 |
| 1214 |
{mso-level-start-at:5; |
| 1215 |
mso-level-number-format:bullet; |
| 1216 |
mso-level-text:-; |
| 1217 |
mso-level-tab-stop:18.0pt; |
| 1218 |
mso-level-number-position:left; |
| 1219 |
margin-left:18.0pt; |
| 1220 |
text-indent:-18.0pt; |
| 1221 |
font-family:"Times New Roman";} |
| 1222 |
@list l37 |
| 1223 |
{mso-list-id:1685204419; |
| 1224 |
mso-list-type:simple; |
| 1225 |
mso-list-template-ids:-1203462186;} |
| 1226 |
@list l37:level1 |
| 1227 |
{mso-level-number-format:roman-lower; |
| 1228 |
mso-level-text:"\(%1\)"; |
| 1229 |
mso-level-tab-stop:72.0pt; |
| 1230 |
mso-level-number-position:left; |
| 1231 |
margin-left:72.0pt; |
| 1232 |
text-indent:-36.0pt;} |
| 1233 |
@list l38 |
| 1234 |
{mso-list-id:1776905994; |
| 1235 |
mso-list-template-ids:687106522;} |
| 1236 |
@list l38:level1 |
| 1237 |
{mso-level-text:%1; |
| 1238 |
mso-level-tab-stop:23.25pt; |
| 1239 |
mso-level-number-position:left; |
| 1240 |
margin-left:23.25pt; |
| 1241 |
text-indent:-23.25pt;} |
| 1242 |
@list l38:level2 |
| 1243 |
{mso-level-text:"%1\.%2"; |
| 1244 |
mso-level-tab-stop:59.25pt; |
| 1245 |
mso-level-number-position:left; |
| 1246 |
margin-left:59.25pt; |
| 1247 |
text-indent:-23.25pt;} |
| 1248 |
@list l38:level3 |
| 1249 |
{mso-level-text:"%1\.%2\.%3"; |
| 1250 |
mso-level-tab-stop:108.0pt; |
| 1251 |
mso-level-number-position:left; |
| 1252 |
text-indent:-36.0pt;} |
| 1253 |
@list l38:level4 |
| 1254 |
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| 1255 |
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| 1256 |
mso-level-number-position:left; |
| 1257 |
text-indent:-36.0pt;} |
| 1258 |
@list l38:level5 |
| 1259 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 1260 |
mso-level-tab-stop:198.0pt; |
| 1261 |
mso-level-number-position:left; |
| 1262 |
margin-left:198.0pt; |
| 1263 |
text-indent:-54.0pt;} |
| 1264 |
@list l38:level6 |
| 1265 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 1266 |
mso-level-tab-stop:234.0pt; |
| 1267 |
mso-level-number-position:left; |
| 1268 |
margin-left:234.0pt; |
| 1269 |
text-indent:-54.0pt;} |
| 1270 |
@list l38:level7 |
| 1271 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 1272 |
mso-level-tab-stop:288.0pt; |
| 1273 |
mso-level-number-position:left; |
| 1274 |
margin-left:288.0pt; |
| 1275 |
text-indent:-72.0pt;} |
| 1276 |
@list l38:level8 |
| 1277 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 1278 |
mso-level-tab-stop:324.0pt; |
| 1279 |
mso-level-number-position:left; |
| 1280 |
margin-left:324.0pt; |
| 1281 |
text-indent:-72.0pt;} |
| 1282 |
@list l38:level9 |
| 1283 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 1284 |
mso-level-tab-stop:378.0pt; |
| 1285 |
mso-level-number-position:left; |
| 1286 |
margin-left:378.0pt; |
| 1287 |
text-indent:-90.0pt;} |
| 1288 |
@list l39 |
| 1289 |
{mso-list-id:1782996239; |
| 1290 |
mso-list-type:simple; |
| 1291 |
mso-list-template-ids:67698689;} |
| 1292 |
@list l39:level1 |
| 1293 |
{mso-level-number-format:bullet; |
| 1294 |
mso-level-text:\F0B7; |
| 1295 |
mso-level-tab-stop:18.0pt; |
| 1296 |
mso-level-number-position:left; |
| 1297 |
margin-left:18.0pt; |
| 1298 |
text-indent:-18.0pt; |
| 1299 |
font-family:Symbol;} |
| 1300 |
@list l40 |
| 1301 |
{mso-list-id:1801924119; |
| 1302 |
mso-list-type:simple; |
| 1303 |
mso-list-template-ids:67698703;} |
| 1304 |
@list l40:level1 |
| 1305 |
{mso-level-tab-stop:18.0pt; |
| 1306 |
mso-level-number-position:left; |
| 1307 |
margin-left:18.0pt; |
| 1308 |
text-indent:-18.0pt;} |
| 1309 |
@list l41 |
| 1310 |
{mso-list-id:1879661257; |
| 1311 |
mso-list-template-ids:406896228;} |
| 1312 |
@list l41:level1 |
| 1313 |
{mso-level-start-at:4; |
| 1314 |
mso-level-text:%1; |
| 1315 |
mso-level-tab-stop:26.25pt; |
| 1316 |
mso-level-number-position:left; |
| 1317 |
margin-left:26.25pt; |
| 1318 |
text-indent:-26.25pt; |
| 1319 |
font-family:Arial; |
| 1320 |
mso-bidi-font-family:"Times New Roman";} |
| 1321 |
@list l41:level2 |
| 1322 |
{mso-level-start-at:2; |
| 1323 |
mso-level-text:"%1\.%2"; |
| 1324 |
mso-level-tab-stop:26.25pt; |
| 1325 |
mso-level-number-position:left; |
| 1326 |
margin-left:26.25pt; |
| 1327 |
text-indent:-26.25pt; |
| 1328 |
font-family:Arial; |
| 1329 |
mso-bidi-font-family:"Times New Roman";} |
| 1330 |
@list l41:level3 |
| 1331 |
{mso-level-start-at:4; |
| 1332 |
mso-level-text:"%1\.%2\.%3"; |
| 1333 |
mso-level-tab-stop:36.0pt; |
| 1334 |
mso-level-number-position:left; |
| 1335 |
margin-left:36.0pt; |
| 1336 |
text-indent:-36.0pt; |
| 1337 |
font-family:Arial; |
| 1338 |
mso-bidi-font-family:"Times New Roman";} |
| 1339 |
@list l41:level4 |
| 1340 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 1341 |
mso-level-tab-stop:54.0pt; |
| 1342 |
mso-level-number-position:left; |
| 1343 |
margin-left:54.0pt; |
| 1344 |
text-indent:-54.0pt; |
| 1345 |
font-family:Arial; |
| 1346 |
mso-bidi-font-family:"Times New Roman";} |
| 1347 |
@list l41:level5 |
| 1348 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 1349 |
mso-level-tab-stop:54.0pt; |
| 1350 |
mso-level-number-position:left; |
| 1351 |
margin-left:54.0pt; |
| 1352 |
text-indent:-54.0pt; |
| 1353 |
font-family:Arial; |
| 1354 |
mso-bidi-font-family:"Times New Roman";} |
| 1355 |
@list l41:level6 |
| 1356 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 1357 |
mso-level-tab-stop:72.0pt; |
| 1358 |
mso-level-number-position:left; |
| 1359 |
margin-left:72.0pt; |
| 1360 |
text-indent:-72.0pt; |
| 1361 |
font-family:Arial; |
| 1362 |
mso-bidi-font-family:"Times New Roman";} |
| 1363 |
@list l41:level7 |
| 1364 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 1365 |
mso-level-tab-stop:72.0pt; |
| 1366 |
mso-level-number-position:left; |
| 1367 |
margin-left:72.0pt; |
| 1368 |
text-indent:-72.0pt; |
| 1369 |
font-family:Arial; |
| 1370 |
mso-bidi-font-family:"Times New Roman";} |
| 1371 |
@list l41:level8 |
| 1372 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 1373 |
mso-level-tab-stop:90.0pt; |
| 1374 |
mso-level-number-position:left; |
| 1375 |
margin-left:90.0pt; |
| 1376 |
text-indent:-90.0pt; |
| 1377 |
font-family:Arial; |
| 1378 |
mso-bidi-font-family:"Times New Roman";} |
| 1379 |
@list l41:level9 |
| 1380 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 1381 |
mso-level-tab-stop:90.0pt; |
| 1382 |
mso-level-number-position:left; |
| 1383 |
margin-left:90.0pt; |
| 1384 |
text-indent:-90.0pt; |
| 1385 |
font-family:Arial; |
| 1386 |
mso-bidi-font-family:"Times New Roman";} |
| 1387 |
@list l42 |
| 1388 |
{mso-list-id:2025206473; |
| 1389 |
mso-list-type:simple; |
| 1390 |
mso-list-template-ids:67698703;} |
| 1391 |
@list l42:level1 |
| 1392 |
{mso-level-tab-stop:18.0pt; |
| 1393 |
mso-level-number-position:left; |
| 1394 |
margin-left:18.0pt; |
| 1395 |
text-indent:-18.0pt;} |
| 1396 |
@list l43 |
| 1397 |
{mso-list-id:2039700182; |
| 1398 |
mso-list-template-ids:-105628832;} |
| 1399 |
@list l43:level1 |
| 1400 |
{mso-level-text:%1; |
| 1401 |
mso-level-tab-stop:20.25pt; |
| 1402 |
mso-level-number-position:left; |
| 1403 |
margin-left:20.25pt; |
| 1404 |
text-indent:-20.25pt;} |
| 1405 |
@list l43:level2 |
| 1406 |
{mso-level-start-at:2; |
| 1407 |
mso-level-text:"%1\.%2"; |
| 1408 |
mso-level-tab-stop:36.0pt; |
| 1409 |
mso-level-number-position:left; |
| 1410 |
margin-left:36.0pt; |
| 1411 |
text-indent:-36.0pt;} |
| 1412 |
@list l43:level3 |
| 1413 |
{mso-level-text:"%1\.%2\.%3"; |
| 1414 |
mso-level-tab-stop:36.0pt; |
| 1415 |
mso-level-number-position:left; |
| 1416 |
margin-left:36.0pt; |
| 1417 |
text-indent:-36.0pt;} |
| 1418 |
@list l43:level4 |
| 1419 |
{mso-level-text:"%1\.%2\.%3\.%4"; |
| 1420 |
mso-level-tab-stop:54.0pt; |
| 1421 |
mso-level-number-position:left; |
| 1422 |
margin-left:54.0pt; |
| 1423 |
text-indent:-54.0pt;} |
| 1424 |
@list l43:level5 |
| 1425 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5"; |
| 1426 |
mso-level-tab-stop:72.0pt; |
| 1427 |
mso-level-number-position:left; |
| 1428 |
margin-left:72.0pt; |
| 1429 |
text-indent:-72.0pt;} |
| 1430 |
@list l43:level6 |
| 1431 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6"; |
| 1432 |
mso-level-tab-stop:72.0pt; |
| 1433 |
mso-level-number-position:left; |
| 1434 |
margin-left:72.0pt; |
| 1435 |
text-indent:-72.0pt;} |
| 1436 |
@list l43:level7 |
| 1437 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7"; |
| 1438 |
mso-level-tab-stop:90.0pt; |
| 1439 |
mso-level-number-position:left; |
| 1440 |
margin-left:90.0pt; |
| 1441 |
text-indent:-90.0pt;} |
| 1442 |
@list l43:level8 |
| 1443 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8"; |
| 1444 |
mso-level-tab-stop:90.0pt; |
| 1445 |
mso-level-number-position:left; |
| 1446 |
margin-left:90.0pt; |
| 1447 |
text-indent:-90.0pt;} |
| 1448 |
@list l43:level9 |
| 1449 |
{mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9"; |
| 1450 |
mso-level-tab-stop:108.0pt; |
| 1451 |
mso-level-number-position:left; |
| 1452 |
margin-left:108.0pt; |
| 1453 |
text-indent:-108.0pt;} |
| 1454 |
ol |
| 1455 |
{margin-bottom:0pt;} |
| 1456 |
ul |
| 1457 |
{margin-bottom:0pt;} |
| 1458 |
--> |
| 1459 |
</style> |
| 1460 |
<!--[if gte mso 9]><xml> |
| 1461 |
<o:shapedefaults v:ext="edit" spidmax="2050"/> |
| 1462 |
</xml><![endif]--><!--[if gte mso 9]><xml> |
| 1463 |
<o:shapelayout v:ext="edit"> |
| 1464 |
<o:idmap v:ext="edit" data="1"/> |
| 1465 |
</o:shapelayout></xml><![endif]--> |
| 1466 |
</head> |
| 1467 |
|
| 1468 |
<body lang=EN-US style='tab-interval:36.0pt'> |
| 1469 |
|
| 1470 |
<div class=Section1> |
| 1471 |
|
| 1472 |
<p class=MsoBodyText align=center style='text-align:center'><a |
| 1473 |
name="_Toc407078231"></a><a name="_Toc407078218"><span style='mso-bookmark: |
| 1474 |
_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></a></p> |
| 1475 |
|
| 1476 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1477 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1478 |
|
| 1479 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1480 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1481 |
|
| 1482 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1483 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1484 |
|
| 1485 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1486 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1487 |
|
| 1488 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1489 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1490 |
|
| 1491 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1492 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1493 |
|
| 1494 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1495 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1496 |
|
| 1497 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1498 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1499 |
style='mso-bidi-font-weight:normal'><span style='font-size:20.0pt;mso-bidi-font-size: |
| 1500 |
10.0pt'>A Parallel Navier-Stokes Ocean Model: Formulation and Documentation<o:p></o:p></span></b></span></span></p> |
| 1501 |
|
| 1502 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1503 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1504 |
style='mso-bidi-font-weight:normal'><span style='font-size:20.0pt;mso-bidi-font-size: |
| 1505 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></span></p> |
| 1506 |
|
| 1507 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1508 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1509 |
style='mso-bidi-font-weight:normal'><span style='font-size:20.0pt;mso-bidi-font-size: |
| 1510 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></span></p> |
| 1511 |
|
| 1512 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1513 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1514 |
style='mso-bidi-font-weight:normal'><span style='font-size:16.0pt;mso-bidi-font-size: |
| 1515 |
10.0pt'>Daniel Jamous, Chris Hill, Alistair Adcroft, John Marshall<o:p></o:p></span></b></span></span></p> |
| 1516 |
|
| 1517 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1518 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1519 |
style='mso-bidi-font-weight:normal'><span style='font-size:16.0pt;mso-bidi-font-size: |
| 1520 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></span></p> |
| 1521 |
|
| 1522 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1523 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1524 |
style='mso-bidi-font-weight:normal'><span style='font-size:16.0pt;mso-bidi-font-size: |
| 1525 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></span></p> |
| 1526 |
|
| 1527 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1528 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1529 |
style='mso-bidi-font-weight:normal'><span style='font-size:16.0pt;mso-bidi-font-size: |
| 1530 |
10.0pt'>December 1997<o:p></o:p></span></b></span></span></p> |
| 1531 |
|
| 1532 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1533 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1534 |
|
| 1535 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1536 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1537 |
|
| 1538 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1539 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1540 |
|
| 1541 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1542 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1543 |
|
| 1544 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1545 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><b |
| 1546 |
style='mso-bidi-font-weight:normal'><span style='font-size:16.0pt;mso-bidi-font-size: |
| 1547 |
10.0pt'>Massachusetts Institute of Technology<o:p></o:p></span></b></span></span></p> |
| 1548 |
|
| 1549 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1550 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1551 |
|
| 1552 |
<p class=MsoBodyText align=center style='text-align:center'><span |
| 1553 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1554 |
|
| 1555 |
<b style='mso-bidi-font-weight:normal'><span style='font-size:14.0pt; |
| 1556 |
mso-bidi-font-size:10.0pt;font-family:Arial;mso-fareast-font-family:"Times New Roman"; |
| 1557 |
mso-bidi-font-family:"Times New Roman";text-transform:uppercase;mso-font-kerning: |
| 1558 |
14.0pt;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language: |
| 1559 |
AR-SA'><br clear=all style='page-break-before:always'> |
| 1560 |
</span></b> |
| 1561 |
|
| 1562 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 1563 |
|
| 1564 |
<h1><span style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><a |
| 1565 |
name="_Toc407169603">CONTENTS</a></span></span></h1> |
| 1566 |
|
| 1567 |
</div> |
| 1568 |
|
| 1569 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078218'><span |
| 1570 |
style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 1571 |
|
| 1572 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1573 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><!--[if supportFields]><span |
| 1574 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1575 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1576 |
style='mso-bookmark:_Toc407078231'><span style="mso-spacerun: yes"> </span>TOC |
| 1577 |
\o "1-3" <span style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1578 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>CONTENTS<span |
| 1579 |
style='mso-tab-count:1 dotted'>...................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1580 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1581 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1582 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169603 \h <span |
| 1583 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1584 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>3<!--[if gte mso 9]><xml> |
| 1585 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300033000000</w:data> |
| 1586 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1587 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1588 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1589 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1590 |
|
| 1591 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1592 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>INTRODUCTION<span |
| 1593 |
style='mso-tab-count:1 dotted'>.............................................................................................................. </span></span></span><!--[if supportFields]><span |
| 1594 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1595 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1596 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169604 \h <span |
| 1597 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1598 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>4<!--[if gte mso 9]><xml> |
| 1599 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300034000000</w:data> |
| 1600 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1601 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1602 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1603 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1604 |
|
| 1605 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1606 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>Chapter 1 Continuous |
| 1607 |
formulation<span style='mso-tab-count:1 dotted'>........................................................... </span></span></span><!--[if supportFields]><span |
| 1608 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1609 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1610 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169605 \h <span |
| 1611 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1612 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>6<!--[if gte mso 9]><xml> |
| 1613 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300035000000</w:data> |
| 1614 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1615 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1616 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1617 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1618 |
|
| 1619 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1620 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.1 The continuous |
| 1621 |
equations of the model ocean<span style='mso-tab-count:1 dotted'>..................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1622 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1623 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1624 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169606 \h <span |
| 1625 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1626 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>6<!--[if gte mso 9]><xml> |
| 1627 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300036000000</w:data> |
| 1628 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1629 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1630 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1631 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1632 |
|
| 1633 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1634 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.2 Boundary conditions<span |
| 1635 |
style='mso-tab-count:1 dotted'>................................................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 1636 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1637 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1638 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169607 \h <span |
| 1639 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1640 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>7<!--[if gte mso 9]><xml> |
| 1641 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300037000000</w:data> |
| 1642 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1643 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1644 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1645 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1646 |
|
| 1647 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1648 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.3 Coordinate systems<span |
| 1649 |
style='mso-tab-count:1 dotted'>.................................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 1650 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1651 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1652 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169608 \h <span |
| 1653 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1654 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>9<!--[if gte mso 9]><xml> |
| 1655 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300038000000</w:data> |
| 1656 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1657 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1658 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1659 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1660 |
|
| 1661 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1662 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.4 Hydrostatic, |
| 1663 |
non-hydrostatic and quasi-hydrostatic forms<span style='mso-tab-count:1 dotted'>............................................................................. </span></span></span><!--[if supportFields]><span |
| 1664 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1665 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1666 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169609 \h <span |
| 1667 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1668 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>11<!--[if gte mso 9]><xml> |
| 1669 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600300039000000</w:data> |
| 1670 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1671 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1672 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1673 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1674 |
|
| 1675 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1676 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.5 Finding the |
| 1677 |
pressure field<span style='mso-tab-count:1 dotted'>.................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1678 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1679 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1680 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169610 \h <span |
| 1681 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1682 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>12<!--[if gte mso 9]><xml> |
| 1683 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310030000000</w:data> |
| 1684 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1685 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1686 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1687 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1688 |
|
| 1689 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1690 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>1.5.1 Depth-averaged |
| 1691 |
pressure</u><span style='mso-tab-count:1 dotted'>................................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 1692 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1693 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1694 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169611 \h <span |
| 1695 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1696 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>12<!--[if gte mso 9]><xml> |
| 1697 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310031000000</w:data> |
| 1698 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1699 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1700 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1701 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1702 |
|
| 1703 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1704 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>1.5.2 Surface, |
| 1705 |
hydrostatic and non-hydrostatic pressure</u><span style='mso-tab-count:1 dotted'>.................................................................................... </span></span></span><!--[if supportFields]><span |
| 1706 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1707 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1708 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169612 \h <span |
| 1709 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1710 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>13<!--[if gte mso 9]><xml> |
| 1711 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310032000000</w:data> |
| 1712 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1713 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1714 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1715 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1716 |
|
| 1717 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1718 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.6 Summary of solution |
| 1719 |
strategies<span style='mso-tab-count:1 dotted'>.......................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1720 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1721 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1722 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169613 \h <span |
| 1723 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1724 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>15<!--[if gte mso 9]><xml> |
| 1725 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310033000000</w:data> |
| 1726 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1727 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1728 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1729 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1730 |
|
| 1731 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1732 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>1.7 Forcing and |
| 1733 |
dissipation<span style='mso-tab-count:1 dotted'>......................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1734 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1735 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1736 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169614 \h <span |
| 1737 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1738 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>16<!--[if gte mso 9]><xml> |
| 1739 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310034000000</w:data> |
| 1740 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1741 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1742 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1743 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1744 |
|
| 1745 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1746 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>1.7.1 Forcing</u><span |
| 1747 |
style='mso-tab-count:1 dotted'>................................................................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 1748 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1749 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1750 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169615 \h <span |
| 1751 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1752 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>16<!--[if gte mso 9]><xml> |
| 1753 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310035000000</w:data> |
| 1754 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1755 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1756 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1757 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1758 |
|
| 1759 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1760 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>1.7.2 Dissipation</u><span |
| 1761 |
style='mso-tab-count:1 dotted'>......................................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1762 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1763 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1764 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169616 \h <span |
| 1765 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1766 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>17<!--[if gte mso 9]><xml> |
| 1767 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310036000000</w:data> |
| 1768 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1769 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1770 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1771 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1772 |
|
| 1773 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1774 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>CHAPTER 2 Discrete |
| 1775 |
formulation.<span style='mso-tab-count:1 dotted'>.............................................................. </span></span></span><!--[if supportFields]><span |
| 1776 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1777 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1778 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169617 \h <span |
| 1779 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1780 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>19<!--[if gte mso 9]><xml> |
| 1781 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310037000000</w:data> |
| 1782 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1783 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1784 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1785 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1786 |
|
| 1787 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1788 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>2.1 Temporal |
| 1789 |
discretization.<span style='mso-tab-count:1 dotted'>....................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1790 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1791 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1792 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169618 \h <span |
| 1793 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1794 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>19<!--[if gte mso 9]><xml> |
| 1795 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310038000000</w:data> |
| 1796 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1797 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1798 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1799 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1800 |
|
| 1801 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1802 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>2.2 Spatial |
| 1803 |
discretization.<span style='mso-tab-count:1 dotted'>............................................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 1804 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1805 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1806 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169619 \h <span |
| 1807 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1808 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>21<!--[if gte mso 9]><xml> |
| 1809 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600310039000000</w:data> |
| 1810 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1811 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1812 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1813 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1814 |
|
| 1815 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1816 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.1 Volume |
| 1817 |
quantities</u><span style='mso-tab-count:1 dotted'>............................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 1818 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1819 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1820 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169620 \h <span |
| 1821 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1822 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>22<!--[if gte mso 9]><xml> |
| 1823 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320030000000</w:data> |
| 1824 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1825 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1826 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1827 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1828 |
|
| 1829 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1830 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.2 Face |
| 1831 |
quantities</u><span style='mso-tab-count:1 dotted'>.................................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 1832 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1833 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1834 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169621 \h <span |
| 1835 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1836 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>24<!--[if gte mso 9]><xml> |
| 1837 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320031000000</w:data> |
| 1838 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1839 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1840 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1841 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1842 |
|
| 1843 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1844 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.3 Coriolis terms</u><span |
| 1845 |
style='mso-tab-count:1 dotted'>..................................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1846 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1847 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1848 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169622 \h <span |
| 1849 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1850 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>25<!--[if gte mso 9]><xml> |
| 1851 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320032000000</w:data> |
| 1852 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1853 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1854 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1855 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1856 |
|
| 1857 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1858 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.4 Pressure |
| 1859 |
gradient force</u><span style='mso-tab-count:1 dotted'>.................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1860 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1861 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1862 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169623 \h <span |
| 1863 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1864 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>25<!--[if gte mso 9]><xml> |
| 1865 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320033000000</w:data> |
| 1866 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1867 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1868 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1869 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1870 |
|
| 1871 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1872 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.5 Forcing and |
| 1873 |
dissipation</u><span style='mso-tab-count:1 dotted'>................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1874 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1875 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1876 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169624 \h <span |
| 1877 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1878 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>25<!--[if gte mso 9]><xml> |
| 1879 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320034000000</w:data> |
| 1880 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1881 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1882 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1883 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1884 |
|
| 1885 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1886 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.6 The C-D scheme</u><span |
| 1887 |
style='mso-tab-count:1 dotted'>................................................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 1888 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1889 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1890 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169625 \h <span |
| 1891 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1892 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>26<!--[if gte mso 9]><xml> |
| 1893 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320035000000</w:data> |
| 1894 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1895 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1896 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1897 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1898 |
|
| 1899 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1900 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.2.7 Conservation |
| 1901 |
properties</u><span style='mso-tab-count:1 dotted'>.................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 1902 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1903 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1904 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169626 \h <span |
| 1905 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1906 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>26<!--[if gte mso 9]><xml> |
| 1907 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320036000000</w:data> |
| 1908 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1909 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1910 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1911 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1912 |
|
| 1913 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1914 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>2.3<span |
| 1915 |
style="mso-spacerun: yes"> </span>The Elliptic problem<span style='mso-tab-count: |
| 1916 |
1 dotted'>.............................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 1917 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1918 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1919 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169627 \h <span |
| 1920 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1921 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>27<!--[if gte mso 9]><xml> |
| 1922 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320037000000</w:data> |
| 1923 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1924 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1925 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1926 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1927 |
|
| 1928 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1929 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.3.1 Discrete |
| 1930 |
formulation</u><span style='mso-tab-count:1 dotted'>......................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1931 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1932 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1933 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169628 \h <span |
| 1934 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1935 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>27<!--[if gte mso 9]><xml> |
| 1936 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320038000000</w:data> |
| 1937 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1938 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1939 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1940 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1941 |
|
| 1942 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1943 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>2.3.2 Preconditioned |
| 1944 |
conjugate-gradient solution method</u><span style='mso-tab-count:1 dotted'>.................................................................................. </span></span></span><!--[if supportFields]><span |
| 1945 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1946 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1947 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169629 \h <span |
| 1948 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1949 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>30<!--[if gte mso 9]><xml> |
| 1950 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600320039000000</w:data> |
| 1951 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1952 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1953 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1954 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1955 |
|
| 1956 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1957 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>CHAPTER 3 PARALLEL |
| 1958 |
IMPLEMENTATION<span style='mso-tab-count:1 dotted'>........................................................ </span></span></span><!--[if supportFields]><span |
| 1959 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1960 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1961 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169630 \h <span |
| 1962 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1963 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>36<!--[if gte mso 9]><xml> |
| 1964 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330030000000</w:data> |
| 1965 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1966 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1967 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1968 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1969 |
|
| 1970 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1971 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>2.1 Enumeration of |
| 1972 |
arrays.<span style='mso-tab-count:1 dotted'>.......................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 1973 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1974 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1975 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169631 \h <span |
| 1976 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1977 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>36<!--[if gte mso 9]><xml> |
| 1978 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330031000000</w:data> |
| 1979 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1980 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1981 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1982 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1983 |
|
| 1984 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 1985 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>Chapter 4<span |
| 1986 |
style="mso-spacerun: yes"> </span>Procedures and variables<span |
| 1987 |
style='mso-tab-count:1 dotted'>.................................................. </span></span></span><!--[if supportFields]><span |
| 1988 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1989 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 1990 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169632 \h <span |
| 1991 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 1992 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>38<!--[if gte mso 9]><xml> |
| 1993 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330032000000</w:data> |
| 1994 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 1995 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 1996 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 1997 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 1998 |
|
| 1999 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2000 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>4.1 Procedures<span |
| 2001 |
style='mso-tab-count:1 dotted'>.............................................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 2002 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2003 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2004 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169633 \h <span |
| 2005 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2006 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>38<!--[if gte mso 9]><xml> |
| 2007 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330033000000</w:data> |
| 2008 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2009 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2010 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2011 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2012 |
|
| 2013 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2014 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>4.1.1 Flow chart</u><span |
| 2015 |
style='mso-tab-count:1 dotted'>........................................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2016 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2017 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2018 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169634 \h <span |
| 2019 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2020 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>38<!--[if gte mso 9]><xml> |
| 2021 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330034000000</w:data> |
| 2022 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2023 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2024 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2025 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2026 |
|
| 2027 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2028 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>4.1.2 Alphabetical |
| 2029 |
list of procedures and 'include' files</u><span style='mso-tab-count:1 dotted'>....................................................................................... </span></span></span><!--[if supportFields]><span |
| 2030 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2031 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2032 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169635 \h <span |
| 2033 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2034 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>40<!--[if gte mso 9]><xml> |
| 2035 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330035000000</w:data> |
| 2036 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2037 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2038 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2039 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2040 |
|
| 2041 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2042 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>4.2 Variables<span |
| 2043 |
style='mso-tab-count:1 dotted'>.................................................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 2044 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2045 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2046 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169636 \h <span |
| 2047 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2048 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>40<!--[if gte mso 9]><xml> |
| 2049 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330036000000</w:data> |
| 2050 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2051 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2052 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2053 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2054 |
|
| 2055 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2056 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>Chapter 5 Getting |
| 2057 |
started: practical considerations<span style='mso-tab-count:1 dotted'>............. </span></span></span><!--[if supportFields]><span |
| 2058 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2059 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2060 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169637 \h <span |
| 2061 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2062 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>41<!--[if gte mso 9]><xml> |
| 2063 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330037000000</w:data> |
| 2064 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2065 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2066 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2067 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2068 |
|
| 2069 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2070 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>5.1 Accessing the code |
| 2071 |
- directory structure<span style='mso-tab-count:1 dotted'>.......................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2072 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2073 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2074 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169638 \h <span |
| 2075 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2076 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>41<!--[if gte mso 9]><xml> |
| 2077 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330038000000</w:data> |
| 2078 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2079 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2080 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2081 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2082 |
|
| 2083 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2084 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>5.2 Configuring the |
| 2085 |
model and setting up a run<span style='mso-tab-count:1 dotted'>..................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2086 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2087 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2088 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169639 \h <span |
| 2089 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2090 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>41<!--[if gte mso 9]><xml> |
| 2091 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600330039000000</w:data> |
| 2092 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2093 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2094 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2095 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2096 |
|
| 2097 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2098 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.1 domain, |
| 2099 |
geometry</u><span style='mso-tab-count:1 dotted'>.............................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 2100 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2101 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2102 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169640 \h <span |
| 2103 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2104 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>42<!--[if gte mso 9]><xml> |
| 2105 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340030000000</w:data> |
| 2106 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2107 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2108 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2109 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2110 |
|
| 2111 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2112 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.2 Equation of |
| 2113 |
state</u><span style='mso-tab-count:1 dotted'>............................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2114 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2115 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2116 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169641 \h <span |
| 2117 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2118 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>42<!--[if gte mso 9]><xml> |
| 2119 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340031000000</w:data> |
| 2120 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2121 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2122 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2123 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2124 |
|
| 2125 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2126 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.3 Hydrostatic, |
| 2127 |
quasi-hydrostatic, or non-hydrostatic regime</u><span style='mso-tab-count: |
| 2128 |
1 dotted'>....................................................................... </span></span></span><!--[if supportFields]><span |
| 2129 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2130 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2131 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169642 \h <span |
| 2132 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2133 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>43<!--[if gte mso 9]><xml> |
| 2134 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340032000000</w:data> |
| 2135 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2136 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2137 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2138 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2139 |
|
| 2140 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2141 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.4 Momentum |
| 2142 |
equations</u><span style='mso-tab-count:1 dotted'>...................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2143 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2144 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2145 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169643 \h <span |
| 2146 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2147 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>43<!--[if gte mso 9]><xml> |
| 2148 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340033000000</w:data> |
| 2149 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2150 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2151 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2152 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2153 |
|
| 2154 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2155 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.5 Diagnosis of |
| 2156 |
pressure</u><span style='mso-tab-count:1 dotted'>...................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2157 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2158 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2159 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169644 \h <span |
| 2160 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2161 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>44<!--[if gte mso 9]><xml> |
| 2162 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340034000000</w:data> |
| 2163 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2164 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2165 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2166 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2167 |
|
| 2168 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2169 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.6 Tracer |
| 2170 |
equations (temperature and salinity)</u><span style='mso-tab-count:1 dotted'>................................................................................................. </span></span></span><!--[if supportFields]><span |
| 2171 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2172 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2173 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169645 \h <span |
| 2174 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2175 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>45<!--[if gte mso 9]><xml> |
| 2176 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340035000000</w:data> |
| 2177 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2178 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2179 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2180 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2181 |
|
| 2182 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2183 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.2.7 Run setup</u><span |
| 2184 |
style='mso-tab-count:1 dotted'>........................................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2185 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2186 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2187 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169646 \h <span |
| 2188 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2189 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>46<!--[if gte mso 9]><xml> |
| 2190 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340036000000</w:data> |
| 2191 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2192 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2193 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2194 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2195 |
|
| 2196 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2197 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>5.3 Compiling, running, |
| 2198 |
and restarting the code<span style='mso-tab-count:1 dotted'>.................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2199 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2200 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2201 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169647 \h <span |
| 2202 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2203 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>47<!--[if gte mso 9]><xml> |
| 2204 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340037000000</w:data> |
| 2205 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2206 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2207 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2208 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2209 |
|
| 2210 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2211 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.3.1 compilation</u><span |
| 2212 |
style='mso-tab-count:1 dotted'>......................................................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2213 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2214 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2215 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169648 \h <span |
| 2216 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2217 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>47<!--[if gte mso 9]><xml> |
| 2218 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340038000000</w:data> |
| 2219 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2220 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2221 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2222 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2223 |
|
| 2224 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2225 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.3.2 execution</u><span |
| 2226 |
style='mso-tab-count:1 dotted'>............................................................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 2227 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2228 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2229 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169649 \h <span |
| 2230 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2231 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>47<!--[if gte mso 9]><xml> |
| 2232 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600340039000000</w:data> |
| 2233 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2234 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2235 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2236 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2237 |
|
| 2238 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2239 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.3.3 output and |
| 2240 |
restart</u><span style='mso-tab-count:1 dotted'>............................................................................................................................................. </span></span></span><!--[if supportFields]><span |
| 2241 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2242 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2243 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169650 \h <span |
| 2244 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2245 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>48<!--[if gte mso 9]><xml> |
| 2246 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350030000000</w:data> |
| 2247 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2248 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2249 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2250 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2251 |
|
| 2252 |
<p class=MsoToc2 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2253 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>5.4 Examples : |
| 2254 |
description of test cases<span style='mso-tab-count:1 dotted'>.................................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2255 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2256 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2257 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169651 \h <span |
| 2258 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2259 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>49<!--[if gte mso 9]><xml> |
| 2260 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350031000000</w:data> |
| 2261 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2262 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2263 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2264 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2265 |
|
| 2266 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2267 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.4.1 Two-layer |
| 2268 |
ocean in a rectangular basin driven by a steady wind-stress</u><span |
| 2269 |
style='mso-tab-count:1 dotted'>................................................. </span></span></span><!--[if supportFields]><span |
| 2270 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2271 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2272 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169652 \h <span |
| 2273 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2274 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>49<!--[if gte mso 9]><xml> |
| 2275 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350032000000</w:data> |
| 2276 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2277 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2278 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2279 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2280 |
|
| 2281 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2282 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.4.2 Neutral ocean |
| 2283 |
in a doubly periodic domain driven by buoyancy forcing</u><span |
| 2284 |
style='mso-tab-count:1 dotted'>................................................ </span></span></span><!--[if supportFields]><span |
| 2285 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2286 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2287 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169653 \h <span |
| 2288 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2289 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>50<!--[if gte mso 9]><xml> |
| 2290 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350033000000</w:data> |
| 2291 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2292 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2293 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2294 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2295 |
|
| 2296 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2297 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.4.3 Exponentially |
| 2298 |
stratified ocean on a wind-driven channel</u><span style='mso-tab-count:1 dotted'>........................................................................... </span></span></span><!--[if supportFields]><span |
| 2299 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2300 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2301 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169654 \h <span |
| 2302 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2303 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>50<!--[if gte mso 9]><xml> |
| 2304 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350034000000</w:data> |
| 2305 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2306 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2307 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2308 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2309 |
|
| 2310 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2311 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.4.4 Global ocean |
| 2312 |
driven by realistic wind and buoyancy forcing</u><span style='mso-tab-count: |
| 2313 |
1 dotted'>.................................................................... </span></span></span><!--[if supportFields]><span |
| 2314 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2315 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2316 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169655 \h <span |
| 2317 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2318 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>50<!--[if gte mso 9]><xml> |
| 2319 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350035000000</w:data> |
| 2320 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2321 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2322 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2323 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2324 |
|
| 2325 |
<p class=MsoToc3 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2326 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><u>5.4.5 Model |
| 2327 |
configuration for the test cases</u><span style='mso-tab-count:1 dotted'>......................................................................................................... </span></span></span><!--[if supportFields]><span |
| 2328 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2329 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2330 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169656 \h <span |
| 2331 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2332 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>51<!--[if gte mso 9]><xml> |
| 2333 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350036000000</w:data> |
| 2334 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2335 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2336 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2337 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2338 |
|
| 2339 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2340 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>APPENDICES<span |
| 2341 |
style='mso-tab-count:1 dotted'>................................................................................................................ </span></span></span><!--[if supportFields]><span |
| 2342 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2343 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2344 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169657 \h <span |
| 2345 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2346 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>53<!--[if gte mso 9]><xml> |
| 2347 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350037000000</w:data> |
| 2348 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2349 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2350 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2351 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2352 |
|
| 2353 |
<p class=MsoToc1 style='tab-stops:right dotted 431.5pt'><span style='mso-bookmark: |
| 2354 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'>References<span |
| 2355 |
style='mso-tab-count:1 dotted'>.............................................................................................................. </span></span></span><!--[if supportFields]><span |
| 2356 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2357 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078218'><span |
| 2358 |
style='mso-bookmark:_Toc407078231'> PAGEREF _Toc407169658 \h <span |
| 2359 |
style='mso-element:field-separator'></span></span></span><![endif]--><span |
| 2360 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'>54<!--[if gte mso 9]><xml> |
| 2361 |
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F0054006F0063003400300037003100360039003600350038000000</w:data> |
| 2362 |
</xml><![endif]--></span></span><!--[if supportFields]><span style='mso-bookmark: |
| 2363 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2364 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2365 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2366 |
|
| 2367 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078218'><span |
| 2368 |
style='mso-bookmark:_Toc407078231'></span></span><!--[if supportFields]><span |
| 2369 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'></span></span><span |
| 2370 |
style='mso-element:field-end'></span><![endif]--><span style='mso-bookmark: |
| 2371 |
_Toc407078218'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2372 |
|
| 2373 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078218'><span |
| 2374 |
style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2375 |
|
| 2376 |
<span style='font-size:11.0pt;mso-bidi-font-size:10.0pt;font-family:Arial; |
| 2377 |
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; |
| 2378 |
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br |
| 2379 |
clear=all style='mso-special-character:line-break;page-break-before:always'> |
| 2380 |
</span> |
| 2381 |
|
| 2382 |
<p class=MsoBodyText><![if !supportEmptyParas]> <![endif]><span |
| 2383 |
style='mso-bookmark:_Toc407078218'><span style='mso-bookmark:_Toc407078231'><o:p></o:p></span></span></p> |
| 2384 |
|
| 2385 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 2386 |
|
| 2387 |
<h1 style='text-align:justify'><span style='mso-bookmark:_Toc407078218'><span |
| 2388 |
style='mso-bookmark:_Toc407078231'><a name="_Toc407090372"></a><a |
| 2389 |
name="_Toc407090575"></a><a name="_Toc407169604"><span style='mso-bookmark: |
| 2390 |
_Toc407090575'><span style='mso-bookmark:_Toc407090372'>INTRODUCTION</span></span></a></span></span><span |
| 2391 |
style='mso-bookmark:_Toc407078231'></span></h1> |
| 2392 |
|
| 2393 |
</div> |
| 2394 |
|
| 2395 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2396 |
|
| 2397 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2398 |
|
| 2399 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 2400 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2401 |
10.0pt;font-family:Palatino'>This manual aims to provide the reader with the |
| 2402 |
information necessary to carry out numerical experiments using the M.I.T GCM. |
| 2403 |
The manual provides a comprehensive description of the numerical paradigm |
| 2404 |
employed by the M.I.T. GCM and a description of the associated program code. |
| 2405 |
Examples showing the use of the code in small process studies and for |
| 2406 |
basin/planetary scale simulations are presented. <o:p></o:p></span></span></p> |
| 2407 |
|
| 2408 |
<p class=MsoBodyText style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2409 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2410 |
|
| 2411 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2412 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Any |
| 2413 |
practical numerical rendition involves a series of compromises.<span |
| 2414 |
style="mso-spacerun: yes"> </span>Our guiding principle has been to devise |
| 2415 |
methods which, as far as is possible, are competitive across a large range of |
| 2416 |
scales from<sub><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" |
| 2417 |
o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" |
| 2418 |
stroked="f"> |
| 2419 |
<v:stroke joinstyle="miter"/> |
| 2420 |
<v:formulas> |
| 2421 |
<v:f eqn="if lineDrawn pixelLineWidth 0"/> |
| 2422 |
<v:f eqn="sum @0 1 0"/> |
| 2423 |
<v:f eqn="sum 0 0 @1"/> |
| 2424 |
<v:f eqn="prod @2 1 2"/> |
| 2425 |
<v:f eqn="prod @3 21600 pixelWidth"/> |
| 2426 |
<v:f eqn="prod @3 21600 pixelHeight"/> |
| 2427 |
<v:f eqn="sum @0 0 1"/> |
| 2428 |
<v:f eqn="prod @6 1 2"/> |
| 2429 |
<v:f eqn="prod @7 21600 pixelWidth"/> |
| 2430 |
<v:f eqn="sum @8 21600 0"/> |
| 2431 |
<v:f eqn="prod @7 21600 pixelHeight"/> |
| 2432 |
<v:f eqn="sum @10 21600 0"/> |
| 2433 |
</v:formulas> |
| 2434 |
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> |
| 2435 |
<o:lock v:ext="edit" aspectratio="t"/> |
| 2436 |
</v:shapetype><v:shape id="_x0000_i1789" type="#_x0000_t75" style='width:36.75pt; |
| 2437 |
height:12pt' o:ole=""> |
| 2438 |
<v:imagedata src="./fulldoc_files/image001.wmz" o:title=""/> |
| 2439 |
</v:shape><![endif]--><![if !vml]><img width=49 height=16 |
| 2440 |
src="./fulldoc_files/image002.gif" v:shapes="_x0000_i1789"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2441 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1789" |
| 2442 |
DrawAspect="Content" ObjectID="_1051901131"> |
| 2443 |
</o:OLEObject> |
| 2444 |
</xml><![endif]-->, the depth of the fluid, right up to horizontal resolutions<sub><!--[if gte vml 1]><v:shape |
| 2445 |
id="_x0000_i1790" type="#_x0000_t75" style='width:39pt;height:18pt' o:ole=""> |
| 2446 |
<v:imagedata src="./fulldoc_files/image003.wmz" o:title=""/> |
| 2447 |
</v:shape><![endif]--><![if !vml]><img width=52 height=24 |
| 2448 |
src="./fulldoc_files/image004.gif" v:shapes="_x0000_i1790"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2449 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1790" |
| 2450 |
DrawAspect="Content" ObjectID="_1051901133"> |
| 2451 |
</o:OLEObject> |
| 2452 |
</xml><![endif]-->, coarser than the Rossby radius of deformation. We did not |
| 2453 |
want to make the hydrostatic assumption <i style='mso-bidi-font-style:normal'>a-priori</i>, |
| 2454 |
since it precludes the study of many interesting small-scale phenomenon.<span |
| 2455 |
style="mso-spacerun: yes"> </span>Rather it was important to us that our |
| 2456 |
approach be also well-suited to the convective, non-hydrostatic limit.<span |
| 2457 |
style="mso-spacerun: yes"> </span>We therefore adopt pressure (or height) as a |
| 2458 |
vertical coordinate and employ a finite volume approach, in which property |
| 2459 |
fluxes are defined normal to the faces that define the volumes, leading to a |
| 2460 |
very natural and robust discrete analogue of divergence.<span |
| 2461 |
style="mso-spacerun: yes"> </span>In the special case that the volumes are of |
| 2462 |
regular shape, the arrangement of the model variables in the horizontal reduces |
| 2463 |
to a C grid, using the nomenclature of Arakawa and Lamb (1977), and so |
| 2464 |
carries with it well-documented strengths and weaknesses in the treatment of |
| 2465 |
gravity, inertial and Rossby wave modes (for a recent discussion see Dukowicz, |
| 2466 |
1995).<o:p></o:p></span></span></p> |
| 2467 |
|
| 2468 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2469 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2470 |
|
| 2471 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2472 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 2473 |
basis for the numerical procedure employed in the M.I.T GCM is the |
| 2474 |
incompressible Navier-Stokes equations. The model integrates forward the |
| 2475 |
Boussinesq</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc407078231'></span><span |
| 2476 |
style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc407078231'><span |
| 2477 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> XE |
| 2478 |
Boussinesq </span></span><![endif]--><span style='mso-bookmark:_Toc407078231'></span><!--[if supportFields]><span |
| 2479 |
style='mso-bookmark:_Toc407078231'></span><span style='mso-element:field-end'></span><![endif]--><span |
| 2480 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2481 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: |
| 2482 |
yes"> </span>approximation to the full Navier-Stokes</span></span><!--[if supportFields]><span |
| 2483 |
style='mso-bookmark:_Toc407078231'></span><span style='mso-element:field-begin'></span><span |
| 2484 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2485 |
10.0pt;font-family:Palatino'> XE Navier-Stokes </span></span><![endif]--><span |
| 2486 |
style='mso-bookmark:_Toc407078231'></span><!--[if supportFields]><span |
| 2487 |
style='mso-bookmark:_Toc407078231'></span><span style='mso-element:field-end'></span><![endif]--><span |
| 2488 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2489 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> </span>equation |
| 2490 |
governing fluid motion. The models numerical integration method is arrived at |
| 2491 |
by utilising the pressure method [Harlow and Welch, 1965; Williams, 1969; |
| 2492 |
Potter, 1976]. In this scheme the continuity relation <sub><!--[if gte vml 1]><v:shape |
| 2493 |
id="_x0000_i1791" type="#_x0000_t75" style='width:39.75pt;height:14.25pt' |
| 2494 |
o:ole="" fillcolor="window"> |
| 2495 |
<v:imagedata src="./fulldoc_files/image005.wmz" o:title=""/> |
| 2496 |
</v:shape><![endif]--><![if !vml]><img width=53 height=19 |
| 2497 |
src="./fulldoc_files/image006.gif" v:shapes="_x0000_i1791"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2498 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1791" |
| 2499 |
DrawAspect="Content" ObjectID="_1051901134"> |
| 2500 |
</o:OLEObject> |
| 2501 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is used to give an |
| 2502 |
elliptic equation for the pressure field. Starting from these basis equations |
| 2503 |
the model is formulated to allow three different solution strategies. In the |
| 2504 |
non-hydrostatic - <b style='mso-bidi-font-weight:normal'>NH -</b> mode of |
| 2505 |
integration, the basis equations are stepped forward without further |
| 2506 |
approximation - in particular full non-hydrostatic dynamics are retained. The |
| 2507 |
hydrostatic primitive equations - <b style='mso-bidi-font-weight:normal'>HPE</b> |
| 2508 |
- mode of the model integrates an approximated form of the full equations, |
| 2509 |
which assumes exact hydrostatic balance. The quasi-hydrostatic - <b |
| 2510 |
style='mso-bidi-font-weight:normal'>QH</b> - mode of integration admits |
| 2511 |
additional Coriolis terms, which augment <b style='mso-bidi-font-weight:normal'>HPE |
| 2512 |
</b>with an analytically exact angular momentum principle.<o:p></o:p></span></span></p> |
| 2513 |
|
| 2514 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2515 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2516 |
|
| 2517 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2518 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 2519 |
kernel algorithm solves the incompressible Navier Stokes equations on the |
| 2520 |
sphere and can be employed as an atmospheric model or as an ocean model in a |
| 2521 |
geometry as complicated as that of the ocean basins with irregular coastlines |
| 2522 |
and islands. The algorithm builds on ideas developed in the computational fluid |
| 2523 |
community.<span style="mso-spacerun: yes"> </span>The numerical challenge is |
| 2524 |
to ensure that the evolving velocity field remains non-divergent; a pressure |
| 2525 |
correction to the velocity field is used to guarantee non-divergence.<span |
| 2526 |
style="mso-spacerun: yes"> </span>The correction step is equivalent to, and is |
| 2527 |
solved as, a Poisson equation for the pressure field with Neumann boundary |
| 2528 |
conditions.<span style="mso-spacerun: yes"> </span>This Poisson inversion is |
| 2529 |
the most computationally demanding part of the algorithm and, because it is not |
| 2530 |
localised in space, presents the biggest challenge in mapping on to parallel |
| 2531 |
computers since it demands communication across the grid to the boundary, and |
| 2532 |
hence between processors.<span style="mso-spacerun: yes"> </span>We have |
| 2533 |
devised a method for solving this Poisson equation which exploits knowledge of |
| 2534 |
the dynamics (by separating the pressure field in to hydrostatic, |
| 2535 |
non-hydrostatic and surface pressure components), the geometry of the ocean |
| 2536 |
basin (they are much wider than they are deep) and naturally lends itself to |
| 2537 |
data-parallel implementation.<span style="mso-spacerun: yes"> </span>The model |
| 2538 |
will, of course, also run on a single processor.<o:p></o:p></span></span></p> |
| 2539 |
|
| 2540 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2541 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2542 |
|
| 2543 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2544 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Much of |
| 2545 |
what is here has been already described in the two reference papers on the |
| 2546 |
model published in the '<i style='mso-bidi-font-style:normal'>Journal of |
| 2547 |
Geophysical Research</i>' [Marshall et al., 1997a,b]. The manual is organized |
| 2548 |
as follows: in Chapter 1, we describe the continuous formulation of the model |
| 2549 |
as well as the different solution strategies employed to find the pressure |
| 2550 |
field for the <b style='mso-bidi-font-weight:normal'>HPE</b>, <b |
| 2551 |
style='mso-bidi-font-weight:normal'>QH</b>, and <b style='mso-bidi-font-weight: |
| 2552 |
normal'>NH</b> modes. This chapter corresponds essentially to sections 3 and 4 |
| 2553 |
of Marshall et al., 1997a. Chapter 2 describes the temporal and spatial |
| 2554 |
discretizations used in the model and the numerical approach used to solve the |
| 2555 |
Elliptic problem for the pressure field. This chapter corresponds essentially to |
| 2556 |
sections 3 and 4 of Marshall et al., 1997b. Chapter 3 is not written yet and is |
| 2557 |
meant to describe the parallel implementation of the model code in Fortran 90 |
| 2558 |
and High Performance Fortran (HPF). A flow chart and an alphabetical list of |
| 2559 |
the procedures and variables are given in Chapter 4. In Chapter 5, the most |
| 2560 |
practical section of the manual, we review what you need to know to run an |
| 2561 |
experiment with the M.I.T. GCM (accessing the code, configuration, compilation, |
| 2562 |
description of output files etc
). We provide some examples that have been |
| 2563 |
published in the literature, ranging from the convective scale up to the |
| 2564 |
planetary/global scale. These examples should help the user to get more |
| 2565 |
familiar with the model. <o:p></o:p></span></span></p> |
| 2566 |
|
| 2567 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2568 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2569 |
|
| 2570 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><b |
| 2571 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2572 |
10.0pt;font-family:Palatino'>It would be nice to include an history of the |
| 2573 |
model in the introduction!<o:p></o:p></span></b></span></p> |
| 2574 |
|
| 2575 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2576 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2577 |
|
| 2578 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2579 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2580 |
|
| 2581 |
</div> |
| 2582 |
|
| 2583 |
<span style='font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family: |
| 2584 |
"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US; |
| 2585 |
mso-bidi-language:AR-SA'><br clear=all style='page-break-before:always; |
| 2586 |
mso-break-type:section-break'> |
| 2587 |
</span> |
| 2588 |
|
| 2589 |
<div class=Section2> |
| 2590 |
|
| 2591 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2592 |
|
| 2593 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 2594 |
|
| 2595 |
<h1><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078219"></a><a |
| 2596 |
name="_Toc407090373"></a><a name="_Toc407090576"></a><a name="_Toc407169605"><span |
| 2597 |
style='mso-bookmark:_Toc407090576'><span style='mso-bookmark:_Toc407090373'><span |
| 2598 |
style='mso-bookmark:_Toc407078219'>Chapter 1 Continuous formulation</span></span></span></a></span></h1> |
| 2599 |
|
| 2600 |
</div> |
| 2601 |
|
| 2602 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2603 |
|
| 2604 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2605 |
|
| 2606 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078220"></a><a |
| 2607 |
name="_Toc407090374"></a><a name="_Toc407090577"></a><a name="_Toc407169606"><span |
| 2608 |
style='mso-bookmark:_Toc407090577'><span style='mso-bookmark:_Toc407090374'><span |
| 2609 |
style='mso-bookmark:_Toc407078220'>1.1 The continuous equations of the model |
| 2610 |
ocean</span></span></span></a></span></h2> |
| 2611 |
|
| 2612 |
<p class=MsoNormal style='text-align:justify;mso-pagination:widow-orphan lines-together; |
| 2613 |
tab-stops:81.0pt'><span style='mso-bookmark:_Toc407078231'><span |
| 2614 |
style='font-size:11.0pt;mso-bidi-font-size:10.0pt;font-family:Arial;mso-bidi-font-family: |
| 2615 |
"Times New Roman"'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2616 |
|
| 2617 |
<p class=MsoNormal style='text-align:justify;mso-pagination:widow-orphan lines-together; |
| 2618 |
tab-stops:81.0pt'><span style='mso-bookmark:_Toc407078231'><span |
| 2619 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 2620 |
state of the ocean at any time is characterized by the distribution of currents |
| 2621 |
<b style='mso-bidi-font-weight:normal'>v</b>, potential temperature <i |
| 2622 |
style='mso-bidi-font-style:normal'>T</i>, salinity <i style='mso-bidi-font-style: |
| 2623 |
normal'>S</i>, pressure <i style='mso-bidi-font-style:normal'>p</i> and density |
| 2624 |
</span></span><span style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style: |
| 2625 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 2626 |
Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 2627 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 2628 |
symbol;mso-symbol-font-family:Symbol'>r</span></span></i></span><span |
| 2629 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2630 |
10.0pt;font-family:Palatino'>. The equations that govern the evolution of these |
| 2631 |
fields, obtained by applying the laws of classical mechanics and thermodynamics |
| 2632 |
to a Boussinesq incompressible fluid are, using height as the vertical |
| 2633 |
coordinate:<o:p></o:p></span></span></p> |
| 2634 |
|
| 2635 |
<p class=MsoNormal style='text-align:justify;mso-pagination:widow-orphan lines-together; |
| 2636 |
tab-stops:81.0pt'><span style='mso-bookmark:_Toc407078231'><span |
| 2637 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2638 |
|
| 2639 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2640 |
style='mso-bookmark:_Toc407078231'><a name="_Ref382795878"></a><a |
| 2641 |
name="_Ref382795966"><span style='mso-bookmark:_Ref382795878'><span |
| 2642 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 2643 |
id="_x0000_i1025" type="#_x0000_t75" style='width:117pt;height:51.75pt' o:ole="" |
| 2644 |
fillcolor="window"> |
| 2645 |
<v:imagedata src="./fulldoc_files/image007.wmz" o:title=""/> |
| 2646 |
</v:shape><![endif]--><![if !vml]><img width=156 height=69 |
| 2647 |
src="./fulldoc_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2648 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" |
| 2649 |
DrawAspect="Content" ObjectID="_1051901136"> |
| 2650 |
</o:OLEObject> |
| 2651 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 2652 |
style="mso-spacerun: yes"> </span></span><span |
| 2653 |
style="mso-spacerun: yes"> </span></span></a></span><span style='mso-bookmark: |
| 2654 |
_Toc407078231'><span style='mso-bookmark:_Ref382795966'><span style='mso-bookmark: |
| 2655 |
_Ref382795878'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 2656 |
font-family:Palatino'>(<span style='mso-field-code:"SEQ \( \\* ARABIC"'>1</span></span></span></span><a |
| 2657 |
name="_Ref382795976"></a></span><span style='mso-bookmark:_Toc407078231'><span |
| 2658 |
style='mso-bookmark:_Ref382795976'><span style='mso-bookmark:_Ref382795878'><span |
| 2659 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>.1.1)</span></span></span></span></p> |
| 2660 |
|
| 2661 |
<p class=MsoNormal style='text-align:justify;page-break-after:avoid'><span |
| 2662 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2663 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2664 |
|
| 2665 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2666 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2667 |
10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1026" |
| 2668 |
type="#_x0000_t75" style='width:99.75pt;height:18pt' o:ole=""> |
| 2669 |
<v:imagedata src="./fulldoc_files/image009.wmz" o:title=""/> |
| 2670 |
</v:shape><![endif]--><![if !vml]><img width=133 height=24 |
| 2671 |
src="./fulldoc_files/image010.gif" v:shapes="_x0000_i1026"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2672 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1026" |
| 2673 |
DrawAspect="Content" ObjectID="_1051901137"> |
| 2674 |
</o:OLEObject> |
| 2675 |
</xml><![endif]--><span style="mso-spacerun: |
| 2676 |
yes"> </span></span><span |
| 2677 |
style="mso-spacerun: yes"> </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 2678 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>(1.1.<span |
| 2679 |
style='mso-field-code:"SEQ \( \\* ARABIC"'>2</span>)</span></span></p> |
| 2680 |
|
| 2681 |
<p class=MsoNormal style='text-align:justify;page-break-after:avoid'><span |
| 2682 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2683 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2684 |
|
| 2685 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2686 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2687 |
10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1027" |
| 2688 |
type="#_x0000_t75" style='width:86.25pt;height:33.75pt' o:ole=""> |
| 2689 |
<v:imagedata src="./fulldoc_files/image011.wmz" o:title=""/> |
| 2690 |
</v:shape><![endif]--><![if !vml]><img width=115 height=45 |
| 2691 |
src="./fulldoc_files/image012.gif" v:shapes="_x0000_i1027"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2692 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1027" |
| 2693 |
DrawAspect="Content" ObjectID="_1051901138"> |
| 2694 |
</o:OLEObject> |
| 2695 |
</xml><![endif]--></span><span style="mso-spacerun: |
| 2696 |
yes"> </span></span><span |
| 2697 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2698 |
10.0pt;font-family:Palatino'>(1.1.<span style='mso-field-code:"SEQ \( \\* ARABIC"'>3</span>)<o:p></o:p></span></span></p> |
| 2699 |
|
| 2700 |
<p class=MsoNormal style='text-align:justify;page-break-after:avoid'><span |
| 2701 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2702 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2703 |
|
| 2704 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2705 |
style='mso-bookmark:_Toc407078231'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1028" |
| 2706 |
type="#_x0000_t75" style='width:83.25pt;height:33.75pt' o:ole="" fillcolor="window"> |
| 2707 |
<v:imagedata src="./fulldoc_files/image013.wmz" o:title=""/> |
| 2708 |
</v:shape><![endif]--><![if !vml]><img width=111 height=45 |
| 2709 |
src="./fulldoc_files/image014.gif" v:shapes="_x0000_i1028"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2710 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028" |
| 2711 |
DrawAspect="Content" ObjectID="_1051901139"> |
| 2712 |
</o:OLEObject> |
| 2713 |
</xml><![endif]--><span style="mso-spacerun: |
| 2714 |
yes"> </span></span><span |
| 2715 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2716 |
10.0pt;font-family:Palatino'>(1.1.<span style='mso-field-code:"SEQ \( \\* ARABIC"'>4</span>)<o:p></o:p></span></span></p> |
| 2717 |
|
| 2718 |
<p class=MsoNormal style='text-align:justify;page-break-after:avoid'><span |
| 2719 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2720 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2721 |
|
| 2722 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2723 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2724 |
10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1029" |
| 2725 |
type="#_x0000_t75" style='width:165.75pt;height:18pt' o:ole=""> |
| 2726 |
<v:imagedata src="./fulldoc_files/image015.wmz" o:title=""/> |
| 2727 |
</v:shape><![endif]--><![if !vml]><img width=221 height=24 |
| 2728 |
src="./fulldoc_files/image016.gif" v:shapes="_x0000_i1029"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2729 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1029" |
| 2730 |
DrawAspect="Content" ObjectID="_1051901140"> |
| 2731 |
</o:OLEObject> |
| 2732 |
</xml><![endif]--><span style="mso-spacerun: |
| 2733 |
yes"> </span></span><span style="mso-spacerun: |
| 2734 |
yes"> </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 2735 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>(1.1.<span |
| 2736 |
style='mso-field-code:"SEQ \( \\* ARABIC"'>5</span>)</span></span><span |
| 2737 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><o:p></o:p></span></span></p> |
| 2738 |
|
| 2739 |
<p class=MsoNormal style='text-align:justify;text-indent:36.0pt;tab-stops:36.0pt'><span |
| 2740 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2741 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2742 |
|
| 2743 |
<p class=MsoNormal style='text-align:justify;tab-stops:36.0pt'><span |
| 2744 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2745 |
10.0pt;font-family:Palatino'>where<o:p></o:p></span></span></p> |
| 2746 |
|
| 2747 |
<p class=MsoNormal style='text-align:justify;text-indent:36.0pt;tab-stops:36.0pt'><span |
| 2748 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2749 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2750 |
|
| 2751 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2752 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2753 |
10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1030" |
| 2754 |
type="#_x0000_t75" style='width:111pt;height:18.75pt' o:ole=""> |
| 2755 |
<v:imagedata src="./fulldoc_files/image017.wmz" o:title=""/> |
| 2756 |
</v:shape><![endif]--><![if !vml]><img width=148 height=25 |
| 2757 |
src="./fulldoc_files/image018.gif" v:shapes="_x0000_i1030"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2758 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1030" |
| 2759 |
DrawAspect="Content" ObjectID="_1051901142"> |
| 2760 |
</o:OLEObject> |
| 2761 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 2762 |
style="mso-spacerun: yes"> </span></span><span |
| 2763 |
style="mso-spacerun: yes"> </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 2764 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>(1.1.<span |
| 2765 |
style='mso-field-code:"SEQ \( \\* ARABIC"'>6</span>)</span></span></p> |
| 2766 |
|
| 2767 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2768 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2769 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2770 |
|
| 2771 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2772 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>is the |
| 2773 |
velocity in the lateral and vertical direction respectively. In (1.1.1), <sub><!--[if gte vml 1]><v:shape |
| 2774 |
id="_x0000_i1031" type="#_x0000_t75" style='width:18pt;height:15.75pt' o:ole=""> |
| 2775 |
<v:imagedata src="./fulldoc_files/image019.wmz" o:title=""/> |
| 2776 |
</v:shape><![endif]--><![if !vml]><img width=24 height=21 |
| 2777 |
src="./fulldoc_files/image020.gif" v:shapes="_x0000_i1031"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2778 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1031" |
| 2779 |
DrawAspect="Content" ObjectID="_1051901143"> |
| 2780 |
</o:OLEObject> |
| 2781 |
</xml><![endif]-->is the pressure-gradient force, where</span></span><span |
| 2782 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2783 |
10.0pt'> <o:p></o:p></span></span></p> |
| 2784 |
|
| 2785 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2786 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2787 |
|
| 2788 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2789 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2790 |
10.0pt'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" |
| 2791 |
style='width:45pt;height:35.25pt' o:ole=""> |
| 2792 |
<v:imagedata src="./fulldoc_files/image021.wmz" o:title=""/> |
| 2793 |
</v:shape><![endif]--><![if !vml]><img width=60 height=47 |
| 2794 |
src="./fulldoc_files/image022.gif" v:shapes="_x0000_i1032"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2795 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1032" |
| 2796 |
DrawAspect="Content" ObjectID="_1051901144"> |
| 2797 |
</o:OLEObject> |
| 2798 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 2799 |
style="mso-spacerun: yes"> </span></span><span |
| 2800 |
style="mso-spacerun: yes"> </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 2801 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>(1.1.<span |
| 2802 |
style='mso-field-code:"SEQ \( \\* ARABIC"'>7</span>)<o:p></o:p></span></span></p> |
| 2803 |
|
| 2804 |
<p class=MsoNormal style='page-break-after:avoid'><span style='mso-bookmark: |
| 2805 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2806 |
|
| 2807 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2808 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>is the |
| 2809 |
dynamic pressure expressed in terms of </span></span><span style='mso-bookmark: |
| 2810 |
_Toc407078231'><i style='mso-bidi-font-style:normal'><span style='font-size: |
| 2811 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino; |
| 2812 |
mso-hansi-font-family:Palatino;mso-char-type:symbol;mso-symbol-font-family: |
| 2813 |
Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>d</span></span></i></span><span |
| 2814 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 2815 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>p</span></i></span><span |
| 2816 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2817 |
10.0pt;font-family:Palatino'>, the deviation of the pressure from that of a |
| 2818 |
resting, hydrostatically balanced ocean<o:p></o:p></span></span></p> |
| 2819 |
|
| 2820 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2821 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2822 |
|
| 2823 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2824 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2825 |
10.0pt'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" |
| 2826 |
style='width:84pt;height:33pt' o:ole=""> |
| 2827 |
<v:imagedata src="./fulldoc_files/image023.wmz" o:title=""/> |
| 2828 |
</v:shape><![endif]--><![if !vml]><img width=112 height=44 |
| 2829 |
src="./fulldoc_files/image024.gif" v:shapes="_x0000_i1033"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2830 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1033" |
| 2831 |
DrawAspect="Content" ObjectID="_1051901145"> |
| 2832 |
</o:OLEObject> |
| 2833 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 2834 |
style="mso-spacerun: yes"> </span></span><span |
| 2835 |
style="mso-spacerun: yes"> </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 2836 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>(1.1.<span |
| 2837 |
style='mso-field-code:"SEQ \( \\* ARABIC"'>8</span>)</span></span></p> |
| 2838 |
|
| 2839 |
<p class=MsoNormal style='page-break-after:avoid'><span style='mso-bookmark: |
| 2840 |
_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2841 |
|
| 2842 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2843 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where,</span><sub><!--[if gte vml 1]><v:shape |
| 2844 |
id="_x0000_i1034" type="#_x0000_t75" style='width:21.75pt;height:18pt' o:ole=""> |
| 2845 |
<v:imagedata src="./fulldoc_files/image025.wmz" o:title=""/> |
| 2846 |
</v:shape><![endif]--><![if !vml]><img width=29 height=24 |
| 2847 |
src="./fulldoc_files/image026.gif" v:shapes="_x0000_i1034"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2848 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1034" |
| 2849 |
DrawAspect="Content" ObjectID="_1051901147"> |
| 2850 |
</o:OLEObject> |
| 2851 |
</xml><![endif]--></span><span style='mso-bookmark:_Toc407078231'><span |
| 2852 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>is a |
| 2853 |
constant reference density. <sub><!--[if gte vml 1]><v:shape id="_x0000_i1035" |
| 2854 |
type="#_x0000_t75" style='width:21pt;height:20.25pt' o:ole="" fillcolor="window"> |
| 2855 |
<v:imagedata src="./fulldoc_files/image027.wmz" o:title=""/> |
| 2856 |
</v:shape><![endif]--><![if !vml]><img width=28 height=27 |
| 2857 |
src="./fulldoc_files/image028.gif" v:shapes="_x0000_i1035"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2858 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035" |
| 2859 |
DrawAspect="Content" ObjectID="_1051901148"> |
| 2860 |
</o:OLEObject> |
| 2861 |
</xml><![endif]-->represents the advective, Coriolis, buoyancy, forcing and |
| 2862 |
dissipative terms in the momentum equations, i.e. in vector form:<o:p></o:p></span></span></p> |
| 2863 |
|
| 2864 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 2865 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2866 |
|
| 2867 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 2868 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 2869 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1036" |
| 2870 |
type="#_x0000_t75" style='width:195.75pt;height:35.25pt' o:ole="" fillcolor="window"> |
| 2871 |
<v:imagedata src="./fulldoc_files/image029.wmz" o:title=""/> |
| 2872 |
</v:shape><![endif]--><![if !vml]><img width=261 height=47 |
| 2873 |
src="./fulldoc_files/image030.gif" v:shapes="_x0000_i1036"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2874 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036" |
| 2875 |
DrawAspect="Content" ObjectID="_1051901149"> |
| 2876 |
</o:OLEObject> |
| 2877 |
</xml><![endif]--><span style="mso-spacerun: |
| 2878 |
yes"> </span>(1.1.9)<o:p></o:p></span></span></p> |
| 2879 |
|
| 2880 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 2881 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 2882 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 2883 |
|
| 2884 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 2885 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In |
| 2886 |
(1.1.9), </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 2887 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 2888 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 2889 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 2890 |
mso-symbol-font-family:Symbol'>W</span></span></span><span style='mso-bookmark: |
| 2891 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 2892 |
font-family:Palatino'> is the angular speed of rotation of the Earth, <b |
| 2893 |
style='mso-bidi-font-weight:normal'>g</b> is gravity and <b style='mso-bidi-font-weight: |
| 2894 |
normal'>F<sub>v</sub></b> and <b style='mso-bidi-font-weight:normal'>D<sub>v</sub></b> |
| 2895 |
are the forcing and dissipative terms, respectively. The explicit expression of |
| 2896 |
<b style='mso-bidi-font-weight:normal'>G<sub>v</sub></b>, component by |
| 2897 |
component, is given in spherical coordinates in section 1.3.<o:p></o:p></span></span></p> |
| 2898 |
|
| 2899 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 2900 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 2901 |
tendencies of temperature and salt are given by<o:p></o:p></span></span></p> |
| 2902 |
|
| 2903 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 2904 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2905 |
|
| 2906 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2907 |
style='mso-bookmark:_Toc407078231'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1037" |
| 2908 |
type="#_x0000_t75" style='width:113.25pt;height:17.25pt' o:ole="" fillcolor="window"> |
| 2909 |
<v:imagedata src="./fulldoc_files/image031.wmz" o:title=""/> |
| 2910 |
</v:shape><![endif]--><![if !vml]><img width=151 height=23 |
| 2911 |
src="./fulldoc_files/image032.gif" v:shapes="_x0000_i1037"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2912 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037" |
| 2913 |
DrawAspect="Content" ObjectID="_1051901151"> |
| 2914 |
</o:OLEObject> |
| 2915 |
</xml><![endif]--><span style="mso-spacerun: |
| 2916 |
yes"> </span></span><span |
| 2917 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2918 |
10.0pt;font-family:Palatino'>(1.1.10)<o:p></o:p></span></span></p> |
| 2919 |
|
| 2920 |
<p class=MsoNormal style='page-break-after:avoid'><span style='mso-bookmark: |
| 2921 |
_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2922 |
|
| 2923 |
<p class=MsoNormal align=right style='text-align:right;page-break-after:avoid'><span |
| 2924 |
style='mso-bookmark:_Toc407078231'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1038" |
| 2925 |
type="#_x0000_t75" style='width:111.75pt;height:18pt' o:ole="" fillcolor="window"> |
| 2926 |
<v:imagedata src="./fulldoc_files/image033.wmz" o:title=""/> |
| 2927 |
</v:shape><![endif]--><![if !vml]><img width=149 height=24 |
| 2928 |
src="./fulldoc_files/image034.gif" v:shapes="_x0000_i1038"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2929 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038" |
| 2930 |
DrawAspect="Content" ObjectID="_1051901152"> |
| 2931 |
</o:OLEObject> |
| 2932 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 2933 |
style="mso-spacerun: |
| 2934 |
yes"> </span></span><span |
| 2935 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2936 |
10.0pt;font-family:Palatino'>(1.1.<span style='mso-field-code:"SEQ \( \\* ARABIC"'>9</span>1)</span></span></p> |
| 2937 |
|
| 2938 |
<p class=MsoNormal style='page-break-after:avoid'><span style='mso-bookmark: |
| 2939 |
_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 2940 |
|
| 2941 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2942 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where </span></span><span |
| 2943 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 2944 |
id="_x0000_i1039" type="#_x0000_t75" style='width:15pt;height:15.75pt' o:ole=""> |
| 2945 |
<v:imagedata src="./fulldoc_files/image035.wmz" o:title=""/> |
| 2946 |
</v:shape><![endif]--><![if !vml]><img width=20 height=21 |
| 2947 |
src="./fulldoc_files/image036.gif" v:shapes="_x0000_i1039"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2948 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1039" |
| 2949 |
DrawAspect="Content" ObjectID="_1051901153"> |
| 2950 |
</o:OLEObject> |
| 2951 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" |
| 2952 |
style='width:14.25pt;height:17.25pt' o:ole=""> |
| 2953 |
<v:imagedata src="./fulldoc_files/image037.wmz" o:title=""/> |
| 2954 |
</v:shape><![endif]--><![if !vml]><img width=19 height=23 |
| 2955 |
src="./fulldoc_files/image038.gif" v:shapes="_x0000_i1040"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2956 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1040" |
| 2957 |
DrawAspect="Content" ObjectID="_1051901154"> |
| 2958 |
</o:OLEObject> |
| 2959 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" |
| 2960 |
style='width:18pt;height:17.25pt' o:ole="" fillcolor="window"> |
| 2961 |
<v:imagedata src="./fulldoc_files/image039.wmz" o:title=""/> |
| 2962 |
</v:shape><![endif]--><![if !vml]><img width=24 height=23 |
| 2963 |
src="./fulldoc_files/image040.gif" v:shapes="_x0000_i1041"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2964 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041" |
| 2965 |
DrawAspect="Content" ObjectID="_1051901155"> |
| 2966 |
</o:OLEObject> |
| 2967 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75" |
| 2968 |
style='width:17.25pt;height:18pt' o:ole="" fillcolor="window"> |
| 2969 |
<v:imagedata src="./fulldoc_files/image041.wmz" o:title=""/> |
| 2970 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 2971 |
src="./fulldoc_files/image042.gif" v:shapes="_x0000_i1042"><![endif]></sub><!--[if gte mso 9]><xml> |
| 2972 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1042" |
| 2973 |
DrawAspect="Content" ObjectID="_1051901157"> |
| 2974 |
</o:OLEObject> |
| 2975 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span></span><span |
| 2976 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 2977 |
10.0pt;font-family:Palatino'>represent the forcing and dissipative terms in the |
| 2978 |
temperature and salt equations respectively.<o:p></o:p></span></span></p> |
| 2979 |
|
| 2980 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2981 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2982 |
|
| 2983 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 2984 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Unlike |
| 2985 |
the prognostic variables <i style='mso-bidi-font-style:normal'>u</i>, <i |
| 2986 |
style='mso-bidi-font-style:normal'>v</i>, <i style='mso-bidi-font-style:normal'>w</i>, |
| 2987 |
<i style='mso-bidi-font-style:normal'>T</i> and <i style='mso-bidi-font-style: |
| 2988 |
normal'>S</i>, the pressure field must be obtained diagnostically. Taking the |
| 2989 |
divergence of (1.1.1) and using the continuity equation (1.1.2), leads to a |
| 2990 |
three-dimensional Elliptic equation for the pressure:<o:p></o:p></span></span></p> |
| 2991 |
|
| 2992 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 2993 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 2994 |
|
| 2995 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 2996 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 2997 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1043" |
| 2998 |
type="#_x0000_t75" style='width:83.25pt;height:18.75pt' o:ole=""> |
| 2999 |
<v:imagedata src="./fulldoc_files/image043.wmz" o:title=""/> |
| 3000 |
</v:shape><![endif]--><![if !vml]><img width=111 height=25 |
| 3001 |
src="./fulldoc_files/image044.gif" v:shapes="_x0000_i1043"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3002 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1043" |
| 3003 |
DrawAspect="Content" ObjectID="_1051901158"> |
| 3004 |
</o:OLEObject> |
| 3005 |
</xml><![endif]--><span style="mso-spacerun: |
| 3006 |
yes"> </span>(1.1.12)<o:p></o:p></span></span></p> |
| 3007 |
|
| 3008 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3009 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3010 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3011 |
|
| 3012 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3013 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>For a |
| 3014 |
given field of F, (1.1.12) must be inverted for <i style='mso-bidi-font-style: |
| 3015 |
normal'>p</i> subject to appropriate choice of boundary conditions.<span |
| 3016 |
style="mso-spacerun: yes"> </span>This method is usually called <i |
| 3017 |
style='mso-bidi-font-style:normal'>The Pressure Method</i><span |
| 3018 |
style="mso-spacerun: yes"> </span>[Harlow and Welch, 1965; Williams, 1969; |
| 3019 |
Potter, 1976]. In the hydrostatic primitive equations case (<b |
| 3020 |
style='mso-bidi-font-weight:normal'>HPE),</b> the 3-d problem, (1.1.12), |
| 3021 |
degenerates in to a 2-d inversion:- see section 1.5.<o:p></o:p></span></span></p> |
| 3022 |
|
| 3023 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3024 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3025 |
|
| 3026 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3027 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3028 |
|
| 3029 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078221"></a><a |
| 3030 |
name="_Toc407090375"></a><a name="_Toc407090578"></a><a name="_Toc407169607"><span |
| 3031 |
style='mso-bookmark:_Toc407090578'><span style='mso-bookmark:_Toc407090375'><span |
| 3032 |
style='mso-bookmark:_Toc407078221'>1.2 Boundary conditions</span></span></span></a></span></h2> |
| 3033 |
|
| 3034 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 3035 |
|
| 3036 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3037 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 3038 |
configuration of the ocean basin is defined by its depth <i style='mso-bidi-font-style: |
| 3039 |
normal'>H</i>(</span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3040 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3041 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3042 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3043 |
mso-symbol-font-family:Symbol'>l</span></span></span><span style='mso-bookmark: |
| 3044 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3045 |
font-family:Palatino'>,</span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3046 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3047 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3048 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3049 |
mso-symbol-font-family:Symbol'>f</span></span></span><span style='mso-bookmark: |
| 3050 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3051 |
font-family:Palatino'>) and allows arbitrary specification of the coastline, |
| 3052 |
bottom topography and connectedness - see Fig.1.<span style="mso-spacerun: |
| 3053 |
yes"> </span>We apply the condition of no normal flow through all solid |
| 3054 |
boundaries - the coasts and the bottom:<o:p></o:p></span></span></p> |
| 3055 |
|
| 3056 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3057 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3058 |
|
| 3059 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3060 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3061 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1044" |
| 3062 |
type="#_x0000_t75" style='width:36pt;height:14.25pt' o:ole=""> |
| 3063 |
<v:imagedata src="./fulldoc_files/image045.wmz" o:title=""/> |
| 3064 |
</v:shape><![endif]--><![if !vml]><img width=48 height=19 |
| 3065 |
src="./fulldoc_files/image046.gif" v:shapes="_x0000_i1044"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3066 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1044" |
| 3067 |
DrawAspect="Content" ObjectID="_1051901159"> |
| 3068 |
</o:OLEObject> |
| 3069 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 3070 |
style="mso-spacerun: |
| 3071 |
yes"> </span>(1.2.1)<o:p></o:p></span></span></p> |
| 3072 |
|
| 3073 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3074 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3075 |
|
| 3076 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3077 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <b |
| 3078 |
style='mso-bidi-font-weight:normal'>n</b> is a vector of unit length normal to |
| 3079 |
the boundary. The kinematic condition (1.2.1) is also applied to the vertical |
| 3080 |
velocity at the surface of the ocean in both free-surface and rigid-lid models. |
| 3081 |
No-slip (<sub><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" |
| 3082 |
style='width:35.25pt;height:15.75pt' o:ole=""> |
| 3083 |
<v:imagedata src="./fulldoc_files/image047.wmz" o:title=""/> |
| 3084 |
</v:shape><![endif]--><![if !vml]><img width=47 height=21 |
| 3085 |
src="./fulldoc_files/image048.gif" v:shapes="_x0000_i1045"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3086 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1045" |
| 3087 |
DrawAspect="Content" ObjectID="_1051901160"> |
| 3088 |
</o:OLEObject> |
| 3089 |
</xml><![endif]-->) or slip (<sub><!--[if gte vml 1]><v:shape id="_x0000_i1046" |
| 3090 |
type="#_x0000_t75" style='width:56.25pt;height:17.25pt' o:ole=""> |
| 3091 |
<v:imagedata src="./fulldoc_files/image049.wmz" o:title=""/> |
| 3092 |
</v:shape><![endif]--><![if !vml]><img width=75 height=23 |
| 3093 |
src="./fulldoc_files/image050.gif" v:shapes="_x0000_i1046"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3094 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1046" |
| 3095 |
DrawAspect="Content" ObjectID="_1051901161"> |
| 3096 |
</o:OLEObject> |
| 3097 |
</xml><![endif]-->) conditions are employed on the tangential component of |
| 3098 |
velocity <sub><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75" |
| 3099 |
style='width:14.25pt;height:17.25pt' o:ole="" fillcolor="window"> |
| 3100 |
<v:imagedata src="./fulldoc_files/image051.wmz" o:title=""/> |
| 3101 |
</v:shape><![endif]--><![if !vml]><img width=19 height=23 |
| 3102 |
src="./fulldoc_files/image052.gif" v:shapes="_x0000_i1047"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3103 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1047" |
| 3104 |
DrawAspect="Content" ObjectID="_1051901163"> |
| 3105 |
</o:OLEObject> |
| 3106 |
</xml><![endif]-->at all solid boundaries, depending on the form chosen for the |
| 3107 |
dissipative terms in the momentum equations - see section 1.7. <o:p></o:p></span></span></p> |
| 3108 |
|
| 3109 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3110 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3111 |
|
| 3112 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3113 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Eq.(1.2.1) |
| 3114 |
implies, making use of (1.1.1), that:<o:p></o:p></span></span></p> |
| 3115 |
|
| 3116 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3117 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3118 |
|
| 3119 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3120 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3121 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1048" |
| 3122 |
type="#_x0000_t75" style='width:63.75pt;height:17.25pt' o:ole=""> |
| 3123 |
<v:imagedata src="./fulldoc_files/image053.wmz" o:title=""/> |
| 3124 |
</v:shape><![endif]--><![if !vml]><img width=85 height=23 |
| 3125 |
src="./fulldoc_files/image054.gif" v:shapes="_x0000_i1048"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3126 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1048" |
| 3127 |
DrawAspect="Content" ObjectID="_1051901164"> |
| 3128 |
</o:OLEObject> |
| 3129 |
</xml><![endif]--><span style="mso-spacerun: |
| 3130 |
yes"> </span>(1.2.2)<o:p></o:p></span></span></p> |
| 3131 |
|
| 3132 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 3133 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3134 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3135 |
|
| 3136 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3137 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>presenting |
| 3138 |
<u>inhomogeneous</u> Neumann boundary conditions to the Elliptic problem |
| 3139 |
(1.1.12). As shown, for example, by Williams (1969), one can exploit classical |
| 3140 |
3D potential theory and, by introducing an appropriately chosen </span></span><span |
| 3141 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3142 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 3143 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 3144 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>d</span></span></span><span |
| 3145 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3146 |
10.0pt;font-family:Palatino'>-function sheet of source-charge, replace the |
| 3147 |
inhomogenous boundary condition on pressure by a homogeneous one. The source term |
| 3148 |
F in (1.1.12) is the divergence of the vector <sub><!--[if gte vml 1]><v:shape |
| 3149 |
id="_x0000_i1049" type="#_x0000_t75" style='width:18pt;height:17.25pt' o:ole=""> |
| 3150 |
<v:imagedata src="./fulldoc_files/image055.wmz" o:title=""/> |
| 3151 |
</v:shape><![endif]--><![if !vml]><img width=24 height=23 |
| 3152 |
src="./fulldoc_files/image056.gif" v:shapes="_x0000_i1049"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3153 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1049" |
| 3154 |
DrawAspect="Content" ObjectID="_1051901165"> |
| 3155 |
</o:OLEObject> |
| 3156 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>By simultaneously |
| 3157 |
setting <sub><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75" |
| 3158 |
style='width:48pt;height:17.25pt' o:ole=""> |
| 3159 |
<v:imagedata src="./fulldoc_files/image057.wmz" o:title=""/> |
| 3160 |
</v:shape><![endif]--><![if !vml]><img width=64 height=23 |
| 3161 |
src="./fulldoc_files/image058.gif" v:shapes="_x0000_i1050"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3162 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1050" |
| 3163 |
DrawAspect="Content" ObjectID="_1051901166"> |
| 3164 |
</o:OLEObject> |
| 3165 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and <sub><!--[if gte vml 1]><v:shape |
| 3166 |
id="_x0000_i1051" type="#_x0000_t75" style='width:45.75pt;height:15.75pt' |
| 3167 |
o:ole="" fillcolor="window"> |
| 3168 |
<v:imagedata src="./fulldoc_files/image059.wmz" o:title=""/> |
| 3169 |
</v:shape><![endif]--><![if !vml]><img width=61 height=21 |
| 3170 |
src="./fulldoc_files/image060.gif" v:shapes="_x0000_i1051"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3171 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051" |
| 3172 |
DrawAspect="Content" ObjectID="_1051901167"> |
| 3173 |
</o:OLEObject> |
| 3174 |
</xml><![endif]-->on the boundary the following self-consistent but simpler <u>homogenised</u> |
| 3175 |
Elliptic problem is obtained:<o:p></o:p></span></span></p> |
| 3176 |
|
| 3177 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3178 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3179 |
|
| 3180 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3181 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3182 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1052" |
| 3183 |
type="#_x0000_t75" style='width:84pt;height:20.25pt' o:ole=""> |
| 3184 |
<v:imagedata src="./fulldoc_files/image061.wmz" o:title=""/> |
| 3185 |
</v:shape><![endif]--><![if !vml]><img width=112 height=27 |
| 3186 |
src="./fulldoc_files/image062.gif" v:shapes="_x0000_i1052"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3187 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1052" |
| 3188 |
DrawAspect="Content" ObjectID="_1051901168"> |
| 3189 |
</o:OLEObject> |
| 3190 |
</xml><![endif]--><span style="mso-spacerun: |
| 3191 |
yes"> </span>(1.2.3)<o:p></o:p></span></span></p> |
| 3192 |
|
| 3193 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3194 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3195 |
|
| 3196 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3197 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where </span></span><span |
| 3198 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 3199 |
id="_x0000_i1053" type="#_x0000_t75" style='width:18pt;height:20.25pt' o:ole="" |
| 3200 |
fillcolor="window"> |
| 3201 |
<v:imagedata src="./fulldoc_files/image063.wmz" o:title=""/> |
| 3202 |
</v:shape><![endif]--><![if !vml]><img width=24 height=27 |
| 3203 |
src="./fulldoc_files/image064.gif" v:shapes="_x0000_i1053"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3204 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1053" |
| 3205 |
DrawAspect="Content" ObjectID="_1051901170"> |
| 3206 |
</o:OLEObject> |
| 3207 |
</xml><![endif]--></span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3208 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 3209 |
style="mso-spacerun: yes"> </span>is a modified </span></span><span |
| 3210 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 3211 |
id="_x0000_i1054" type="#_x0000_t75" style='width:18pt;height:17.25pt' o:ole=""> |
| 3212 |
<v:imagedata src="./fulldoc_files/image065.wmz" o:title=""/> |
| 3213 |
</v:shape><![endif]--><![if !vml]><img width=24 height=23 |
| 3214 |
src="./fulldoc_files/image066.gif" v:shapes="_x0000_i1054"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3215 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1054" |
| 3216 |
DrawAspect="Content" ObjectID="_1051901171"> |
| 3217 |
</o:OLEObject> |
| 3218 |
</xml><![endif]--></span></span><span style='mso-bookmark:_Toc407078231'><b |
| 3219 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3220 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> </span></span></b></span><span |
| 3221 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3222 |
10.0pt;font-family:Palatino'>such that </span></span><span style='mso-bookmark: |
| 3223 |
_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 3224 |
id="_x0000_i1055" type="#_x0000_t75" style='width:48.75pt;height:20.25pt' |
| 3225 |
o:ole="" fillcolor="window"> |
| 3226 |
<v:imagedata src="./fulldoc_files/image067.wmz" o:title=""/> |
| 3227 |
</v:shape><![endif]--><![if !vml]><img width=65 height=27 |
| 3228 |
src="./fulldoc_files/image068.gif" v:shapes="_x0000_i1055"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3229 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1055" |
| 3230 |
DrawAspect="Content" ObjectID="_1051901172"> |
| 3231 |
</o:OLEObject> |
| 3232 |
</xml><![endif]--></span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3233 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>.<span |
| 3234 |
style="mso-spacerun: yes"> </span>As is implied by (1.2.2) the modified |
| 3235 |
boundary condition becomes:<o:p></o:p></span></span></p> |
| 3236 |
|
| 3237 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3238 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3239 |
|
| 3240 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3241 |
_Toc407078231'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1056" type="#_x0000_t75" |
| 3242 |
style='width:45.75pt;height:15.75pt' o:ole="" fillcolor="window"> |
| 3243 |
<v:imagedata src="./fulldoc_files/image069.wmz" o:title=""/> |
| 3244 |
</v:shape><![endif]--><![if !vml]><img width=61 height=21 |
| 3245 |
src="./fulldoc_files/image070.gif" v:shapes="_x0000_i1056"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3246 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1056" |
| 3247 |
DrawAspect="Content" ObjectID="_1051901173"> |
| 3248 |
</o:OLEObject> |
| 3249 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 3250 |
style="mso-spacerun: |
| 3251 |
yes"> </span></span><span |
| 3252 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3253 |
10.0pt;font-family:Palatino'>(1.2.4)</span></span></p> |
| 3254 |
|
| 3255 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3256 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino; |
| 3257 |
text-transform:uppercase'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3258 |
|
| 3259 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3260 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>At the |
| 3261 |
ocean bottom and side the diffusive flux of heat and salt is set to zero:<o:p></o:p></span></span></p> |
| 3262 |
|
| 3263 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3264 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3265 |
|
| 3266 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3267 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3268 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1057" |
| 3269 |
type="#_x0000_t75" style='width:81pt;height:30.75pt' o:ole=""> |
| 3270 |
<v:imagedata src="./fulldoc_files/image071.wmz" o:title=""/> |
| 3271 |
</v:shape><![endif]--><![if !vml]><img width=108 height=41 |
| 3272 |
src="./fulldoc_files/image072.gif" v:shapes="_x0000_i1057"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3273 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1057" |
| 3274 |
DrawAspect="Content" ObjectID="_1051901175"> |
| 3275 |
</o:OLEObject> |
| 3276 |
</xml><![endif]--><span style="mso-spacerun: |
| 3277 |
yes"> </span>(1.2.5)<o:p></o:p></span></span></p> |
| 3278 |
|
| 3279 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3280 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3281 |
|
| 3282 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3283 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 3284 |
id="_x0000_i1792" type="#_x0000_t75" style='width:17.25pt;height:17.25pt' |
| 3285 |
o:ole=""> |
| 3286 |
<v:imagedata src="./fulldoc_files/image073.wmz" o:title=""/> |
| 3287 |
</v:shape><![endif]--><![if !vml]><img width=23 height=23 |
| 3288 |
src="./fulldoc_files/image074.gif" v:shapes="_x0000_i1792"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3289 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1792" |
| 3290 |
DrawAspect="Content" ObjectID="_1051901176"> |
| 3291 |
</o:OLEObject> |
| 3292 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is a diffusion |
| 3293 |
coefficient normal to the boundary.<o:p></o:p></span></span></p> |
| 3294 |
|
| 3295 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3296 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3297 |
|
| 3298 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3299 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3300 |
10.0pt;font-family:Palatino'>Include Fig.1 here: schematic diagram of an ocean |
| 3301 |
basin showing the irregular geometry: coastlines and islands.<o:p></o:p></span></b></span></p> |
| 3302 |
|
| 3303 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078222"></a><a |
| 3304 |
name="_Toc407090376"></a><a name="_Toc407090579"></a><a name="_Toc407169608"><span |
| 3305 |
style='mso-bookmark:_Toc407090579'><span style='mso-bookmark:_Toc407090376'><span |
| 3306 |
style='mso-bookmark:_Toc407078222'>1.3 Coordinate systems</span></span></span></a></span></h2> |
| 3307 |
|
| 3308 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3309 |
style='font-size:11.0pt;mso-bidi-font-size:10.0pt;font-family:Arial;mso-bidi-font-family: |
| 3310 |
"Times New Roman"'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3311 |
|
| 3312 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3313 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In this |
| 3314 |
section, the explicit expression of </span></span><span style='mso-bookmark: |
| 3315 |
_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 3316 |
id="_x0000_i1058" type="#_x0000_t75" style='width:18pt;height:17.25pt' o:ole=""> |
| 3317 |
<v:imagedata src="./fulldoc_files/image065.wmz" o:title=""/> |
| 3318 |
</v:shape><![endif]--><![if !vml]><img width=24 height=23 |
| 3319 |
src="./fulldoc_files/image075.gif" v:shapes="_x0000_i1058"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3320 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1058" |
| 3321 |
DrawAspect="Content" ObjectID="_1051901177"> |
| 3322 |
</o:OLEObject> |
| 3323 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span></span><span |
| 3324 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3325 |
10.0pt;font-family:Palatino'>in spherical coordinates is given. <i |
| 3326 |
style='mso-bidi-font-style:normal'>u</i>, <i style='mso-bidi-font-style:normal'>v</i>, |
| 3327 |
<i style='mso-bidi-font-style:normal'>w</i> the velocity components in the |
| 3328 |
zonal, meridional and vertical direction respectively, are given by (see Fig.2) |
| 3329 |
:</span></span><span style='mso-bookmark:_Toc407078231'><span style='font-size: |
| 3330 |
12.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></span></p> |
| 3331 |
|
| 3332 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3333 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3334 |
|
| 3335 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3336 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><sub><!--[if gte vml 1]><v:shape |
| 3337 |
id="_x0000_i1059" type="#_x0000_t75" style='width:72.75pt;height:95.25pt' |
| 3338 |
o:ole=""> |
| 3339 |
<v:imagedata src="./fulldoc_files/image076.wmz" o:title=""/> |
| 3340 |
</v:shape><![endif]--><![if !vml]><img width=97 height=127 |
| 3341 |
src="./fulldoc_files/image077.gif" v:shapes="_x0000_i1059"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3342 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1059" |
| 3343 |
DrawAspect="Content" ObjectID="_1051901178"> |
| 3344 |
</o:OLEObject> |
| 3345 |
</xml><![endif]--><span style="mso-spacerun: |
| 3346 |
yes"> </span>(1.3.1)<o:p></o:p></span></span></p> |
| 3347 |
|
| 3348 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3349 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3350 |
|
| 3351 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3352 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Here </span></span><span |
| 3353 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 3354 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3355 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3356 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3357 |
mso-symbol-font-family:Symbol'>f</span></span></i></span><span |
| 3358 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3359 |
10.0pt;font-family:Palatino'> is the latitude, </span></span><span |
| 3360 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 3361 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3362 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3363 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3364 |
mso-symbol-font-family:Symbol'>l</span></span></i></span><span |
| 3365 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3366 |
10.0pt;font-family:Palatino'> the longitude, <i style='mso-bidi-font-style: |
| 3367 |
normal'>r</i> the radial distance of the particle from the center of the earth, |
| 3368 |
</span></span><span style='mso-bookmark:_Toc407078231'><span style='font-size: |
| 3369 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino; |
| 3370 |
mso-hansi-font-family:Palatino;mso-char-type:symbol;mso-symbol-font-family: |
| 3371 |
Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>W</span></span></span><span |
| 3372 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3373 |
10.0pt;font-family:Palatino'> is the angular speed of rotation of the Earth and |
| 3374 |
<i style='mso-bidi-font-style:normal'>D/Dt</i> is the total derivative.<o:p></o:p></span></span></p> |
| 3375 |
|
| 3376 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3377 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3378 |
|
| 3379 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3380 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3381 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3382 |
|
| 3383 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3384 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3385 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3386 |
|
| 3387 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3388 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3389 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3390 |
|
| 3391 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3392 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3393 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3394 |
|
| 3395 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3396 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3397 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3398 |
|
| 3399 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3400 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3401 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3402 |
|
| 3403 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3404 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3405 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3406 |
|
| 3407 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3408 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3409 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3410 |
|
| 3411 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3412 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3413 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3414 |
|
| 3415 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3416 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3417 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3418 |
|
| 3419 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3420 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3421 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3422 |
|
| 3423 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3424 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3425 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3426 |
|
| 3427 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3428 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3429 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3430 |
|
| 3431 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3432 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3433 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3434 |
|
| 3435 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3436 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3437 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3438 |
|
| 3439 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3440 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3441 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3442 |
|
| 3443 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 3444 |
style='mso-bookmark:_Toc407078231'><b style='mso-bidi-font-weight:normal'><span |
| 3445 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Include |
| 3446 |
Fig.2 here<o:p></o:p></span></b></span></p> |
| 3447 |
|
| 3448 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3449 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3450 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3451 |
|
| 3452 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3453 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3454 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3455 |
|
| 3456 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3457 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3458 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3459 |
|
| 3460 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3461 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3462 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3463 |
|
| 3464 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3465 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3466 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3467 |
|
| 3468 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3469 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3470 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3471 |
|
| 3472 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3473 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3474 |
10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></span></p> |
| 3475 |
|
| 3476 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><b |
| 3477 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 3478 |
10.0pt'>Fig.2.</span></b></span><span style='mso-bookmark:_Toc407078231'><span |
| 3479 |
style='font-size:9.0pt;mso-bidi-font-size:10.0pt'> </span></span><span |
| 3480 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3481 |
10.0pt;font-family:Palatino'>The spherical polar velocities (<i |
| 3482 |
style='mso-bidi-font-style:normal'>u</i>,<i style='mso-bidi-font-style:normal'>v</i>,<i |
| 3483 |
style='mso-bidi-font-style:normal'>w</i>), the latitude is </span></span><span |
| 3484 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 3485 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3486 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3487 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3488 |
mso-symbol-font-family:Symbol'>f</span></span></i></span><span |
| 3489 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3490 |
10.0pt;font-family:Palatino'> and the longitude </span></span><span |
| 3491 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 3492 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3493 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3494 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3495 |
mso-symbol-font-family:Symbol'>l</span></span></i></span><span |
| 3496 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3497 |
10.0pt;font-family:Palatino'>.<o:p></o:p></span></span></p> |
| 3498 |
|
| 3499 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3500 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3501 |
|
| 3502 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3503 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 3504 |
id="_x0000_i1060" type="#_x0000_t75" style='width:87.75pt;height:20.25pt' |
| 3505 |
o:ole=""> |
| 3506 |
<v:imagedata src="./fulldoc_files/image078.wmz" o:title=""/> |
| 3507 |
</v:shape><![endif]--><![if !vml]><img width=117 height=27 |
| 3508 |
src="./fulldoc_files/image079.gif" v:shapes="_x0000_i1060"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3509 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1060" |
| 3510 |
DrawAspect="Content" ObjectID="_1051901179"> |
| 3511 |
</o:OLEObject> |
| 3512 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are inertial, |
| 3513 |
Coriolis, metric, gravitational, and forcing/ dissipation terms in the zonal, |
| 3514 |
meridional and vertical directions defined by</span></span><a style='mso-footnote-id: |
| 3515 |
ftn1' href="#_ftn1" name="_ftnref1" title=""><span style='mso-bookmark:_Toc407078231'><span |
| 3516 |
class=MsoFootnoteReference><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3517 |
10.0pt;font-family:Palatino'><span style='mso-special-character:footnote'><![if !supportFootnotes]>[1]<![endif]></span></span></span></span></a><span |
| 3518 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3519 |
10.0pt;font-family:Palatino'>:<o:p></o:p></span></span></p> |
| 3520 |
|
| 3521 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3522 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3523 |
|
| 3524 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3525 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3526 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1061" |
| 3527 |
type="#_x0000_t75" style='width:275.25pt;height:108pt' o:ole="" fillcolor="window"> |
| 3528 |
<v:imagedata src="./fulldoc_files/image080.wmz" o:title=""/> |
| 3529 |
</v:shape><![endif]--><![if !vml]><img width=367 height=144 |
| 3530 |
src="./fulldoc_files/image081.gif" v:shapes="_x0000_i1061"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3531 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1061" |
| 3532 |
DrawAspect="Content" ObjectID="_1051901181"> |
| 3533 |
</o:OLEObject> |
| 3534 |
</xml><![endif]--><sub><!--[if gte vml 1]><v:shape id="_x0000_i1062" type="#_x0000_t75" |
| 3535 |
style='width:9pt;height:15.75pt' o:ole=""> |
| 3536 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 3537 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 3538 |
src="./fulldoc_files/image083.gif" v:shapes="_x0000_i1062"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3539 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1062" |
| 3540 |
DrawAspect="Content" ObjectID="_1051901182"> |
| 3541 |
</o:OLEObject> |
| 3542 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>(1.3.2)<o:p></o:p></span></span></p> |
| 3543 |
|
| 3544 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3545 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3546 |
|
| 3547 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3548 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3549 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1793" |
| 3550 |
type="#_x0000_t75" style='width:159.75pt;height:93.75pt' o:ole="" fillcolor="window"> |
| 3551 |
<v:imagedata src="./fulldoc_files/image084.wmz" o:title=""/> |
| 3552 |
</v:shape><![endif]--><![if !vml]><img width=213 height=125 |
| 3553 |
src="./fulldoc_files/image085.gif" v:shapes="_x0000_i1793"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3554 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1793" |
| 3555 |
DrawAspect="Content" ObjectID="_1051901183"> |
| 3556 |
</o:OLEObject> |
| 3557 |
</xml><![endif]--><sub><!--[if gte vml 1]><v:shape id="_x0000_i1794" type="#_x0000_t75" |
| 3558 |
style='width:9pt;height:15.75pt' o:ole=""> |
| 3559 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 3560 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 3561 |
src="./fulldoc_files/image086.gif" v:shapes="_x0000_i1794"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3562 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1794" |
| 3563 |
DrawAspect="Content" ObjectID="_1051901184"> |
| 3564 |
</o:OLEObject> |
| 3565 |
</xml><![endif]--><span style="mso-spacerun: |
| 3566 |
yes"> </span>(1.3.3)<o:p></o:p></span></span></p> |
| 3567 |
|
| 3568 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3569 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3570 |
|
| 3571 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3572 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3573 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1795" |
| 3574 |
type="#_x0000_t75" style='width:191.25pt;height:141.75pt' o:ole="" |
| 3575 |
fillcolor="window"> |
| 3576 |
<v:imagedata src="./fulldoc_files/image087.wmz" o:title=""/> |
| 3577 |
</v:shape><![endif]--><![if !vml]><img width=255 height=189 |
| 3578 |
src="./fulldoc_files/image088.gif" v:shapes="_x0000_i1795"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3579 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1795" |
| 3580 |
DrawAspect="Content" ObjectID="_1051901186"> |
| 3581 |
</o:OLEObject> |
| 3582 |
</xml><![endif]--><sub><!--[if gte vml 1]><v:shape id="_x0000_i1796" type="#_x0000_t75" |
| 3583 |
style='width:9pt;height:15.75pt' o:ole=""> |
| 3584 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 3585 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 3586 |
src="./fulldoc_files/image089.gif" v:shapes="_x0000_i1796"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3587 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1796" |
| 3588 |
DrawAspect="Content" ObjectID="_1051901187"> |
| 3589 |
</o:OLEObject> |
| 3590 |
</xml><![endif]--><span style="mso-spacerun: |
| 3591 |
yes"> </span>(1.3.4)<o:p></o:p></span></span></p> |
| 3592 |
|
| 3593 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3594 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3595 |
|
| 3596 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3597 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 3598 |
id="_x0000_i1797" type="#_x0000_t75" style='width:17.25pt;height:18pt' o:ole="" |
| 3599 |
fillcolor="window"> |
| 3600 |
<v:imagedata src="./fulldoc_files/image090.wmz" o:title=""/> |
| 3601 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 3602 |
src="./fulldoc_files/image091.gif" v:shapes="_x0000_i1797"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3603 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1797" |
| 3604 |
DrawAspect="Content" ObjectID="_1051901188"> |
| 3605 |
</o:OLEObject> |
| 3606 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are non-conservative |
| 3607 |
forces acting on the fluid.<span style="mso-spacerun: yes"> </span>The precise |
| 3608 |
forms of the <sub><!--[if gte vml 1]><v:shape id="_x0000_i1798" type="#_x0000_t75" |
| 3609 |
style='width:17.25pt;height:18pt' o:ole="" fillcolor="window"> |
| 3610 |
<v:imagedata src="./fulldoc_files/image092.wmz" o:title=""/> |
| 3611 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 3612 |
src="./fulldoc_files/image093.gif" v:shapes="_x0000_i1798"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3613 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1798" |
| 3614 |
DrawAspect="Content" ObjectID="_1051901189"> |
| 3615 |
</o:OLEObject> |
| 3616 |
</xml><![endif]-->s which are available in the model are described in section |
| 3617 |
1.7.<o:p></o:p></span></span></p> |
| 3618 |
|
| 3619 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3620 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3621 |
|
| 3622 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3623 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 3624 |
tendency of the temperature and salt are given by:<o:p></o:p></span></span></p> |
| 3625 |
|
| 3626 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3627 |
style='font-size:9.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3628 |
|
| 3629 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3630 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3631 |
|
| 3632 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3633 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3634 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1799" |
| 3635 |
type="#_x0000_t75" style='width:75.75pt;height:36pt' o:ole="" fillcolor="window"> |
| 3636 |
<v:imagedata src="./fulldoc_files/image094.wmz" o:title=""/> |
| 3637 |
</v:shape><![endif]--><![if !vml]><img width=101 height=48 |
| 3638 |
src="./fulldoc_files/image095.gif" v:shapes="_x0000_i1799"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3639 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1799" |
| 3640 |
DrawAspect="Content" ObjectID="_1051901191"> |
| 3641 |
</o:OLEObject> |
| 3642 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 3643 |
style="mso-spacerun: |
| 3644 |
yes"> </span>(1.3.5)<o:p></o:p></span></span></p> |
| 3645 |
|
| 3646 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3647 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3648 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3649 |
|
| 3650 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3651 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3652 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1800" |
| 3653 |
type="#_x0000_t75" style='width:75pt;height:36pt' o:ole="" fillcolor="window"> |
| 3654 |
<v:imagedata src="./fulldoc_files/image096.wmz" o:title=""/> |
| 3655 |
</v:shape><![endif]--><![if !vml]><img width=100 height=48 |
| 3656 |
src="./fulldoc_files/image097.gif" v:shapes="_x0000_i1800"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3657 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1800" |
| 3658 |
DrawAspect="Content" ObjectID="_1051901192"> |
| 3659 |
</o:OLEObject> |
| 3660 |
</xml><![endif]--><span style="mso-spacerun: |
| 3661 |
yes"> </span>(1.3.6)<o:p></o:p></span></span></p> |
| 3662 |
|
| 3663 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3664 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3665 |
|
| 3666 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3667 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where </span></span><span |
| 3668 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 3669 |
id="_x0000_i1801" type="#_x0000_t75" style='width:15pt;height:15.75pt' o:ole=""> |
| 3670 |
<v:imagedata src="./fulldoc_files/image035.wmz" o:title=""/> |
| 3671 |
</v:shape><![endif]--><![if !vml]><img width=20 height=21 |
| 3672 |
src="./fulldoc_files/image098.gif" v:shapes="_x0000_i1801"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3673 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1801" |
| 3674 |
DrawAspect="Content" ObjectID="_1051901193"> |
| 3675 |
</o:OLEObject> |
| 3676 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1802" type="#_x0000_t75" |
| 3677 |
style='width:14.25pt;height:17.25pt' o:ole=""> |
| 3678 |
<v:imagedata src="./fulldoc_files/image037.wmz" o:title=""/> |
| 3679 |
</v:shape><![endif]--><![if !vml]><img width=19 height=23 |
| 3680 |
src="./fulldoc_files/image099.gif" v:shapes="_x0000_i1802"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3681 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1802" |
| 3682 |
DrawAspect="Content" ObjectID="_1051901194"> |
| 3683 |
</o:OLEObject> |
| 3684 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1803" type="#_x0000_t75" |
| 3685 |
style='width:18pt;height:17.25pt' o:ole="" fillcolor="window"> |
| 3686 |
<v:imagedata src="./fulldoc_files/image039.wmz" o:title=""/> |
| 3687 |
</v:shape><![endif]--><![if !vml]><img width=24 height=23 |
| 3688 |
src="./fulldoc_files/image100.gif" v:shapes="_x0000_i1803"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3689 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1803" |
| 3690 |
DrawAspect="Content" ObjectID="_1051901195"> |
| 3691 |
</o:OLEObject> |
| 3692 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1804" type="#_x0000_t75" |
| 3693 |
style='width:17.25pt;height:18pt' o:ole="" fillcolor="window"> |
| 3694 |
<v:imagedata src="./fulldoc_files/image041.wmz" o:title=""/> |
| 3695 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 3696 |
src="./fulldoc_files/image101.gif" v:shapes="_x0000_i1804"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3697 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1804" |
| 3698 |
DrawAspect="Content" ObjectID="_1051901197"> |
| 3699 |
</o:OLEObject> |
| 3700 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span></span><span |
| 3701 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3702 |
10.0pt;font-family:Palatino'>are the forcing/dissipation terms in the T and S |
| 3703 |
equations respectively; they are described in section 1.7.<o:p></o:p></span></span></p> |
| 3704 |
|
| 3705 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3706 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3707 |
|
| 3708 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3709 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In the |
| 3710 |
above the grad (</span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3711 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3712 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3713 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3714 |
mso-symbol-font-family:Symbol'>Ñ</span></span></span><span style='mso-bookmark: |
| 3715 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3716 |
font-family:Palatino'>) and div (</span></span><span style='mso-bookmark: |
| 3717 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3718 |
font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 3719 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 3720 |
symbol;mso-symbol-font-family:Symbol'>Ñ</span></span></span><span |
| 3721 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3722 |
10.0pt;font-family:Palatino'>.) operators are defined by, in spherical |
| 3723 |
coordinates:<o:p></o:p></span></span></p> |
| 3724 |
|
| 3725 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3726 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3727 |
|
| 3728 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3729 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3730 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1805" |
| 3731 |
type="#_x0000_t75" style='width:135pt;height:36pt' o:ole="" fillcolor="window"> |
| 3732 |
<v:imagedata src="./fulldoc_files/image102.wmz" o:title=""/> |
| 3733 |
</v:shape><![endif]--><![if !vml]><img width=180 height=48 |
| 3734 |
src="./fulldoc_files/image103.gif" v:shapes="_x0000_i1805"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3735 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1805" |
| 3736 |
DrawAspect="Content" ObjectID="_1051901198"> |
| 3737 |
</o:OLEObject> |
| 3738 |
</xml><![endif]--><span style="mso-spacerun: |
| 3739 |
yes"> </span>(1.3.7)<o:p></o:p></span></span></p> |
| 3740 |
|
| 3741 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3742 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3743 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3744 |
|
| 3745 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3746 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3747 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1806" |
| 3748 |
type="#_x0000_t75" style='width:230.25pt;height:36.75pt' o:ole=""> |
| 3749 |
<v:imagedata src="./fulldoc_files/image104.wmz" o:title=""/> |
| 3750 |
</v:shape><![endif]--><![if !vml]><img width=307 height=49 |
| 3751 |
src="./fulldoc_files/image105.gif" v:shapes="_x0000_i1806"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3752 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1806" |
| 3753 |
DrawAspect="Content" ObjectID="_1051901199"> |
| 3754 |
</o:OLEObject> |
| 3755 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 3756 |
</span>(1.3.8)<o:p></o:p></span></span></p> |
| 3757 |
|
| 3758 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3759 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3760 |
|
| 3761 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3762 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>A |
| 3763 |
consistent Cartesian version of the model can also readily be posed - it does |
| 3764 |
not carry metric terms and cos</span></span><span style='mso-bookmark:_Toc407078231'><i |
| 3765 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3766 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 3767 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 3768 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>f</span></span></i></span><span |
| 3769 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3770 |
10.0pt;font-family:Palatino'> Coriolis terms - see Appendix.<o:p></o:p></span></span></p> |
| 3771 |
|
| 3772 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3773 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino; |
| 3774 |
text-transform:uppercase'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3775 |
|
| 3776 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3777 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino; |
| 3778 |
text-transform:uppercase'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3779 |
|
| 3780 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078223"></a><a |
| 3781 |
name="_Toc407090377"></a><a name="_Toc407090580"></a><a name="_Toc407169609"><span |
| 3782 |
style='mso-bookmark:_Toc407090580'><span style='mso-bookmark:_Toc407090377'><span |
| 3783 |
style='mso-bookmark:_Toc407078223'>1.4 Hydrostatic, non-hydrostatic and |
| 3784 |
quasi-hydrostatic forms</span></span></span></a></span></h2> |
| 3785 |
|
| 3786 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3787 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3788 |
|
| 3789 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3790 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In the |
| 3791 |
non-hydrostatic model all terms in equations (1.3.2 </span></span><span |
| 3792 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3793 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 3794 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 3795 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>®</span></span></span><span |
| 3796 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3797 |
10.0pt;font-family:Palatino'> 1.3.4) are retained.<span style="mso-spacerun: |
| 3798 |
yes"> </span>A three dimensional elliptic equation (1.2.3) must be solved with |
| 3799 |
boundary conditions (1.2.4).<span style="mso-spacerun: yes"> </span>It is |
| 3800 |
important to note that use of the full <b style='mso-bidi-font-weight:normal'>NH</b> |
| 3801 |
does not admit any new fast waves in to the system - the incompressible |
| 3802 |
condition (1.1.2) has already filtered out acoustic modes.<span |
| 3803 |
style="mso-spacerun: yes"> </span>It does, however, ensure that the gravity |
| 3804 |
waves are treated accurately with an exact dispersion relation.<o:p></o:p></span></span></p> |
| 3805 |
|
| 3806 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3807 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3808 |
|
| 3809 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3810 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3811 |
|
| 3812 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 3813 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3814 |
10.0pt;font-family:Palatino'>NH</span></b></span><span style='mso-bookmark: |
| 3815 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3816 |
font-family:Palatino'> has the following energy equation:<o:p></o:p></span></span></p> |
| 3817 |
|
| 3818 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3819 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3820 |
|
| 3821 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 3822 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3823 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1807" |
| 3824 |
type="#_x0000_t75" style='width:234pt;height:32.25pt' o:ole=""> |
| 3825 |
<v:imagedata src="./fulldoc_files/image106.wmz" o:title=""/> |
| 3826 |
</v:shape><![endif]--><![if !vml]><img width=312 height=43 |
| 3827 |
src="./fulldoc_files/image107.gif" v:shapes="_x0000_i1807"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3828 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1807" |
| 3829 |
DrawAspect="Content" ObjectID="_1051901201"> |
| 3830 |
</o:OLEObject> |
| 3831 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 3832 |
</span>(1.4.1)<o:p></o:p></span></span></p> |
| 3833 |
|
| 3834 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3835 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3836 |
|
| 3837 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3838 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 3839 |
id="_x0000_i1808" type="#_x0000_t75" style='width:59.25pt;height:15.75pt' |
| 3840 |
o:ole=""> |
| 3841 |
<v:imagedata src="./fulldoc_files/image108.wmz" o:title=""/> |
| 3842 |
</v:shape><![endif]--><![if !vml]><img width=79 height=21 |
| 3843 |
src="./fulldoc_files/image109.gif" v:shapes="_x0000_i1808"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3844 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1808" |
| 3845 |
DrawAspect="Content" ObjectID="_1051901202"> |
| 3846 |
</o:OLEObject> |
| 3847 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the |
| 3848 |
three-dimensional velocity vector, <i style='mso-bidi-font-style:normal'>Q</i> |
| 3849 |
is the buoyancy forcing, <b style='mso-bidi-font-weight:normal'>F</b> |
| 3850 |
represents the forcing/dissipation terms in the momentum equations, and <sub><!--[if gte vml 1]><v:shape |
| 3851 |
id="_x0000_i1809" type="#_x0000_t75" style='width:45pt;height:35.25pt' o:ole=""> |
| 3852 |
<v:imagedata src="./fulldoc_files/image110.wmz" o:title=""/> |
| 3853 |
</v:shape><![endif]--><![if !vml]><img width=60 height=47 |
| 3854 |
src="./fulldoc_files/image111.gif" v:shapes="_x0000_i1809"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3855 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1809" |
| 3856 |
DrawAspect="Content" ObjectID="_1051901203"> |
| 3857 |
</o:OLEObject> |
| 3858 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>Note that the |
| 3859 |
pressure work term </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3860 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1810" |
| 3861 |
type="#_x0000_t75" style='width:36.75pt;height:15.75pt' o:ole=""> |
| 3862 |
<v:imagedata src="./fulldoc_files/image112.wmz" o:title=""/> |
| 3863 |
</v:shape><![endif]--><![if !vml]><img width=49 height=21 |
| 3864 |
src="./fulldoc_files/image113.gif" v:shapes="_x0000_i1810"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3865 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1810" |
| 3866 |
DrawAspect="Content" ObjectID="_1051901204"> |
| 3867 |
</o:OLEObject> |
| 3868 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span></span><span |
| 3869 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3870 |
10.0pt;font-family:Palatino'>vanishes when integrated over the ocean basin if |
| 3871 |
all bounding surfaces, including the upper one, are assumed rigid. <b |
| 3872 |
style='mso-bidi-font-weight:normal'>NH</b> has a complete angular momentum |
| 3873 |
principle - see White and Bromley, 1995; Marshall et.al.1997a.<span |
| 3874 |
style='text-transform:uppercase'><o:p></o:p></span></span></span></p> |
| 3875 |
|
| 3876 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3877 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3878 |
|
| 3879 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3880 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In <b |
| 3881 |
style='mso-bidi-font-weight:normal'>HPE</b> all the underlined terms in Eqs. |
| 3882 |
(1.3.2 </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3883 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3884 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3885 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3886 |
mso-symbol-font-family:Symbol'>®</span></span></span><span style='mso-bookmark: |
| 3887 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 3888 |
font-family:Palatino'> 1.3.4) are neglected and <i style='mso-bidi-font-style: |
| 3889 |
normal'>r</i> is replaced by <i style='mso-bidi-font-style:normal'>a</i>, |
| 3890 |
the mean radius of the earth.<span style="mso-spacerun: yes"> </span>The 3-d |
| 3891 |
Elliptic problem reduces to a 2-dimensional one since once the pressure is |
| 3892 |
known at one level (we choose this level to be the surface) then it can be |
| 3893 |
computed at all other levels from the hydrostatic relation.<span |
| 3894 |
style="mso-spacerun: yes"> </span>An energy equation analogous to (1.4.1) is |
| 3895 |
obtained except that the contribution of<sub><!--[if gte vml 1]><v:shape id="_x0000_i1811" |
| 3896 |
type="#_x0000_t75" style='width:17.25pt;height:15.75pt' o:ole=""> |
| 3897 |
<v:imagedata src="./fulldoc_files/image114.wmz" o:title=""/> |
| 3898 |
</v:shape><![endif]--><![if !vml]><img width=23 height=21 |
| 3899 |
src="./fulldoc_files/image115.gif" v:shapes="_x0000_i1811"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3900 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1811" |
| 3901 |
DrawAspect="Content" ObjectID="_1051901206"> |
| 3902 |
</o:OLEObject> |
| 3903 |
</xml><![endif]-->to the kinetic energy is absent and, on the rhs, only the |
| 3904 |
horizontal components of the frictional forces do work. In <b style='mso-bidi-font-weight: |
| 3905 |
normal'>QH</b> only the terms underlined twice in Eqs. (1.3.2 </span></span><span |
| 3906 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3907 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 3908 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 3909 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>®</span></span></span><span |
| 3910 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3911 |
10.0pt;font-family:Palatino'> 1.3.4) are neglected and, simultaneously, the |
| 3912 |
shallow atmosphere approximation is relaxed.<span style="mso-spacerun: yes"> |
| 3913 |
</span>Thus <u>all</u> the metric terms must be retained and the full variation |
| 3914 |
of the radial position of a particle monitored. <b style='mso-bidi-font-weight: |
| 3915 |
normal'>QH</b> has good energetic credentials - they are the same as for <b |
| 3916 |
style='mso-bidi-font-weight:normal'>HPE</b>.<span style="mso-spacerun: yes"> |
| 3917 |
</span>Importantly, however, it has the same angular momentum principle as <b |
| 3918 |
style='mso-bidi-font-weight:normal'>NH</b> - see Marshall et.al., 1997a. Again |
| 3919 |
in <b style='mso-bidi-font-weight:normal'>QH</b>, the 3-d elliptic problem is |
| 3920 |
reduced to a 2-d one.<span style="mso-spacerun: yes"> </span>Strict balance |
| 3921 |
between gravity and vertical pressure gradients is not imposed, however, since |
| 3922 |
the 2</span></span><span style='mso-bookmark:_Toc407078231'><span |
| 3923 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 3924 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 3925 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 3926 |
mso-symbol-font-family:Symbol'>W</span></span></span><span style='mso-bookmark: |
| 3927 |
_Toc407078231'><i style='mso-bidi-font-style:normal'><span style='font-size: |
| 3928 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>u</span></i></span><span |
| 3929 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3930 |
10.0pt;font-family:Palatino'>cos</span></span><span style='mso-bookmark:_Toc407078231'><i |
| 3931 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3932 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 3933 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 3934 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>f</span></span></i></span><span |
| 3935 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3936 |
10.0pt;font-family:Palatino'> Coriolis term plays a role in balancing <i |
| 3937 |
style='mso-bidi-font-style:normal'>g</i> in (1.3.4).<o:p></o:p></span></span></p> |
| 3938 |
|
| 3939 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3940 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3941 |
|
| 3942 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3943 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3944 |
|
| 3945 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078224"></a><a |
| 3946 |
name="_Toc407090378"></a><a name="_Toc407090581"></a><a name="_Toc407169610"><span |
| 3947 |
style='mso-bookmark:_Toc407090581'><span style='mso-bookmark:_Toc407090378'><span |
| 3948 |
style='mso-bookmark:_Toc407078224'>1.5 Finding the pressure field</span></span></span></a></span></h2> |
| 3949 |
|
| 3950 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3951 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3952 |
|
| 3953 |
<h3><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078225"></a><a |
| 3954 |
name="_Toc407090379"></a><a name="_Toc407090582"></a><a name="_Toc407169611"><span |
| 3955 |
style='mso-bookmark:_Toc407090582'><span style='mso-bookmark:_Toc407090379'><span |
| 3956 |
style='mso-bookmark:_Toc407078225'><u>1.5.1 Depth-averaged pressure</u></span></span></span></a><u><o:p></o:p></u></span></h3> |
| 3957 |
|
| 3958 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 3959 |
|
| 3960 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3961 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>If the |
| 3962 |
ocean had a flat bottom, then (1.2.3) could readily be solved by projecting <i |
| 3963 |
style='mso-bidi-font-style:normal'>p</i> on to the eigenfunctions of the <sub><!--[if gte vml 1]><v:shape |
| 3964 |
id="_x0000_i1812" type="#_x0000_t75" style='width:17.25pt;height:15.75pt' |
| 3965 |
o:ole="" fillcolor="window"> |
| 3966 |
<v:imagedata src="./fulldoc_files/image116.wmz" o:title=""/> |
| 3967 |
</v:shape><![endif]--><![if !vml]><img width=23 height=21 |
| 3968 |
src="./fulldoc_files/image117.gif" v:shapes="_x0000_i1812"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3969 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1812" |
| 3970 |
DrawAspect="Content" ObjectID="_1051901208"> |
| 3971 |
</o:OLEObject> |
| 3972 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>operator with |
| 3973 |
boundary condition (1.2.4) applied at the (flat) upper and lower boundaries (see |
| 3974 |
Marshall et al., 1997a). Here such a modal approach can not be employed because |
| 3975 |
the geometry can be as complex as that of an ocean basin. However, the modal |
| 3976 |
approach points to the advantage of separating out, as far as is possible, the |
| 3977 |
depth-averaged pressure field.<o:p></o:p></span></span></p> |
| 3978 |
|
| 3979 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 3980 |
style='font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 3981 |
|
| 3982 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 3983 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>For an |
| 3984 |
arbitrary function </span></span><span style='mso-bookmark:_Toc407078231'><i |
| 3985 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3986 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 3987 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 3988 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>y</span></span></i></span><span |
| 3989 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 3990 |
10.0pt;font-family:Palatino'> we can define its vertical average <sub><!--[if gte vml 1]><v:shape |
| 3991 |
id="_x0000_i1813" type="#_x0000_t75" style='width:20.25pt;height:20.25pt' |
| 3992 |
o:ole=""> |
| 3993 |
<v:imagedata src="./fulldoc_files/image118.wmz" o:title=""/> |
| 3994 |
</v:shape><![endif]--><![if !vml]><img width=27 height=27 |
| 3995 |
src="./fulldoc_files/image119.gif" v:shapes="_x0000_i1813"><![endif]></sub><!--[if gte mso 9]><xml> |
| 3996 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1813" |
| 3997 |
DrawAspect="Content" ObjectID="_1051901209"> |
| 3998 |
</o:OLEObject> |
| 3999 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>as:<o:p></o:p></span></span></p> |
| 4000 |
|
| 4001 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4002 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4003 |
|
| 4004 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4005 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4006 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1814" |
| 4007 |
type="#_x0000_t75" style='width:111pt;height:36.75pt' o:ole=""> |
| 4008 |
<v:imagedata src="./fulldoc_files/image120.wmz" o:title=""/> |
| 4009 |
</v:shape><![endif]--><![if !vml]><img width=148 height=49 |
| 4010 |
src="./fulldoc_files/image121.gif" v:shapes="_x0000_i1814"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4011 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1814" |
| 4012 |
DrawAspect="Content" ObjectID="_1051901210"> |
| 4013 |
</o:OLEObject> |
| 4014 |
</xml><![endif]--><span style="mso-spacerun: |
| 4015 |
yes"> </span>(1.5.1)<o:p></o:p></span></span></p> |
| 4016 |
|
| 4017 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4018 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4019 |
|
| 4020 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4021 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <i |
| 4022 |
style='mso-bidi-font-style:normal'>H=H(</i></span></span><span |
| 4023 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 4024 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 4025 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 4026 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 4027 |
mso-symbol-font-family:Symbol'>l</span></span></i></span><span |
| 4028 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 4029 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>,</span></i></span><span |
| 4030 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 4031 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 4032 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 4033 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 4034 |
mso-symbol-font-family:Symbol'>f</span></span></i></span><span |
| 4035 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 4036 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>)</span></i></span><span |
| 4037 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4038 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> </span>is the |
| 4039 |
local depth.<o:p></o:p></span></span></p> |
| 4040 |
|
| 4041 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4042 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4043 |
|
| 4044 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4045 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 4046 |
vertically-averaged gradient operator is then:<o:p></o:p></span></span></p> |
| 4047 |
|
| 4048 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4049 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4050 |
|
| 4051 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4052 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4053 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1815" |
| 4054 |
type="#_x0000_t75" style='width:177.75pt;height:30.75pt' o:ole=""> |
| 4055 |
<v:imagedata src="./fulldoc_files/image122.wmz" o:title=""/> |
| 4056 |
</v:shape><![endif]--><![if !vml]><img width=237 height=41 |
| 4057 |
src="./fulldoc_files/image123.gif" v:shapes="_x0000_i1815"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4058 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1815" |
| 4059 |
DrawAspect="Content" ObjectID="_1051901212"> |
| 4060 |
</o:OLEObject> |
| 4061 |
</xml><![endif]--><span style="mso-spacerun: |
| 4062 |
yes"> </span>(1.5.2)<o:p></o:p></span></span></p> |
| 4063 |
|
| 4064 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4065 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4066 |
|
| 4067 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4068 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 4069 |
vertical integral of the horizontal component of (1.1.1) is then, using the |
| 4070 |
rule (1.5.2) :<o:p></o:p></span></span></p> |
| 4071 |
|
| 4072 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4073 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4074 |
|
| 4075 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4076 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4077 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1063" |
| 4078 |
type="#_x0000_t75" style='width:228pt;height:32.25pt' o:ole=""> |
| 4079 |
<v:imagedata src="./fulldoc_files/image124.wmz" o:title=""/> |
| 4080 |
</v:shape><![endif]--><![if !vml]><img width=304 height=43 |
| 4081 |
src="./fulldoc_files/image125.gif" v:shapes="_x0000_i1063"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4082 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1063" |
| 4083 |
DrawAspect="Content" ObjectID="_1051901213"> |
| 4084 |
</o:OLEObject> |
| 4085 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 4086 |
</span>(1.5.3)<o:p></o:p></span></span></p> |
| 4087 |
|
| 4088 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4089 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4090 |
|
| 4091 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4092 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Since |
| 4093 |
there can be no net convergence of mass over the water column, we have, |
| 4094 |
assuming a rigid lid at the surface (see next chapter and appendix for the free |
| 4095 |
surface case):<o:p></o:p></span></span></p> |
| 4096 |
|
| 4097 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4098 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4099 |
|
| 4100 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4101 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4102 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1064" |
| 4103 |
type="#_x0000_t75" style='width:78.75pt;height:18.75pt' o:ole=""> |
| 4104 |
<v:imagedata src="./fulldoc_files/image126.wmz" o:title=""/> |
| 4105 |
</v:shape><![endif]--><![if !vml]><img width=105 height=25 |
| 4106 |
src="./fulldoc_files/image127.gif" v:shapes="_x0000_i1064"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4107 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1064" |
| 4108 |
DrawAspect="Content" ObjectID="_1051901214"> |
| 4109 |
</o:OLEObject> |
| 4110 |
</xml><![endif]--><span style="mso-spacerun: |
| 4111 |
yes"> </span>(1.5.4)<o:p></o:p></span></span></p> |
| 4112 |
|
| 4113 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4114 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4115 |
|
| 4116 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4117 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>At this |
| 4118 |
point, and following Bryan (1969), ocean modelers often introduce a stream |
| 4119 |
function for the depth-averaged flow. However, as argued by Dukowicz et al. |
| 4120 |
(1993) (see also Marshall et al., 1997a), it is advantageous to couch the |
| 4121 |
inversion problem in terms of pressure rather than a stream function. Applying |
| 4122 |
the horizontal gradient operator to (1.5.3) and making use of (1.5.4), we |
| 4123 |
obtain our desired equation for the depth-averaged pressure:<o:p></o:p></span></span></p> |
| 4124 |
|
| 4125 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4126 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4127 |
|
| 4128 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4129 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4130 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1065" |
| 4131 |
type="#_x0000_t75" style='width:165pt;height:21.75pt' o:ole=""> |
| 4132 |
<v:imagedata src="./fulldoc_files/image128.wmz" o:title=""/> |
| 4133 |
</v:shape><![endif]--><![if !vml]><img width=220 height=29 |
| 4134 |
src="./fulldoc_files/image129.gif" v:shapes="_x0000_i1065"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4135 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1065" |
| 4136 |
DrawAspect="Content" ObjectID="_1051901216"> |
| 4137 |
</o:OLEObject> |
| 4138 |
</xml><![endif]--><span style="mso-spacerun: |
| 4139 |
yes"> </span>(1.5.5)<o:p></o:p></span></span></p> |
| 4140 |
|
| 4141 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4142 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4143 |
|
| 4144 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4145 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where<o:p></o:p></span></span></p> |
| 4146 |
|
| 4147 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4148 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4149 |
|
| 4150 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4151 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4152 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1066" |
| 4153 |
type="#_x0000_t75" style='width:108.75pt;height:20.25pt' o:ole=""> |
| 4154 |
<v:imagedata src="./fulldoc_files/image130.wmz" o:title=""/> |
| 4155 |
</v:shape><![endif]--><![if !vml]><img width=145 height=27 |
| 4156 |
src="./fulldoc_files/image131.gif" v:shapes="_x0000_i1066"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4157 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1066" |
| 4158 |
DrawAspect="Content" ObjectID="_1051901217"> |
| 4159 |
</o:OLEObject> |
| 4160 |
</xml><![endif]--><span style="mso-spacerun: |
| 4161 |
yes"> </span>(1.5.6)<o:p></o:p></span></span></p> |
| 4162 |
|
| 4163 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4164 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4165 |
|
| 4166 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4167 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>It is |
| 4168 |
now clear that if the ocean has a flat bottom (<i style='mso-bidi-font-style: |
| 4169 |
normal'>H</i>=constant) then <sub><!--[if gte vml 1]><v:shape id="_x0000_i1067" |
| 4170 |
type="#_x0000_t75" style='width:51pt;height:15.75pt' o:ole="" fillcolor="window"> |
| 4171 |
<v:imagedata src="./fulldoc_files/image132.wmz" o:title=""/> |
| 4172 |
</v:shape><![endif]--><![if !vml]><img width=68 height=21 |
| 4173 |
src="./fulldoc_files/image133.gif" v:shapes="_x0000_i1067"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4174 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1067" |
| 4175 |
DrawAspect="Content" ObjectID="_1051901218"> |
| 4176 |
</o:OLEObject> |
| 4177 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and equation (1.5.5) |
| 4178 |
does not have any pressure-dependent terms on the right-hand side and can be |
| 4179 |
solved unambiguously for <sub><!--[if gte vml 1]><v:shape id="_x0000_i1068" |
| 4180 |
type="#_x0000_t75" style='width:18pt;height:20.25pt' o:ole=""> |
| 4181 |
<v:imagedata src="./fulldoc_files/image134.wmz" o:title=""/> |
| 4182 |
</v:shape><![endif]--><![if !vml]><img width=24 height=27 |
| 4183 |
src="./fulldoc_files/image135.gif" v:shapes="_x0000_i1068"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4184 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1068" |
| 4185 |
DrawAspect="Content" ObjectID="_1051901219"> |
| 4186 |
</o:OLEObject> |
| 4187 |
</xml><![endif]-->. But if the depth of the basin varies from point to point |
| 4188 |
one cannot solve for the depth-averaged pressure without knowledge of <sub><!--[if gte vml 1]><v:shape |
| 4189 |
id="_x0000_i1069" type="#_x0000_t75" style='width:32.25pt;height:15.75pt' |
| 4190 |
o:ole="" fillcolor="window"> |
| 4191 |
<v:imagedata src="./fulldoc_files/image136.wmz" o:title=""/> |
| 4192 |
</v:shape><![endif]--><![if !vml]><img width=43 height=21 |
| 4193 |
src="./fulldoc_files/image137.gif" v:shapes="_x0000_i1069"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4194 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1069" |
| 4195 |
DrawAspect="Content" ObjectID="_1051901220"> |
| 4196 |
</o:OLEObject> |
| 4197 |
</xml><![endif]-->. We can, however, make progress by separating the pressure |
| 4198 |
field in to hydrostatic, non-hydrostatic and surface pressure parts.<o:p></o:p></span></span></p> |
| 4199 |
|
| 4200 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078231'><span |
| 4201 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4202 |
|
| 4203 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078231'><b |
| 4204 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4205 |
10.0pt;font-family:Palatino'>Add something about free-surface case here.<o:p></o:p></span></b></span></p> |
| 4206 |
|
| 4207 |
<h3><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078226"></a><a |
| 4208 |
name="_Toc407090380"></a><a name="_Toc407090583"></a><a name="_Toc407169612"><span |
| 4209 |
style='mso-bookmark:_Toc407090583'><span style='mso-bookmark:_Toc407090380'><span |
| 4210 |
style='mso-bookmark:_Toc407078226'><u>1.5.2 Surface, hydrostatic and |
| 4211 |
non-hydrostatic pressure</u></span></span></span></a><u><o:p></o:p></u></span></h3> |
| 4212 |
|
| 4213 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4214 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4215 |
|
| 4216 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4217 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Let us |
| 4218 |
write the pressure p as a sum of three terms:<o:p></o:p></span></span></p> |
| 4219 |
|
| 4220 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4221 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4222 |
|
| 4223 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4224 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4225 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1070" |
| 4226 |
type="#_x0000_t75" style='width:234.75pt;height:17.25pt' o:ole=""> |
| 4227 |
<v:imagedata src="./fulldoc_files/image138.wmz" o:title=""/> |
| 4228 |
</v:shape><![endif]--><![if !vml]><img width=313 height=23 |
| 4229 |
src="./fulldoc_files/image139.gif" v:shapes="_x0000_i1070"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4230 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1070" |
| 4231 |
DrawAspect="Content" ObjectID="_1051901222"> |
| 4232 |
</o:OLEObject> |
| 4233 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 4234 |
style="mso-spacerun: yes"> </span>(1.5.7)<o:p></o:p></span></span></p> |
| 4235 |
|
| 4236 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4237 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4238 |
|
| 4239 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4240 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 4241 |
first term,<sub><!--[if gte vml 1]><v:shape id="_x0000_i1816" type="#_x0000_t75" |
| 4242 |
style='width:15pt;height:17.25pt' o:ole=""> |
| 4243 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4244 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4245 |
src="./fulldoc_files/image141.gif" v:shapes="_x0000_i1816"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4246 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1816" |
| 4247 |
DrawAspect="Content" ObjectID="_1051901223"> |
| 4248 |
</o:OLEObject> |
| 4249 |
</xml><![endif]-->, only varies in the horizontal and is independent of depth. |
| 4250 |
The second term is the hydrostatic pressure defined in terms of the weight of |
| 4251 |
water in a vertical column above the depth <i style='mso-bidi-font-style:normal'>z,<o:p></o:p></i></span></span></p> |
| 4252 |
|
| 4253 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4254 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4255 |
|
| 4256 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4257 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4258 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1071" |
| 4259 |
type="#_x0000_t75" style='width:104.25pt;height:36.75pt' o:ole=""> |
| 4260 |
<v:imagedata src="./fulldoc_files/image142.wmz" o:title=""/> |
| 4261 |
</v:shape><![endif]--><![if !vml]><img width=139 height=49 |
| 4262 |
src="./fulldoc_files/image143.gif" v:shapes="_x0000_i1071"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4263 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1071" |
| 4264 |
DrawAspect="Content" ObjectID="_1051901224"> |
| 4265 |
</o:OLEObject> |
| 4266 |
</xml><![endif]--><span style="mso-spacerun: |
| 4267 |
yes"> </span>(1.5.8a)<o:p></o:p></span></span></p> |
| 4268 |
|
| 4269 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4270 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4271 |
|
| 4272 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4273 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <o:p></o:p></span></span></p> |
| 4274 |
|
| 4275 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4276 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4277 |
|
| 4278 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4279 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4280 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1072" |
| 4281 |
type="#_x0000_t75" style='width:177.75pt;height:45pt' o:ole=""> |
| 4282 |
<v:imagedata src="./fulldoc_files/image144.wmz" o:title=""/> |
| 4283 |
</v:shape><![endif]--><![if !vml]><img width=237 height=60 |
| 4284 |
src="./fulldoc_files/image145.gif" v:shapes="_x0000_i1072"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4285 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1072" |
| 4286 |
DrawAspect="Content" ObjectID="_1051901225"> |
| 4287 |
</o:OLEObject> |
| 4288 |
</xml><![endif]--><span style="mso-spacerun: |
| 4289 |
yes"> </span>(1.5.8b)<o:p></o:p></span></span></p> |
| 4290 |
|
| 4291 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4292 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4293 |
|
| 4294 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4295 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Note |
| 4296 |
that (1.5.8) is a generalized statement of hydrostatic balance, balancing |
| 4297 |
vertical pressure gradients with gravity and, in <b style='mso-bidi-font-weight: |
| 4298 |
normal'>QH</b>, also Coriolis and metric terms.<o:p></o:p></span></span></p> |
| 4299 |
|
| 4300 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4301 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4302 |
|
| 4303 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4304 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>It |
| 4305 |
should be noted that the pressure at the rigid lid,<sub><!--[if gte vml 1]><v:shape |
| 4306 |
id="_x0000_i1073" type="#_x0000_t75" style='width:41.25pt;height:15.75pt' |
| 4307 |
o:ole=""> |
| 4308 |
<v:imagedata src="./fulldoc_files/image146.wmz" o:title=""/> |
| 4309 |
</v:shape><![endif]--><![if !vml]><img width=55 height=21 |
| 4310 |
src="./fulldoc_files/image147.gif" v:shapes="_x0000_i1073"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4311 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1073" |
| 4312 |
DrawAspect="Content" ObjectID="_1051901227"> |
| 4313 |
</o:OLEObject> |
| 4314 |
</xml><![endif]-->, has a contribution from both<sub><!--[if gte vml 1]><v:shape |
| 4315 |
id="_x0000_i1074" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 4316 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4317 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4318 |
src="./fulldoc_files/image148.gif" v:shapes="_x0000_i1074"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4319 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1074" |
| 4320 |
DrawAspect="Content" ObjectID="_1051901228"> |
| 4321 |
</o:OLEObject> |
| 4322 |
</xml><![endif]--> and<sub><!--[if gte vml 1]><v:shape id="_x0000_i1075" |
| 4323 |
type="#_x0000_t75" style='width:21.75pt;height:17.25pt' o:ole=""> |
| 4324 |
<v:imagedata src="./fulldoc_files/image149.wmz" o:title=""/> |
| 4325 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 4326 |
src="./fulldoc_files/image150.gif" v:shapes="_x0000_i1075"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4327 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1075" |
| 4328 |
DrawAspect="Content" ObjectID="_1051901229"> |
| 4329 |
</o:OLEObject> |
| 4330 |
</xml><![endif]--> (by definition,<sub><!--[if gte vml 1]><v:shape id="_x0000_i1076" |
| 4331 |
type="#_x0000_t75" style='width:42pt;height:15.75pt' o:ole=""> |
| 4332 |
<v:imagedata src="./fulldoc_files/image151.wmz" o:title=""/> |
| 4333 |
</v:shape><![endif]--><![if !vml]><img width=56 height=21 |
| 4334 |
src="./fulldoc_files/image152.gif" v:shapes="_x0000_i1076"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4335 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1076" |
| 4336 |
DrawAspect="Content" ObjectID="_1051901230"> |
| 4337 |
</o:OLEObject> |
| 4338 |
</xml><![endif]-->, at z=0).<span style="mso-spacerun: yes"> </span>In the |
| 4339 |
hydrostatic limit<sub><!--[if gte vml 1]><v:shape id="_x0000_i1077" type="#_x0000_t75" |
| 4340 |
style='width:21.75pt;height:17.25pt' o:ole=""> |
| 4341 |
<v:imagedata src="./fulldoc_files/image149.wmz" o:title=""/> |
| 4342 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 4343 |
src="./fulldoc_files/image153.gif" v:shapes="_x0000_i1077"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4344 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1077" |
| 4345 |
DrawAspect="Content" ObjectID="_1051901231"> |
| 4346 |
</o:OLEObject> |
| 4347 |
</xml><![endif]-->= 0 and<sub><!--[if gte vml 1]><v:shape id="_x0000_i1078" |
| 4348 |
type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 4349 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4350 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4351 |
src="./fulldoc_files/image154.gif" v:shapes="_x0000_i1078"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4352 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1078" |
| 4353 |
DrawAspect="Content" ObjectID="_1051901232"> |
| 4354 |
</o:OLEObject> |
| 4355 |
</xml><![endif]--> is the surface pressure.<o:p></o:p></span></span></p> |
| 4356 |
|
| 4357 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4358 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4359 |
|
| 4360 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4361 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>By |
| 4362 |
substituting Eq. (1.5.7) in (1.5.5) an equation for<sub><!--[if gte vml 1]><v:shape |
| 4363 |
id="_x0000_i1079" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 4364 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4365 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4366 |
src="./fulldoc_files/image155.gif" v:shapes="_x0000_i1079"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4367 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1079" |
| 4368 |
DrawAspect="Content" ObjectID="_1051901234"> |
| 4369 |
</o:OLEObject> |
| 4370 |
</xml><![endif]--> results:<o:p></o:p></span></span></p> |
| 4371 |
|
| 4372 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4373 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4374 |
|
| 4375 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4376 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4377 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1080" |
| 4378 |
type="#_x0000_t75" style='width:294pt;height:24.75pt' o:ole=""> |
| 4379 |
<v:imagedata src="./fulldoc_files/image156.wmz" o:title=""/> |
| 4380 |
</v:shape><![endif]--><![if !vml]><img width=392 height=33 |
| 4381 |
src="./fulldoc_files/image157.gif" v:shapes="_x0000_i1080"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4382 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1080" |
| 4383 |
DrawAspect="Content" ObjectID="_1051901235"> |
| 4384 |
</o:OLEObject> |
| 4385 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>(1.5.9)<o:p></o:p></span></span></p> |
| 4386 |
|
| 4387 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4388 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4389 |
|
| 4390 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4391 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where </span></span><span |
| 4392 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 4393 |
id="_x0000_i1081" type="#_x0000_t75" style='width:18.75pt;height:15.75pt' |
| 4394 |
o:ole=""> |
| 4395 |
<v:imagedata src="./fulldoc_files/image158.wmz" o:title=""/> |
| 4396 |
</v:shape><![endif]--><![if !vml]><img width=25 height=21 |
| 4397 |
src="./fulldoc_files/image159.gif" v:shapes="_x0000_i1081"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4398 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1081" |
| 4399 |
DrawAspect="Content" ObjectID="_1051901236"> |
| 4400 |
</o:OLEObject> |
| 4401 |
</xml><![endif]--></span></span><span style='mso-bookmark:_Toc407078231'><span |
| 4402 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 4403 |
style="mso-spacerun: yes"> </span>is given by:<o:p></o:p></span></span></p> |
| 4404 |
|
| 4405 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4406 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4407 |
|
| 4408 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4409 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4410 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1082" |
| 4411 |
type="#_x0000_t75" style='width:297pt;height:21.75pt' o:ole=""> |
| 4412 |
<v:imagedata src="./fulldoc_files/image160.wmz" o:title=""/> |
| 4413 |
</v:shape><![endif]--><![if !vml]><img width=396 height=29 |
| 4414 |
src="./fulldoc_files/image161.gif" v:shapes="_x0000_i1082"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4415 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1082" |
| 4416 |
DrawAspect="Content" ObjectID="_1051901238"> |
| 4417 |
</o:OLEObject> |
| 4418 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>(1.5.10)<o:p></o:p></span></span></p> |
| 4419 |
|
| 4420 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4421 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4422 |
|
| 4423 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4424 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In<b |
| 4425 |
style='mso-bidi-font-weight:normal'> HPE </b>and<b style='mso-bidi-font-weight: |
| 4426 |
normal'> QH</b> the (doubly) underlined terms on the rhs of (1.5.9), which |
| 4427 |
depend on the non-hydrostatic pressure, are set to zero and<sub><!--[if gte vml 1]><v:shape |
| 4428 |
id="_x0000_i1083" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 4429 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4430 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4431 |
src="./fulldoc_files/image162.gif" v:shapes="_x0000_i1083"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4432 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1083" |
| 4433 |
DrawAspect="Content" ObjectID="_1051901239"> |
| 4434 |
</o:OLEObject> |
| 4435 |
</xml><![endif]--> is found by solving:<o:p></o:p></span></span></p> |
| 4436 |
|
| 4437 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4438 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4439 |
|
| 4440 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4441 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4442 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1084" |
| 4443 |
type="#_x0000_t75" style='width:122.25pt;height:17.25pt' o:ole=""> |
| 4444 |
<v:imagedata src="./fulldoc_files/image163.wmz" o:title=""/> |
| 4445 |
</v:shape><![endif]--><![if !vml]><img width=163 height=23 |
| 4446 |
src="./fulldoc_files/image164.gif" v:shapes="_x0000_i1084"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4447 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1084" |
| 4448 |
DrawAspect="Content" ObjectID="_1051901240"> |
| 4449 |
</o:OLEObject> |
| 4450 |
</xml><![endif]--><span style="mso-spacerun: |
| 4451 |
yes"> </span>(1.5.11)<o:p></o:p></span></span></p> |
| 4452 |
|
| 4453 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4454 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4455 |
|
| 4456 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4457 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 4458 |
vertical velocity is obtained through integration of the continuity equation |
| 4459 |
vertically:<o:p></o:p></span></span></p> |
| 4460 |
|
| 4461 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4462 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4463 |
|
| 4464 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4465 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4466 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1085" |
| 4467 |
type="#_x0000_t75" style='width:84pt;height:36.75pt' o:ole=""> |
| 4468 |
<v:imagedata src="./fulldoc_files/image165.wmz" o:title=""/> |
| 4469 |
</v:shape><![endif]--><![if !vml]><img width=112 height=49 |
| 4470 |
src="./fulldoc_files/image166.gif" v:shapes="_x0000_i1085"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4471 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1085" |
| 4472 |
DrawAspect="Content" ObjectID="_1051901241"> |
| 4473 |
</o:OLEObject> |
| 4474 |
</xml><![endif]--><span style="mso-spacerun: |
| 4475 |
yes"> </span>(1.5.12)<o:p></o:p></span></span></p> |
| 4476 |
|
| 4477 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4478 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4479 |
|
| 4480 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4481 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In<b |
| 4482 |
style='mso-bidi-font-weight:normal'> NH</b>, instead, we first solve (1.5.11) |
| 4483 |
to give a provisional solution for<sub><!--[if gte vml 1]><v:shape id="_x0000_i1817" |
| 4484 |
type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 4485 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4486 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4487 |
src="./fulldoc_files/image167.gif" v:shapes="_x0000_i1817"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4488 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1817" |
| 4489 |
DrawAspect="Content" ObjectID="_1051901242"> |
| 4490 |
</o:OLEObject> |
| 4491 |
</xml><![endif]--> and then find<sub><!--[if gte vml 1]><v:shape id="_x0000_i1818" |
| 4492 |
type="#_x0000_t75" style='width:21.75pt;height:17.25pt' o:ole=""> |
| 4493 |
<v:imagedata src="./fulldoc_files/image168.wmz" o:title=""/> |
| 4494 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 4495 |
src="./fulldoc_files/image169.gif" v:shapes="_x0000_i1818"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4496 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1818" |
| 4497 |
DrawAspect="Content" ObjectID="_1051901244"> |
| 4498 |
</o:OLEObject> |
| 4499 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>from the Elliptic |
| 4500 |
equation obtained by substituting (1.5.7) in to (1.1.1), and noting, as before, |
| 4501 |
that <sub><!--[if gte vml 1]><v:shape id="_x0000_i1819" type="#_x0000_t75" |
| 4502 |
style='width:36.75pt;height:14.25pt' o:ole=""> |
| 4503 |
<v:imagedata src="./fulldoc_files/image170.wmz" o:title=""/> |
| 4504 |
</v:shape><![endif]--><![if !vml]><img width=49 height=19 |
| 4505 |
src="./fulldoc_files/image171.gif" v:shapes="_x0000_i1819"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4506 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1819" |
| 4507 |
DrawAspect="Content" ObjectID="_1051901245"> |
| 4508 |
</o:OLEObject> |
| 4509 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>at each point in the fluid:<o:p></o:p></span></span></p> |
| 4510 |
|
| 4511 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4512 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4513 |
|
| 4514 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4515 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4516 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1086" |
| 4517 |
type="#_x0000_t75" style='width:162.75pt;height:33pt' o:ole=""> |
| 4518 |
<v:imagedata src="./fulldoc_files/image172.wmz" o:title=""/> |
| 4519 |
</v:shape><![endif]--><![if !vml]><img width=217 height=44 |
| 4520 |
src="./fulldoc_files/image173.gif" v:shapes="_x0000_i1086"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4521 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1086" |
| 4522 |
DrawAspect="Content" ObjectID="_1051901246"> |
| 4523 |
</o:OLEObject> |
| 4524 |
</xml><![endif]--><span style="mso-spacerun: |
| 4525 |
yes"> </span>(1.5.13a)<o:p></o:p></span></span></p> |
| 4526 |
|
| 4527 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4528 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4529 |
|
| 4530 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4531 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where<o:p></o:p></span></span></p> |
| 4532 |
|
| 4533 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4534 |
style='font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4535 |
|
| 4536 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4537 |
_Toc407078231'><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 4538 |
id="_x0000_i1087" type="#_x0000_t75" style='width:2in;height:18pt' o:ole=""> |
| 4539 |
<v:imagedata src="./fulldoc_files/image174.wmz" o:title=""/> |
| 4540 |
</v:shape><![endif]--><![if !vml]><img width=192 height=24 |
| 4541 |
src="./fulldoc_files/image175.gif" v:shapes="_x0000_i1087"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4542 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1087" |
| 4543 |
DrawAspect="Content" ObjectID="_1051901247"> |
| 4544 |
</o:OLEObject> |
| 4545 |
</xml><![endif]--><span style="mso-spacerun: |
| 4546 |
yes"> </span></span></span><span |
| 4547 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4548 |
10.0pt;font-family:Palatino'>(1.5.13b)</span></span><span style='mso-bookmark: |
| 4549 |
_Toc407078231'><span style='font-family:Palatino'><o:p></o:p></span></span></p> |
| 4550 |
|
| 4551 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 4552 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4553 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4554 |
|
| 4555 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4556 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Eq.(1.5.13) |
| 4557 |
is solved with the boundary conditions:<o:p></o:p></span></span></p> |
| 4558 |
|
| 4559 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4560 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4561 |
|
| 4562 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4563 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4564 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1088" |
| 4565 |
type="#_x0000_t75" style='width:56.25pt;height:17.25pt' o:ole=""> |
| 4566 |
<v:imagedata src="./fulldoc_files/image176.wmz" o:title=""/> |
| 4567 |
</v:shape><![endif]--><![if !vml]><img width=75 height=23 |
| 4568 |
src="./fulldoc_files/image177.gif" v:shapes="_x0000_i1088"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4569 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1088" |
| 4570 |
DrawAspect="Content" ObjectID="_1051901249"> |
| 4571 |
</o:OLEObject> |
| 4572 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 4573 |
style="mso-spacerun: yes"> </span>(1.5.14)<o:p></o:p></span></span></p> |
| 4574 |
|
| 4575 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4576 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4577 |
|
| 4578 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4579 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>If the |
| 4580 |
flow is close to hydrostatic balance then the 3-d inversion converges rapidly |
| 4581 |
because <sub><!--[if gte vml 1]><v:shape id="_x0000_i1089" type="#_x0000_t75" |
| 4582 |
style='width:21.75pt;height:17.25pt' o:ole=""> |
| 4583 |
<v:imagedata src="./fulldoc_files/image168.wmz" o:title=""/> |
| 4584 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 4585 |
src="./fulldoc_files/image178.gif" v:shapes="_x0000_i1089"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4586 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1089" |
| 4587 |
DrawAspect="Content" ObjectID="_1051901250"> |
| 4588 |
</o:OLEObject> |
| 4589 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is then only a small |
| 4590 |
correction to the hydrostatic pressure field.<o:p></o:p></span></span></p> |
| 4591 |
|
| 4592 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4593 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4594 |
|
| 4595 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4596 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 4597 |
solution <sub><!--[if gte vml 1]><v:shape id="_x0000_i1090" type="#_x0000_t75" |
| 4598 |
style='width:21.75pt;height:17.25pt' o:ole=""> |
| 4599 |
<v:imagedata src="./fulldoc_files/image149.wmz" o:title=""/> |
| 4600 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 4601 |
src="./fulldoc_files/image179.gif" v:shapes="_x0000_i1090"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4602 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1090" |
| 4603 |
DrawAspect="Content" ObjectID="_1051901251"> |
| 4604 |
</o:OLEObject> |
| 4605 |
</xml><![endif]-->to (1.5.13) and (1.5.14) does not vanish at the upper |
| 4606 |
surface, and so refines the pressure at z=0; it is in this sense that the <sub><!--[if gte vml 1]><v:shape |
| 4607 |
id="_x0000_i1091" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 4608 |
<v:imagedata src="./fulldoc_files/image140.wmz" o:title=""/> |
| 4609 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 4610 |
src="./fulldoc_files/image180.gif" v:shapes="_x0000_i1091"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4611 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1091" |
| 4612 |
DrawAspect="Content" ObjectID="_1051901252"> |
| 4613 |
</o:OLEObject> |
| 4614 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>obtained from |
| 4615 |
(1.5.11) is provisional.<span style="mso-spacerun: yes"> </span>In the |
| 4616 |
interior of the fluid non-hydrostatic pressure gradients,<sub><!--[if gte vml 1]><v:shape |
| 4617 |
id="_x0000_i1092" type="#_x0000_t75" style='width:29.25pt;height:17.25pt' |
| 4618 |
o:ole=""> |
| 4619 |
<v:imagedata src="./fulldoc_files/image181.wmz" o:title=""/> |
| 4620 |
</v:shape><![endif]--><![if !vml]><img width=39 height=23 |
| 4621 |
src="./fulldoc_files/image182.gif" v:shapes="_x0000_i1092"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4622 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1092" |
| 4623 |
DrawAspect="Content" ObjectID="_1051901253"> |
| 4624 |
</o:OLEObject> |
| 4625 |
</xml><![endif]-->, drive motion:- <i style='mso-bidi-font-style:normal'>w</i> |
| 4626 |
is found by prognostic integration of the vertical velocity equation:<o:p></o:p></span></span></p> |
| 4627 |
|
| 4628 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4629 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4630 |
|
| 4631 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4632 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4633 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1093" |
| 4634 |
type="#_x0000_t75" style='width:84pt;height:30.75pt' o:ole=""> |
| 4635 |
<v:imagedata src="./fulldoc_files/image183.wmz" o:title=""/> |
| 4636 |
</v:shape><![endif]--><![if !vml]><img width=112 height=41 |
| 4637 |
src="./fulldoc_files/image184.gif" v:shapes="_x0000_i1093"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4638 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1093" |
| 4639 |
DrawAspect="Content" ObjectID="_1051901254"> |
| 4640 |
</o:OLEObject> |
| 4641 |
</xml><![endif]--><span style="mso-spacerun: |
| 4642 |
yes"> </span>(1.5.15a)<o:p></o:p></span></span></p> |
| 4643 |
|
| 4644 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4645 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4646 |
|
| 4647 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4648 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where<o:p></o:p></span></span></p> |
| 4649 |
|
| 4650 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4651 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4652 |
|
| 4653 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 4654 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4655 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1094" |
| 4656 |
type="#_x0000_t75" style='width:66pt;height:26.25pt' o:ole=""> |
| 4657 |
<v:imagedata src="./fulldoc_files/image185.wmz" o:title=""/> |
| 4658 |
</v:shape><![endif]--><![if !vml]><img width=88 height=35 |
| 4659 |
src="./fulldoc_files/image186.gif" v:shapes="_x0000_i1094"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4660 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1094" |
| 4661 |
DrawAspect="Content" ObjectID="_1051901256"> |
| 4662 |
</o:OLEObject> |
| 4663 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 4664 |
style="mso-spacerun: yes"> </span>(1.5.15b)<o:p></o:p></span></span></p> |
| 4665 |
|
| 4666 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4667 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4668 |
|
| 4669 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4670 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Note |
| 4671 |
that in (1.5.15), the vertical gradient of the hydrostatic pressure has been |
| 4672 |
canceled out with </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 4673 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1095" |
| 4674 |
type="#_x0000_t75" style='width:9pt;height:14.25pt' o:ole=""> |
| 4675 |
<v:imagedata src="./fulldoc_files/image187.wmz" o:title=""/> |
| 4676 |
</v:shape><![endif]--><![if !vml]><img width=12 height=19 |
| 4677 |
src="./fulldoc_files/image188.gif" v:shapes="_x0000_i1095"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4678 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1095" |
| 4679 |
DrawAspect="Content" ObjectID="_1051901257"> |
| 4680 |
</o:OLEObject> |
| 4681 |
</xml><![endif]-->, </span></span><span style='mso-bookmark:_Toc407078231'><span |
| 4682 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Eq.(1.5.8b)</span></span><span |
| 4683 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'>, </span></span><span |
| 4684 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4685 |
10.0pt;font-family:Palatino'>rendering it suitable for prognostic integration.<o:p></o:p></span></span></p> |
| 4686 |
|
| 4687 |
<p class=MsoNormalIndent style='margin-left:0pt'><span style='mso-bookmark: |
| 4688 |
_Toc407078231'><u><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></span></p> |
| 4689 |
|
| 4690 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4691 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4692 |
|
| 4693 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078227"></a><a |
| 4694 |
name="_Toc407090381"></a><a name="_Toc407090584"></a><a name="_Toc407169613"><span |
| 4695 |
style='mso-bookmark:_Toc407090584'><span style='mso-bookmark:_Toc407090381'><span |
| 4696 |
style='mso-bookmark:_Toc407078227'>1.6 Summary of solution strategies</span></span></span></a></span></h2> |
| 4697 |
|
| 4698 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4699 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4700 |
|
| 4701 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4702 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 4703 |
method of solution employed in the <b style='mso-bidi-font-weight:normal'>HPE</b>, |
| 4704 |
<b style='mso-bidi-font-weight:normal'>QH</b> and <b style='mso-bidi-font-weight: |
| 4705 |
normal'>NH</b> models are summarized in Fig.3 below.<o:p></o:p></span></span></p> |
| 4706 |
|
| 4707 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4708 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4709 |
|
| 4710 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4711 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4712 |
|
| 4713 |
<div style='mso-element:frame;mso-element-frame-width:407.45pt;mso-element-frame-height: |
| 4714 |
324.05pt;mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4715 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'> |
| 4716 |
|
| 4717 |
<table cellspacing=0 cellpadding=0 hspace=0 vspace=0 width=555 height=432 |
| 4718 |
align=left> |
| 4719 |
<tr> |
| 4720 |
<td valign=top align=left height=432 style='padding-top:0pt;padding-right: |
| 4721 |
9.0pt;padding-bottom:0pt;padding-left:9.0pt'> |
| 4722 |
<div style='border:solid windowtext .75pt;padding:1.0pt 1.0pt 1.0pt 1.0pt'> |
| 4723 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4724 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4725 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4726 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4727 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4728 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4729 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4730 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4731 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4732 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4733 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4734 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4735 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4736 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4737 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4738 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4739 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4740 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4741 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><!--[if gte vml 1]><v:rect |
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id="_x0000_s1032" style='position:absolute;margin-left:46.8pt;margin-top:3.85pt; |
| 4743 |
width:259.25pt;height:50.45pt;z-index:4;mso-position-horizontal-relative:text; |
| 4744 |
mso-position-vertical-relative:text' o:allowincell="f" filled="f"/><![endif]--><![if !vml]><span |
| 4745 |
style='mso-ignore:vglayout'> |
| 4746 |
<table cellpadding=0 cellspacing=0 align=left> |
| 4747 |
<tr> |
| 4748 |
<td width=62 height=5></td> |
| 4749 |
</tr> |
| 4750 |
<tr> |
| 4751 |
<td></td> |
| 4752 |
<td><img width=347 height=68 src="./fulldoc_files/image189.gif" v:shapes="_x0000_s1032"></td> |
| 4753 |
</tr> |
| 4754 |
</table> |
| 4755 |
</span><![endif]><span style='mso-bookmark:_Toc407078231'></span><span |
| 4756 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4757 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4758 |
<br style='mso-ignore:vglayout' clear=ALL> |
| 4759 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4760 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4761 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4762 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4763 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4764 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4765 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> |
| 4766 |
</span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1096" type="#_x0000_t75" |
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style='width:122.25pt;height:17.25pt' o:ole=""> |
| 4768 |
<v:imagedata src="./fulldoc_files/image163.wmz" o:title=""/> |
| 4769 |
</v:shape><![endif]--><![if !vml]><img width=163 height=23 |
| 4770 |
src="./fulldoc_files/image190.gif" v:shapes="_x0000_i1096"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4771 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1096" |
| 4772 |
DrawAspect="Content" ObjectID="_1051901258"> |
| 4773 |
</o:OLEObject> |
| 4774 |
</xml><![endif]--><span style='mso-tab-count:1'> </span>;<span |
| 4775 |
style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1097" |
| 4776 |
type="#_x0000_t75" style='width:105pt;height:36.75pt' o:ole=""> |
| 4777 |
<v:imagedata src="./fulldoc_files/image191.wmz" o:title=""/> |
| 4778 |
</v:shape><![endif]--><![if !vml]><img width=140 height=49 |
| 4779 |
src="./fulldoc_files/image192.gif" v:shapes="_x0000_i1097"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4780 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1097" |
| 4781 |
DrawAspect="Content" ObjectID="_1051901260"> |
| 4782 |
</o:OLEObject> |
| 4783 |
</xml><![endif]--><o:p></o:p></span></span></p> |
| 4784 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4785 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4786 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4787 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4788 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><!--[if gte vml 1]><v:line |
| 4789 |
id="_x0000_s1033" style='position:absolute;flip:x;z-index:5; |
| 4790 |
mso-position-horizontal-relative:text;mso-position-vertical-relative:text' |
| 4791 |
from="46.8pt,3.4pt" to="176.45pt,118.65pt" o:allowincell="f"> |
| 4792 |
<v:stroke startarrowwidth="narrow" startarrowlength="short" endarrow="block" |
| 4793 |
endarrowwidth="narrow" endarrowlength="short"/> |
| 4794 |
</v:line><v:line id="_x0000_s1034" style='position:absolute;z-index:6; |
| 4795 |
mso-position-horizontal-relative:text;mso-position-vertical-relative:text' |
| 4796 |
from="176.4pt,3.4pt" to="306.05pt,118.65pt" o:allowincell="f"> |
| 4797 |
<v:stroke startarrowwidth="narrow" startarrowlength="short" endarrow="block" |
| 4798 |
endarrowwidth="narrow" endarrowlength="short"/> |
| 4799 |
</v:line><![endif]--><![if !vml]><span style='mso-ignore:vglayout'> |
| 4800 |
<table cellpadding=0 cellspacing=0 align=left> |
| 4801 |
<tr> |
| 4802 |
<td width=61 height=4></td> |
| 4803 |
</tr> |
| 4804 |
<tr> |
| 4805 |
<td></td> |
| 4806 |
<td><img width=349 height=156 src="./fulldoc_files/image193.gif" v:shapes="_x0000_s1033 _x0000_s1034"></td> |
| 4807 |
</tr> |
| 4808 |
</table> |
| 4809 |
</span><![endif]><span style='mso-bookmark:_Toc407078231'></span><span |
| 4810 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4811 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4812 |
<br style='mso-ignore:vglayout' clear=ALL> |
| 4813 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4814 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4815 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4816 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4817 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4818 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4819 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> </span><o:p></o:p></span></span></p> |
| 4820 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4821 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4822 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4823 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4824 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4825 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4826 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: |
| 4827 |
yes"> </span><o:p></o:p></span></span></p> |
| 4828 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4829 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4830 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4831 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4832 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4833 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4834 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: |
| 4835 |
yes"> </span><b style='mso-bidi-font-weight:normal'>HPE</b> |
| 4836 |
and <b style='mso-bidi-font-weight:normal'>QH</b><span style="mso-spacerun: |
| 4837 |
yes"> </span><span style="mso-spacerun: |
| 4838 |
yes"> </span><b style='mso-bidi-font-weight:normal'>NH</b><o:p></o:p></span></span></p> |
| 4839 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4840 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4841 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4842 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4843 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4844 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4845 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4846 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4847 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4848 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4849 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4850 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4851 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4852 |
10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4853 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4854 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4855 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4856 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4857 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4858 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4859 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: |
| 4860 |
yes"> |
| 4861 |
</span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1820" type="#_x0000_t75" |
| 4862 |
style='width:159.75pt;height:18.75pt' o:ole=""> |
| 4863 |
<v:imagedata src="./fulldoc_files/image194.wmz" o:title=""/> |
| 4864 |
</v:shape><![endif]--><![if !vml]><img width=213 height=25 |
| 4865 |
src="./fulldoc_files/image195.gif" v:shapes="_x0000_i1820"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4866 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1820" |
| 4867 |
DrawAspect="Content" ObjectID="_1051901261"> |
| 4868 |
</o:OLEObject> |
| 4869 |
</xml><![endif]--><o:p></o:p></span></span></p> |
| 4870 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4871 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4872 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4873 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4874 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4875 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4876 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: |
| 4877 |
yes"> </span><o:p></o:p></span></span></p> |
| 4878 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4879 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4880 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4881 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4882 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4883 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4884 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 4885 |
id="_x0000_i1821" type="#_x0000_t75" style='width:134.25pt;height:30.75pt' |
| 4886 |
o:ole=""> |
| 4887 |
<v:imagedata src="./fulldoc_files/image196.wmz" o:title=""/> |
| 4888 |
</v:shape><![endif]--><![if !vml]><img width=179 height=41 |
| 4889 |
src="./fulldoc_files/image197.gif" v:shapes="_x0000_i1821"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4890 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1821" |
| 4891 |
DrawAspect="Content" ObjectID="_1051901262"> |
| 4892 |
</o:OLEObject> |
| 4893 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 4894 |
id="_x0000_i1822" type="#_x0000_t75" style='width:9pt;height:15.75pt' o:ole=""> |
| 4895 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 4896 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 4897 |
src="./fulldoc_files/image198.gif" v:shapes="_x0000_i1822"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4898 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1822" |
| 4899 |
DrawAspect="Content" ObjectID="_1051901264"> |
| 4900 |
</o:OLEObject> |
| 4901 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 4902 |
id="_x0000_i1823" type="#_x0000_t75" style='width:165.75pt;height:30.75pt' |
| 4903 |
o:ole=""> |
| 4904 |
<v:imagedata src="./fulldoc_files/image199.wmz" o:title=""/> |
| 4905 |
</v:shape><![endif]--><![if !vml]><img width=221 height=41 |
| 4906 |
src="./fulldoc_files/image200.gif" v:shapes="_x0000_i1823"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4907 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1823" |
| 4908 |
DrawAspect="Content" ObjectID="_1051901265"> |
| 4909 |
</o:OLEObject> |
| 4910 |
</xml><![endif]--><o:p></o:p></span></span></p> |
| 4911 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4912 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4913 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4914 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4915 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4916 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4917 |
10.0pt;font-family:Palatino'><span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 4918 |
id="_x0000_i1098" type="#_x0000_t75" style='width:84pt;height:36.75pt' |
| 4919 |
o:ole=""> |
| 4920 |
<v:imagedata src="./fulldoc_files/image165.wmz" o:title=""/> |
| 4921 |
</v:shape><![endif]--><![if !vml]><img width=112 height=49 |
| 4922 |
src="./fulldoc_files/image201.gif" v:shapes="_x0000_i1098"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4923 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1098" |
| 4924 |
DrawAspect="Content" ObjectID="_1051901266"> |
| 4925 |
</o:OLEObject> |
| 4926 |
</xml><![endif]--><span style='mso-tab-count:1'> </span><span |
| 4927 |
style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 4928 |
id="_x0000_i1099" type="#_x0000_t75" style='width:84pt;height:30.75pt' |
| 4929 |
o:ole=""> |
| 4930 |
<v:imagedata src="./fulldoc_files/image202.wmz" o:title=""/> |
| 4931 |
</v:shape><![endif]--><![if !vml]><img width=112 height=41 |
| 4932 |
src="./fulldoc_files/image203.gif" v:shapes="_x0000_i1099"><![endif]></sub><!--[if gte mso 9]><xml> |
| 4933 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1099" |
| 4934 |
DrawAspect="Content" ObjectID="_1051901267"> |
| 4935 |
</o:OLEObject> |
| 4936 |
</xml><![endif]--><o:p></o:p></span></span></p> |
| 4937 |
<p class=MsoNormal style='border:none;mso-border-alt:solid windowtext .75pt; |
| 4938 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 4939 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 4940 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 4941 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 4942 |
style='mso-bookmark:_Toc407078231'><span style='font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4943 |
</div> |
| 4944 |
</td> |
| 4945 |
</tr> |
| 4946 |
</table> |
| 4947 |
|
| 4948 |
</div> |
| 4949 |
|
| 4950 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4951 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4952 |
|
| 4953 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><b |
| 4954 |
style='mso-bidi-font-weight:normal'><span style='font-size:9.0pt;mso-bidi-font-size: |
| 4955 |
10.0pt;font-family:Palatino'>Fig.3</span></b></span><span style='mso-bookmark: |
| 4956 |
_Toc407078231'><span style='font-size:9.0pt;mso-bidi-font-size:10.0pt; |
| 4957 |
font-family:Palatino'>.<span style="mso-spacerun: yes"> </span>Outline of |
| 4958 |
hydrostatic <b style='mso-bidi-font-weight:normal'>(HPE)</b>, quasi-hydrostatic |
| 4959 |
<b style='mso-bidi-font-weight:normal'>(QH)</b> and non-hydrostatic <b |
| 4960 |
style='mso-bidi-font-weight:normal'>(NH)</b> algorithms.<o:p></o:p></span></span></p> |
| 4961 |
|
| 4962 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 4963 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 4964 |
|
| 4965 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 4966 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>There |
| 4967 |
is no penalty in implementing <b style='mso-bidi-font-weight:normal'>QH</b> |
| 4968 |
over <b style='mso-bidi-font-weight:normal'>HPE</b> except, of course, some |
| 4969 |
complication that goes with the inclusion of cos</span></span><span |
| 4970 |
style='mso-bookmark:_Toc407078231'><i style='mso-bidi-font-style:normal'><span |
| 4971 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 4972 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 4973 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 4974 |
mso-symbol-font-family:Symbol'>f</span></span></i></span><span |
| 4975 |
style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 4976 |
10.0pt;font-family:Palatino'> Coriolis terms and the relaxation of the shallow |
| 4977 |
atmosphere approximation.<span style="mso-spacerun: yes"> </span>But this |
| 4978 |
leads to negligible increase in computation.<span style="mso-spacerun: yes"> |
| 4979 |
</span>In <b style='mso-bidi-font-weight:normal'>NH</b>, in contrast, one |
| 4980 |
additional elliptic equation - a three-dimensional one - must be inverted.<span |
| 4981 |
style="mso-spacerun: yes"> </span>However we show that this overhead of the <b |
| 4982 |
style='mso-bidi-font-weight:normal'>NH</b> model is essentially negligible in |
| 4983 |
the hydrostatic limit (as the non-hydrostatic parameter <i style='mso-bidi-font-style: |
| 4984 |
normal'>N</i></span></span><span style='mso-bookmark:_Toc407078231'><span |
| 4985 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 4986 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 4987 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 4988 |
mso-symbol-font-family:Symbol'>®</span></span></span><span style='mso-bookmark: |
| 4989 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 4990 |
font-family:Palatino'>0 - see appendix II) resulting in a non-hydrostatic |
| 4991 |
algorithm that, in the hydrostatic limit, is as computationally economic as the |
| 4992 |
<b style='mso-bidi-font-weight:normal'>HPEs</b>.<o:p></o:p></span></span></p> |
| 4993 |
|
| 4994 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 4995 |
|
| 4996 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 4997 |
|
| 4998 |
<h2><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078228"></a><a |
| 4999 |
name="_Toc407090382"></a><a name="_Toc407090585"></a><a name="_Toc407169614"><span |
| 5000 |
style='mso-bookmark:_Toc407090585'><span style='mso-bookmark:_Toc407090382'><span |
| 5001 |
style='mso-bookmark:_Toc407078228'>1.7 Forcing and dissipation</span></span></span></a></span></h2> |
| 5002 |
|
| 5003 |
<h3><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078229"></a><a |
| 5004 |
name="_Toc407090383"></a><a name="_Toc407090586"></a><a name="_Toc407169615"><span |
| 5005 |
style='mso-bookmark:_Toc407090586'><span style='mso-bookmark:_Toc407090383'><span |
| 5006 |
style='mso-bookmark:_Toc407078229'><u>1.7.1 Forcing</u></span></span></span></a><u><o:p></o:p></u></span></h3> |
| 5007 |
|
| 5008 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078231'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5009 |
|
| 5010 |
<p class=MsoNormal style='text-align:justify'><!--[if gte vml 1]><o:wrapblock><v:shape |
| 5011 |
id="_x0000_s1036" type="#_x0000_t75" style='position:absolute;left:0; |
| 5012 |
text-align:left;margin-left:327.6pt;margin-top:0;width:9pt;height:17pt; |
| 5013 |
z-index:7;mso-position-horizontal-relative:text; |
| 5014 |
mso-position-vertical-relative:text' o:allowincell="f"> |
| 5015 |
<v:imagedata src="./fulldoc_files/image204.wmz" o:title=""/> |
| 5016 |
<w:wrap type="topAndBottom"/> |
| 5017 |
</v:shape><![if gte mso 9]><o:OLEObject Type="Embed" ProgID="Equation.3" |
| 5018 |
ShapeID="_x0000_s1036" DrawAspect="Content" ObjectID="_1051901268"> |
| 5019 |
</o:OLEObject> |
| 5020 |
<![endif]><![endif]--><![if !vml]><span style='mso-ignore:vglayout'> |
| 5021 |
<table cellpadding=0 cellspacing=0> |
| 5022 |
<tr> |
| 5023 |
<td width=437 height=0></td> |
| 5024 |
</tr> |
| 5025 |
<tr> |
| 5026 |
<td></td> |
| 5027 |
<td><img width=12 height=23 src="./fulldoc_files/image205.gif" v:shapes="_x0000_s1036"></td> |
| 5028 |
</tr> |
| 5029 |
</table> |
| 5030 |
</span><![endif]><!--[if gte vml 1]></o:wrapblock><![endif]--><br |
| 5031 |
style='mso-ignore:vglayout' clear=ALL> |
| 5032 |
<span style='mso-bookmark:_Toc407078231'><span style='font-size:12.0pt; |
| 5033 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>In the momentum equations, the |
| 5034 |
forcing comes from the action of the wind at the sea surface and is represented |
| 5035 |
by a term <sub><!--[if gte vml 1]><v:shape id="_x0000_i1100" type="#_x0000_t75" |
| 5036 |
style='width:17.25pt;height:18.75pt' o:ole="" fillcolor="window"> |
| 5037 |
<v:imagedata src="./fulldoc_files/image206.wmz" o:title=""/> |
| 5038 |
</v:shape><![endif]--><![if !vml]><img width=23 height=25 |
| 5039 |
src="./fulldoc_files/image207.gif" v:shapes="_x0000_i1100"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5040 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1100" |
| 5041 |
DrawAspect="Content" ObjectID="_1051901270"> |
| 5042 |
</o:OLEObject> |
| 5043 |
</xml><![endif]-->such that:<o:p></o:p></span></span></p> |
| 5044 |
|
| 5045 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5046 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5047 |
|
| 5048 |
<br style='mso-ignore:vglayout' clear=ALL> |
| 5049 |
|
| 5050 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5051 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5052 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1101" |
| 5053 |
type="#_x0000_t75" style='width:1in;height:35.25pt' o:ole="" fillcolor="window"> |
| 5054 |
<v:imagedata src="./fulldoc_files/image208.wmz" o:title=""/> |
| 5055 |
</v:shape><![endif]--><![if !vml]><img width=96 height=47 |
| 5056 |
src="./fulldoc_files/image209.gif" v:shapes="_x0000_i1101"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5057 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1101" |
| 5058 |
DrawAspect="Content" ObjectID="_1051901271"> |
| 5059 |
</o:OLEObject> |
| 5060 |
</xml><![endif]--><span style="mso-spacerun: |
| 5061 |
yes"> </span>(1.7.1)<o:p></o:p></span></span></p> |
| 5062 |
|
| 5063 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5064 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5065 |
|
| 5066 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5067 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <b |
| 5068 |
style='mso-bidi-font-weight:normal'>X</b> is the stress such that:<o:p></o:p></span></span></p> |
| 5069 |
|
| 5070 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5071 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5072 |
|
| 5073 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5074 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5075 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1102" |
| 5076 |
type="#_x0000_t75" style='width:93pt;height:18pt' o:ole="" fillcolor="window"> |
| 5077 |
<v:imagedata src="./fulldoc_files/image210.wmz" o:title=""/> |
| 5078 |
</v:shape><![endif]--><![if !vml]><img width=124 height=24 |
| 5079 |
src="./fulldoc_files/image211.gif" v:shapes="_x0000_i1102"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5080 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1102" |
| 5081 |
DrawAspect="Content" ObjectID="_1051901272"> |
| 5082 |
</o:OLEObject> |
| 5083 |
</xml><![endif]--><span style="mso-spacerun: |
| 5084 |
yes"> </span>(1.7.2)<o:p></o:p></span></span></p> |
| 5085 |
|
| 5086 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5087 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5088 |
|
| 5089 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5090 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5091 |
id="_x0000_i1103" type="#_x0000_t75" style='width:12.75pt;height:18pt' o:ole="" |
| 5092 |
fillcolor="window"> |
| 5093 |
<v:imagedata src="./fulldoc_files/image212.wmz" o:title=""/> |
| 5094 |
</v:shape><![endif]--><![if !vml]><img width=17 height=24 |
| 5095 |
src="./fulldoc_files/image213.gif" v:shapes="_x0000_i1103"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5096 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1103" |
| 5097 |
DrawAspect="Content" ObjectID="_1051901273"> |
| 5098 |
</o:OLEObject> |
| 5099 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and <sub><!--[if gte vml 1]><v:shape |
| 5100 |
id="_x0000_i1104" type="#_x0000_t75" style='width:12.75pt;height:18pt' o:ole="" |
| 5101 |
fillcolor="window"> |
| 5102 |
<v:imagedata src="./fulldoc_files/image214.wmz" o:title=""/> |
| 5103 |
</v:shape><![endif]--><![if !vml]><img width=17 height=24 |
| 5104 |
src="./fulldoc_files/image215.gif" v:shapes="_x0000_i1104"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5105 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1104" |
| 5106 |
DrawAspect="Content" ObjectID="_1051901274"> |
| 5107 |
</o:OLEObject> |
| 5108 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are the zonal and |
| 5109 |
meridional components of the wind stress at the sea surface. Similarly, |
| 5110 |
buoyancy forcing at the sea surface induce forcing terms in the temperature and |
| 5111 |
salinity equations:<o:p></o:p></span></span></p> |
| 5112 |
|
| 5113 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5114 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5115 |
|
| 5116 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5117 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5118 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1105" |
| 5119 |
type="#_x0000_t75" style='width:83.25pt;height:35.25pt' o:ole="" fillcolor="window"> |
| 5120 |
<v:imagedata src="./fulldoc_files/image216.wmz" o:title=""/> |
| 5121 |
</v:shape><![endif]--><![if !vml]><img width=111 height=47 |
| 5122 |
src="./fulldoc_files/image217.gif" v:shapes="_x0000_i1105"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5123 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1105" |
| 5124 |
DrawAspect="Content" ObjectID="_1051901276"> |
| 5125 |
</o:OLEObject> |
| 5126 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 5127 |
</span><span style="mso-spacerun: |
| 5128 |
yes"> </span>(1.7.3)<o:p></o:p></span></span></p> |
| 5129 |
|
| 5130 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5131 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5132 |
|
| 5133 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5134 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5135 |
id="_x0000_i1106" type="#_x0000_t75" style='width:17.25pt;height:18.75pt' |
| 5136 |
o:ole="" fillcolor="window"> |
| 5137 |
<v:imagedata src="./fulldoc_files/image218.wmz" o:title=""/> |
| 5138 |
</v:shape><![endif]--><![if !vml]><img width=23 height=25 |
| 5139 |
src="./fulldoc_files/image219.gif" v:shapes="_x0000_i1106"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5140 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1106" |
| 5141 |
DrawAspect="Content" ObjectID="_1051901277"> |
| 5142 |
</o:OLEObject> |
| 5143 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the specific heat |
| 5144 |
of the ocean and <i style='mso-bidi-font-style:normal'>Q</i> the heat flux such |
| 5145 |
that:<o:p></o:p></span></span></p> |
| 5146 |
|
| 5147 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5148 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5149 |
|
| 5150 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5151 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5152 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1107" |
| 5153 |
type="#_x0000_t75" style='width:69.75pt;height:18pt' o:ole="" fillcolor="window"> |
| 5154 |
<v:imagedata src="./fulldoc_files/image220.wmz" o:title=""/> |
| 5155 |
</v:shape><![endif]--><![if !vml]><img width=93 height=24 |
| 5156 |
src="./fulldoc_files/image221.gif" v:shapes="_x0000_i1107"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5157 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1107" |
| 5158 |
DrawAspect="Content" ObjectID="_1051901278"> |
| 5159 |
</o:OLEObject> |
| 5160 |
</xml><![endif]--><span style="mso-spacerun: |
| 5161 |
yes"> </span>(1.7.4)<o:p></o:p></span></span></p> |
| 5162 |
|
| 5163 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5164 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5165 |
|
| 5166 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5167 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5168 |
id="_x0000_i1108" type="#_x0000_t75" style='width:15.75pt;height:18pt' o:ole="" |
| 5169 |
fillcolor="window"> |
| 5170 |
<v:imagedata src="./fulldoc_files/image222.wmz" o:title=""/> |
| 5171 |
</v:shape><![endif]--><![if !vml]><img width=21 height=24 |
| 5172 |
src="./fulldoc_files/image223.gif" v:shapes="_x0000_i1108"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5173 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1108" |
| 5174 |
DrawAspect="Content" ObjectID="_1051901279"> |
| 5175 |
</o:OLEObject> |
| 5176 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the air-sea heat |
| 5177 |
flux. Similarly:<o:p></o:p></span></span></p> |
| 5178 |
|
| 5179 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5180 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5181 |
|
| 5182 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5183 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5184 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1109" |
| 5185 |
type="#_x0000_t75" style='width:42.75pt;height:30.75pt' o:ole="" fillcolor="window"> |
| 5186 |
<v:imagedata src="./fulldoc_files/image224.wmz" o:title=""/> |
| 5187 |
</v:shape><![endif]--><![if !vml]><img width=57 height=41 |
| 5188 |
src="./fulldoc_files/image225.gif" v:shapes="_x0000_i1109"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5189 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1109" |
| 5190 |
DrawAspect="Content" ObjectID="_1051901280"> |
| 5191 |
</o:OLEObject> |
| 5192 |
</xml><![endif]--><span style="mso-spacerun: |
| 5193 |
yes"> </span>(1.7.5)<o:p></o:p></span></span></p> |
| 5194 |
|
| 5195 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5196 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5197 |
|
| 5198 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5199 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <i |
| 5200 |
style='mso-bidi-font-style:normal'>e</i> is the freshwater flux such that:<o:p></o:p></span></span></p> |
| 5201 |
|
| 5202 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5203 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5204 |
|
| 5205 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5206 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5207 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1110" |
| 5208 |
type="#_x0000_t75" style='width:108.75pt;height:18.75pt' o:ole="" fillcolor="window"> |
| 5209 |
<v:imagedata src="./fulldoc_files/image226.wmz" o:title=""/> |
| 5210 |
</v:shape><![endif]--><![if !vml]><img width=145 height=25 |
| 5211 |
src="./fulldoc_files/image227.gif" v:shapes="_x0000_i1110"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5212 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1110" |
| 5213 |
DrawAspect="Content" ObjectID="_1051901281"> |
| 5214 |
</o:OLEObject> |
| 5215 |
</xml><![endif]--><span style="mso-spacerun: |
| 5216 |
yes"> </span>(1.7.6)<o:p></o:p></span></span></p> |
| 5217 |
|
| 5218 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5219 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5220 |
|
| 5221 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5222 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5223 |
id="_x0000_i1111" type="#_x0000_t75" style='width:20.25pt;height:18.75pt' |
| 5224 |
o:ole="" fillcolor="window"> |
| 5225 |
<v:imagedata src="./fulldoc_files/image228.wmz" o:title=""/> |
| 5226 |
</v:shape><![endif]--><![if !vml]><img width=27 height=25 |
| 5227 |
src="./fulldoc_files/image229.gif" v:shapes="_x0000_i1111"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5228 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1111" |
| 5229 |
DrawAspect="Content" ObjectID="_1051901283"> |
| 5230 |
</o:OLEObject> |
| 5231 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is a (constant) |
| 5232 |
reference salinity and <i style='mso-bidi-font-style:normal'>E</i> and <i |
| 5233 |
style='mso-bidi-font-style:normal'>P</i> are the evaporation and precipitation |
| 5234 |
rates, respectively. Often, the heat and freshwater fluxes at the sea surface |
| 5235 |
are parameterized by restoring the surface temperature and salinity to observed |
| 5236 |
values. In this case, terms of the form <sub><!--[if gte vml 1]><v:shape id="_x0000_i1112" |
| 5237 |
type="#_x0000_t75" style='width:60.75pt;height:18pt' o:ole="" fillcolor="window"> |
| 5238 |
<v:imagedata src="./fulldoc_files/image230.wmz" o:title=""/> |
| 5239 |
</v:shape><![endif]--><![if !vml]><img width=81 height=24 |
| 5240 |
src="./fulldoc_files/image231.gif" v:shapes="_x0000_i1112"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5241 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1112" |
| 5242 |
DrawAspect="Content" ObjectID="_1051901284"> |
| 5243 |
</o:OLEObject> |
| 5244 |
</xml><![endif]-->, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1113" type="#_x0000_t75" |
| 5245 |
style='width:62.25pt;height:18pt' o:ole="" fillcolor="window"> |
| 5246 |
<v:imagedata src="./fulldoc_files/image232.wmz" o:title=""/> |
| 5247 |
</v:shape><![endif]--><![if !vml]><img width=83 height=24 |
| 5248 |
src="./fulldoc_files/image233.gif" v:shapes="_x0000_i1113"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5249 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1113" |
| 5250 |
DrawAspect="Content" ObjectID="_1051901285"> |
| 5251 |
</o:OLEObject> |
| 5252 |
</xml><![endif]-->, where <sub><!--[if gte vml 1]><v:shape id="_x0000_i1114" |
| 5253 |
type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole="" fillcolor="window"> |
| 5254 |
<v:imagedata src="./fulldoc_files/image234.wmz" o:title=""/> |
| 5255 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 5256 |
src="./fulldoc_files/image235.gif" v:shapes="_x0000_i1114"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5257 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1114" |
| 5258 |
DrawAspect="Content" ObjectID="_1051901286"> |
| 5259 |
</o:OLEObject> |
| 5260 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and <sub><!--[if gte vml 1]><v:shape |
| 5261 |
id="_x0000_i1115" type="#_x0000_t75" style='width:15.75pt;height:18pt' o:ole="" |
| 5262 |
fillcolor="window"> |
| 5263 |
<v:imagedata src="./fulldoc_files/image236.wmz" o:title=""/> |
| 5264 |
</v:shape><![endif]--><![if !vml]><img width=21 height=24 |
| 5265 |
src="./fulldoc_files/image237.gif" v:shapes="_x0000_i1115"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5266 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1115" |
| 5267 |
DrawAspect="Content" ObjectID="_1051901287"> |
| 5268 |
</o:OLEObject> |
| 5269 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are relaxation |
| 5270 |
time-scale constants, are added to, or replace, the surface terms in equations |
| 5271 |
(1.7.3) and (1.7.5).<o:p></o:p></span></span></p> |
| 5272 |
|
| 5273 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5274 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5275 |
|
| 5276 |
<h3><span style='mso-bookmark:_Toc407078231'><a name="_Toc407078230"></a><a |
| 5277 |
name="_Toc407090384"></a><a name="_Toc407090587"></a><a name="_Toc407169616"><span |
| 5278 |
style='mso-bookmark:_Toc407090587'><span style='mso-bookmark:_Toc407090384'><span |
| 5279 |
style='mso-bookmark:_Toc407078230'><u>1.7.2 Dissipation</u></span></span></span></a><u><o:p></o:p></u></span></h3> |
| 5280 |
|
| 5281 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5282 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5283 |
|
| 5284 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5285 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 5286 |
forms of friction available in the model for momentum are Laplacian and |
| 5287 |
biharmonic frictions:<o:p></o:p></span></span></p> |
| 5288 |
|
| 5289 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5290 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5291 |
|
| 5292 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5293 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5294 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1116" |
| 5295 |
type="#_x0000_t75" style='width:153pt;height:33pt' o:ole="" fillcolor="window"> |
| 5296 |
<v:imagedata src="./fulldoc_files/image238.wmz" o:title=""/> |
| 5297 |
</v:shape><![endif]--><![if !vml]><img width=204 height=44 |
| 5298 |
src="./fulldoc_files/image239.gif" v:shapes="_x0000_i1116"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5299 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1116" |
| 5300 |
DrawAspect="Content" ObjectID="_1051901288"> |
| 5301 |
</o:OLEObject> |
| 5302 |
</xml><![endif]--><a name="_Hlt406563553"></a><span style="mso-spacerun: |
| 5303 |
yes"> </span>(1.7.7)<o:p></o:p></span></span></p> |
| 5304 |
|
| 5305 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5306 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5307 |
|
| 5308 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5309 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5310 |
id="_x0000_i1117" type="#_x0000_t75" style='width:14.25pt;height:18pt' o:ole="" |
| 5311 |
fillcolor="window"> |
| 5312 |
<v:imagedata src="./fulldoc_files/image240.wmz" o:title=""/> |
| 5313 |
</v:shape><![endif]--><![if !vml]><img width=19 height=24 |
| 5314 |
src="./fulldoc_files/image241.gif" v:shapes="_x0000_i1117"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5315 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1117" |
| 5316 |
DrawAspect="Content" ObjectID="_1051901290"> |
| 5317 |
</o:OLEObject> |
| 5318 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and <sub><!--[if gte vml 1]><v:shape |
| 5319 |
id="_x0000_i1118" type="#_x0000_t75" style='width:14.25pt;height:18pt' o:ole="" |
| 5320 |
fillcolor="window"> |
| 5321 |
<v:imagedata src="./fulldoc_files/image242.wmz" o:title=""/> |
| 5322 |
</v:shape><![endif]--><![if !vml]><img width=19 height=24 |
| 5323 |
src="./fulldoc_files/image243.gif" v:shapes="_x0000_i1118"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5324 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1118" |
| 5325 |
DrawAspect="Content" ObjectID="_1051901291"> |
| 5326 |
</o:OLEObject> |
| 5327 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are (constant) |
| 5328 |
horizontal and vertical viscosity coefficients and <sub><!--[if gte vml 1]><v:shape |
| 5329 |
id="_x0000_i1119" type="#_x0000_t75" style='width:14.25pt;height:17.25pt' |
| 5330 |
o:ole="" fillcolor="window"> |
| 5331 |
<v:imagedata src="./fulldoc_files/image244.wmz" o:title=""/> |
| 5332 |
</v:shape><![endif]--><![if !vml]><img width=19 height=23 |
| 5333 |
src="./fulldoc_files/image245.gif" v:shapes="_x0000_i1119"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5334 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1119" |
| 5335 |
DrawAspect="Content" ObjectID="_1051901292"> |
| 5336 |
</o:OLEObject> |
| 5337 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the horizontal |
| 5338 |
coefficient for biharmonic friction. These coefficients are the same for all |
| 5339 |
velocity components.<o:p></o:p></span></span></p> |
| 5340 |
|
| 5341 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5342 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5343 |
|
| 5344 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5345 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 5346 |
dissipation terms for the temperature and salinity equations have a similar |
| 5347 |
form except that the diffusion tensor can be non diagonal and have varying |
| 5348 |
coefficients (see appendix on the parameterization of eddy fluxes of heat and |
| 5349 |
salt).<o:p></o:p></span></span></p> |
| 5350 |
|
| 5351 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5352 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5353 |
|
| 5354 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5355 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5356 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1120" |
| 5357 |
type="#_x0000_t75" style='width:167.25pt;height:20.25pt' o:ole="" fillcolor="window"> |
| 5358 |
<v:imagedata src="./fulldoc_files/image246.wmz" o:title=""/> |
| 5359 |
</v:shape><![endif]--><![if !vml]><img width=223 height=27 |
| 5360 |
src="./fulldoc_files/image247.gif" v:shapes="_x0000_i1120"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5361 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1120" |
| 5362 |
DrawAspect="Content" ObjectID="_1051901293"> |
| 5363 |
</o:OLEObject> |
| 5364 |
</xml><![endif]--><span style="mso-spacerun: |
| 5365 |
yes"> </span>(1.7.8)<o:p></o:p></span></span></p> |
| 5366 |
|
| 5367 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5368 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5369 |
|
| 5370 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5371 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5372 |
id="_x0000_i1121" type="#_x0000_t75" style='width:14.25pt;height:18.75pt' |
| 5373 |
o:ole="" fillcolor="window"> |
| 5374 |
<v:imagedata src="./fulldoc_files/image248.wmz" o:title=""/> |
| 5375 |
</v:shape><![endif]--><![if !vml]><img width=19 height=25 |
| 5376 |
src="./fulldoc_files/image249.gif" v:shapes="_x0000_i1121"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5377 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1121" |
| 5378 |
DrawAspect="Content" ObjectID="_1051901294"> |
| 5379 |
</o:OLEObject> |
| 5380 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the diffusion |
| 5381 |
tensor and <sub><!--[if gte vml 1]><v:shape id="_x0000_i1122" type="#_x0000_t75" |
| 5382 |
style='width:17.25pt;height:17.25pt' o:ole="" fillcolor="window"> |
| 5383 |
<v:imagedata src="./fulldoc_files/image250.wmz" o:title=""/> |
| 5384 |
</v:shape><![endif]--><![if !vml]><img width=23 height=23 |
| 5385 |
src="./fulldoc_files/image251.gif" v:shapes="_x0000_i1122"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5386 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1122" |
| 5387 |
DrawAspect="Content" ObjectID="_1051901295"> |
| 5388 |
</o:OLEObject> |
| 5389 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>the horizontal |
| 5390 |
coefficient for biharmonic diffusion. In the simplest case where the |
| 5391 |
subgrid-scale fluxes of heat and salt are parameterized with constant |
| 5392 |
horizontal and vertical diffusion coefficients, <sub><!--[if gte vml 1]><v:shape |
| 5393 |
id="_x0000_i1123" type="#_x0000_t75" style='width:14.25pt;height:18.75pt' |
| 5394 |
o:ole="" fillcolor="window"> |
| 5395 |
<v:imagedata src="./fulldoc_files/image248.wmz" o:title=""/> |
| 5396 |
</v:shape><![endif]--><![if !vml]><img width=19 height=25 |
| 5397 |
src="./fulldoc_files/image252.gif" v:shapes="_x0000_i1123"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5398 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1123" |
| 5399 |
DrawAspect="Content" ObjectID="_1051901297"> |
| 5400 |
</o:OLEObject> |
| 5401 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is reduced to a |
| 5402 |
diagonal matrix with constant coefficients:<o:p></o:p></span></span></p> |
| 5403 |
|
| 5404 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5405 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5406 |
|
| 5407 |
<p class=MsoNormal align=right style='text-align:right'><span style='mso-bookmark: |
| 5408 |
_Toc407078231'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5409 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1124" |
| 5410 |
type="#_x0000_t75" style='width:104.25pt;height:56.25pt' o:ole="" fillcolor="window"> |
| 5411 |
<v:imagedata src="./fulldoc_files/image253.wmz" o:title=""/> |
| 5412 |
</v:shape><![endif]--><![if !vml]><img width=139 height=75 |
| 5413 |
src="./fulldoc_files/image254.gif" v:shapes="_x0000_i1124"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5414 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1124" |
| 5415 |
DrawAspect="Content" ObjectID="_1051901298"> |
| 5416 |
</o:OLEObject> |
| 5417 |
</xml><![endif]--><span style="mso-spacerun: |
| 5418 |
yes"> </span>(1.7.9)<o:p></o:p></span></span></p> |
| 5419 |
|
| 5420 |
<p class=MsoNormal><span style='mso-bookmark:_Toc407078231'><span |
| 5421 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 5422 |
|
| 5423 |
<p class=MsoNormal style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><span |
| 5424 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 5425 |
id="_x0000_i1125" type="#_x0000_t75" style='width:17.25pt;height:18pt' o:ole="" |
| 5426 |
fillcolor="window"> |
| 5427 |
<v:imagedata src="./fulldoc_files/image255.wmz" o:title=""/> |
| 5428 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 5429 |
src="./fulldoc_files/image256.gif" v:shapes="_x0000_i1125"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5430 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1125" |
| 5431 |
DrawAspect="Content" ObjectID="_1051901299"> |
| 5432 |
</o:OLEObject> |
| 5433 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and <sub><!--[if gte vml 1]><v:shape |
| 5434 |
id="_x0000_i1126" type="#_x0000_t75" style='width:17.25pt;height:18pt' o:ole="" |
| 5435 |
fillcolor="window"> |
| 5436 |
<v:imagedata src="./fulldoc_files/image257.wmz" o:title=""/> |
| 5437 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 5438 |
src="./fulldoc_files/image258.gif" v:shapes="_x0000_i1126"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5439 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1126" |
| 5440 |
DrawAspect="Content" ObjectID="_1051901300"> |
| 5441 |
</o:OLEObject> |
| 5442 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are the horizontal |
| 5443 |
and vertical diffusion coefficients. Different values for temperature and |
| 5444 |
salinity can be specified. More physically-based parameterizations, such as |
| 5445 |
Gent-McWilliams - GM - or Green-Stone - GS -, are variants on (1.7.8), (1.7.9) |
| 5446 |
and are described in the appendix.<o:p></o:p></span></span></p> |
| 5447 |
|
| 5448 |
</div> |
| 5449 |
|
| 5450 |
<span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino; |
| 5451 |
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; |
| 5452 |
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br |
| 5453 |
clear=all style='page-break-before:always;mso-break-type:section-break'> |
| 5454 |
</span> |
| 5455 |
|
| 5456 |
<div class=Section3> |
| 5457 |
|
| 5458 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 5459 |
|
| 5460 |
<h1 style='text-align:justify'><span style='mso-bookmark:_Toc407078231'><a |
| 5461 |
name="_Toc407090385"></a><a name="_Toc407090588"></a><a name="_Toc407169617"><span |
| 5462 |
style='mso-bookmark:_Toc407090588'><span style='mso-bookmark:_Toc407090385'>CHAPTER |
| 5463 |
2 Discrete formulation.</span></span></a></span></h1> |
| 5464 |
|
| 5465 |
</div> |
| 5466 |
|
| 5467 |
<p class=MsoBodyText><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 5468 |
|
| 5469 |
<p class=MsoBodyText><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 5470 |
|
| 5471 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5472 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 5473 |
continuum equations employed are discretized using a finite volume strategy. In |
| 5474 |
this approach the domain to be simulated is divided into cells and the |
| 5475 |
evolution of the fluid is simulated, by stepping forward discrete forms of the |
| 5476 |
Navier-Stokes equations integrated over these cells. In the limit that the |
| 5477 |
cells have a regular cuboid structure the model is identical to a finite |
| 5478 |
difference model.<o:p></o:p></span></p> |
| 5479 |
|
| 5480 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5481 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5482 |
|
| 5483 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 5484 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The variables are stepped |
| 5485 |
forward in time using a quasi-second-order Adams-Bashforth time-stepping |
| 5486 |
scheme.<span style="mso-spacerun: yes"> </span>The pressure field, which |
| 5487 |
ensures that evolving currents remain non-divergent, is found by inversion of |
| 5488 |
Elliptic operators.<span style="mso-spacerun: yes"> </span>In <b |
| 5489 |
style='mso-bidi-font-weight:normal'>HPE</b> and <b style='mso-bidi-font-weight: |
| 5490 |
normal'>QH</b> a 2-d Elliptic problem must be inverted; in <b style='mso-bidi-font-weight: |
| 5491 |
normal'>NH</b> the elliptic problem is 3-dimensional.<span style="mso-spacerun: |
| 5492 |
yes"> </span>A major objective is to make this 3-D inversion - the overhead |
| 5493 |
of <b style='mso-bidi-font-weight:normal'>NH</b> - efficient and hence |
| 5494 |
non-hydrostatic modeling affordable.<span style="mso-spacerun: yes"> |
| 5495 |
</span>The pressure field is separated in to surface pressure,<sub><!--[if gte vml 1]><v:shape |
| 5496 |
id="_x0000_i1127" type="#_x0000_t75" style='width:15pt;height:15pt' o:ole=""> |
| 5497 |
<v:imagedata src="./fulldoc_files/image259.wmz" o:title=""/> |
| 5498 |
</v:shape><![endif]--><![if !vml]><img width=20 height=20 |
| 5499 |
src="./fulldoc_files/image260.gif" v:shapes="_x0000_i1127"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5500 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1127" |
| 5501 |
DrawAspect="Content" ObjectID="_1051901302"> |
| 5502 |
</o:OLEObject> |
| 5503 |
</xml><![endif]-->, hydrostatic pressure, <sub><!--[if gte vml 1]><v:shape |
| 5504 |
id="_x0000_i1128" type="#_x0000_t75" style='width:21pt;height:15.75pt' o:ole=""> |
| 5505 |
<v:imagedata src="./fulldoc_files/image261.wmz" o:title=""/> |
| 5506 |
</v:shape><![endif]--><![if !vml]><img width=28 height=21 |
| 5507 |
src="./fulldoc_files/image262.gif" v:shapes="_x0000_i1128"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5508 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1128" |
| 5509 |
DrawAspect="Content" ObjectID="_1051901303"> |
| 5510 |
</o:OLEObject> |
| 5511 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and non-hydrostatic |
| 5512 |
pressure, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1129" type="#_x0000_t75" |
| 5513 |
style='width:21.75pt;height:17.25pt' o:ole=""> |
| 5514 |
<v:imagedata src="./fulldoc_files/image263.wmz" o:title=""/> |
| 5515 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 5516 |
src="./fulldoc_files/image264.gif" v:shapes="_x0000_i1129"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5517 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1129" |
| 5518 |
DrawAspect="Content" ObjectID="_1051901304"> |
| 5519 |
</o:OLEObject> |
| 5520 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and the component |
| 5521 |
parts found sequentially.<span style="mso-spacerun: yes"> </span>In the 3-D |
| 5522 |
inversion for <sub><!--[if gte vml 1]><v:shape id="_x0000_i1130" type="#_x0000_t75" |
| 5523 |
style='width:21.75pt;height:17.25pt' o:ole=""> |
| 5524 |
<v:imagedata src="./fulldoc_files/image263.wmz" o:title=""/> |
| 5525 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 5526 |
src="./fulldoc_files/image265.gif" v:shapes="_x0000_i1130"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5527 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1130" |
| 5528 |
DrawAspect="Content" ObjectID="_1051901305"> |
| 5529 |
</o:OLEObject> |
| 5530 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>a preconditioner is |
| 5531 |
used which, in the hydrostatic limit, is an exact integral of the Elliptic |
| 5532 |
operator, and so leads to an algorithm that seamlessly moves from |
| 5533 |
non-hydrostatic to hydrostatic limits.<span style="mso-spacerun: yes"> |
| 5534 |
</span>Thus, in the hydrostatic limit, the <b style='mso-bidi-font-weight:normal'>NH</b> |
| 5535 |
is fast, competitive with the fastest ocean climate models in use today based |
| 5536 |
on the <b style='mso-bidi-font-weight:normal'>HPEs</b>.<span |
| 5537 |
style="mso-spacerun: yes"> </span>But as the resolution is increased the model |
| 5538 |
dynamics asymptotes smoothly to the Navier Stokes equations.<span |
| 5539 |
style='text-transform:uppercase'><o:p></o:p></span></span></p> |
| 5540 |
|
| 5541 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 5542 |
|
| 5543 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 5544 |
|
| 5545 |
<h2 style='text-align:justify'><a name="_Toc407078232"></a><a |
| 5546 |
name="_Toc407090386"></a><a name="_Toc407090589"></a><a name="_Toc407169618"><span |
| 5547 |
style='mso-bookmark:_Toc407090589'><span style='mso-bookmark:_Toc407090386'><span |
| 5548 |
style='mso-bookmark:_Toc407078232'>2.1 Temporal discretization.</span></span></span></a></h2> |
| 5549 |
|
| 5550 |
<p class=MsoBodyText style='margin-left:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 5551 |
|
| 5552 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5553 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>We |
| 5554 |
write (1.1.1</span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5555 |
font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 5556 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 5557 |
symbol;mso-symbol-font-family:Symbol'>®</span></span><span style='font-size: |
| 5558 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>1.1.4) in semi-discrete |
| 5559 |
form to second order in the time step </span><i style='mso-bidi-font-style: |
| 5560 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 5561 |
Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 5562 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 5563 |
symbol;mso-symbol-font-family:Symbol'>D</span></span></i><i style='mso-bidi-font-style: |
| 5564 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 5565 |
Palatino'>t</span></i><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5566 |
font-family:Palatino'> in which, as yet, only time is discretized, and using |
| 5567 |
the notation of chapter 1 (see Fig.3):<o:p></o:p></span></p> |
| 5568 |
|
| 5569 |
<p class=MsoBodyText style='margin-left:0pt'><span style='font-size:12.0pt; |
| 5570 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5571 |
|
| 5572 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 5573 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5574 |
id="_x0000_i1131" type="#_x0000_t75" style='width:228pt;height:35.25pt' o:ole=""> |
| 5575 |
<v:imagedata src="./fulldoc_files/image266.wmz" o:title=""/> |
| 5576 |
</v:shape><![endif]--><![if !vml]><img width=304 height=47 |
| 5577 |
src="./fulldoc_files/image267.gif" v:shapes="_x0000_i1131"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5578 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1131" |
| 5579 |
DrawAspect="Content" ObjectID="_1051901306"> |
| 5580 |
</o:OLEObject> |
| 5581 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 5582 |
</span>(2.1.1)<o:p></o:p></span></p> |
| 5583 |
|
| 5584 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5585 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5586 |
|
| 5587 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 5588 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5589 |
id="_x0000_i1132" type="#_x0000_t75" style='width:135.75pt;height:42.75pt' |
| 5590 |
o:ole=""> |
| 5591 |
<v:imagedata src="./fulldoc_files/image268.wmz" o:title=""/> |
| 5592 |
</v:shape><![endif]--><![if !vml]><img width=181 height=57 |
| 5593 |
src="./fulldoc_files/image269.gif" v:shapes="_x0000_i1132"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5594 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1132" |
| 5595 |
DrawAspect="Content" ObjectID="_1051901308"> |
| 5596 |
</o:OLEObject> |
| 5597 |
</xml><![endif]--><span style="mso-spacerun: |
| 5598 |
yes"> </span>(2.1.2)<o:p></o:p></span></p> |
| 5599 |
|
| 5600 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5601 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5602 |
|
| 5603 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 5604 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5605 |
id="_x0000_i1133" type="#_x0000_t75" style='width:105pt;height:33pt' o:ole=""> |
| 5606 |
<v:imagedata src="./fulldoc_files/image270.wmz" o:title=""/> |
| 5607 |
</v:shape><![endif]--><![if !vml]><img width=140 height=44 |
| 5608 |
src="./fulldoc_files/image271.gif" v:shapes="_x0000_i1133"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5609 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1133" |
| 5610 |
DrawAspect="Content" ObjectID="_1051901309"> |
| 5611 |
</o:OLEObject> |
| 5612 |
</xml><![endif]--><span style="mso-spacerun: |
| 5613 |
yes"> </span><span |
| 5614 |
style="mso-spacerun: yes"> </span>(2.1.3)<o:p></o:p></span></p> |
| 5615 |
|
| 5616 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5617 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5618 |
|
| 5619 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 5620 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5621 |
id="_x0000_i1824" type="#_x0000_t75" style='width:141.75pt;height:42.75pt' |
| 5622 |
o:ole=""> |
| 5623 |
<v:imagedata src="./fulldoc_files/image272.wmz" o:title=""/> |
| 5624 |
</v:shape><![endif]--><![if !vml]><img width=189 height=57 |
| 5625 |
src="./fulldoc_files/image273.gif" v:shapes="_x0000_i1824"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5626 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1824" |
| 5627 |
DrawAspect="Content" ObjectID="_1051901310"> |
| 5628 |
</o:OLEObject> |
| 5629 |
</xml><![endif]--><span style="mso-spacerun: |
| 5630 |
yes"> </span>(2.1.4)<o:p></o:p></span></p> |
| 5631 |
|
| 5632 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5633 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5634 |
|
| 5635 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5636 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In |
| 5637 |
(2.1.1), we employ a tracer parameter <i style='mso-bidi-font-style:normal'>q</i> |
| 5638 |
which takes on the value zero in the <b style='mso-bidi-font-weight:normal'>HPEs</b> |
| 5639 |
and <b style='mso-bidi-font-weight:normal'>QH</b>, and the value unity in <b |
| 5640 |
style='mso-bidi-font-weight:normal'>NH</b>.<o:p></o:p></span></p> |
| 5641 |
|
| 5642 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5643 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5644 |
|
| 5645 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5646 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Given |
| 5647 |
that the <sub><!--[if gte vml 1]><v:shape id="_x0000_i1825" type="#_x0000_t75" |
| 5648 |
style='width:12.75pt;height:14.25pt' o:ole=""> |
| 5649 |
<v:imagedata src="./fulldoc_files/image274.wmz" o:title=""/> |
| 5650 |
</v:shape><![endif]--><![if !vml]><img width=17 height=19 |
| 5651 |
src="./fulldoc_files/image275.gif" v:shapes="_x0000_i1825"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5652 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1825" |
| 5653 |
DrawAspect="Content" ObjectID="_1051901311"> |
| 5654 |
</o:OLEObject> |
| 5655 |
</xml><![endif]-->s are known at time level <i style='mso-bidi-font-style: |
| 5656 |
normal'>n</i>, an accurate explicit form for the time-stepping which involves |
| 5657 |
just two time levels is the Adams-Bashforth method (AB2) which makes use of |
| 5658 |
time-levels <i style='mso-bidi-font-style:normal'>n</i> and <i |
| 5659 |
style='mso-bidi-font-style:normal'>n</i>-1 thus:<o:p></o:p></span></p> |
| 5660 |
|
| 5661 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5662 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5663 |
|
| 5664 |
<p class=MsoBodyText align=right style='text-align:right'><span |
| 5665 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5666 |
id="_x0000_i1134" type="#_x0000_t75" style='width:195pt;height:35.25pt' o:ole=""> |
| 5667 |
<v:imagedata src="./fulldoc_files/image276.wmz" o:title=""/> |
| 5668 |
</v:shape><![endif]--><![if !vml]><img width=260 height=47 |
| 5669 |
src="./fulldoc_files/image277.gif" v:shapes="_x0000_i1134"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5670 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1134" |
| 5671 |
DrawAspect="Content" ObjectID="_1051901313"> |
| 5672 |
</o:OLEObject> |
| 5673 |
</xml><![endif]--><span style="mso-spacerun: |
| 5674 |
yes"> </span>(2.1.5)<o:p></o:p></span></p> |
| 5675 |
|
| 5676 |
<p class=MsoBodyText style='margin-left:0pt'><span style='font-size:12.0pt; |
| 5677 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5678 |
|
| 5679 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5680 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>AB2 is |
| 5681 |
a linear extrapolation in time to a point that is just, by an amount </span><i |
| 5682 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 5683 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 5684 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 5685 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>e</span></span></i><span |
| 5686 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>, on |
| 5687 |
the <i style='mso-bidi-font-style:normal'>n</i>+1 side of the mid-point<sub><!--[if gte vml 1]><v:shape |
| 5688 |
id="_x0000_i1135" type="#_x0000_t75" style='width:21.75pt;height:27pt' o:ole="" |
| 5689 |
fillcolor="window"> |
| 5690 |
<v:imagedata src="./fulldoc_files/image278.wmz" o:title=""/> |
| 5691 |
</v:shape><![endif]--><![if !vml]><img width=29 height=36 |
| 5692 |
src="./fulldoc_files/image279.gif" v:shapes="_x0000_i1135"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5693 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1135" |
| 5694 |
DrawAspect="Content" ObjectID="_1051901314"> |
| 5695 |
</o:OLEObject> |
| 5696 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>AB2 has the |
| 5697 |
advantage of being quasi-second-order in time. A computational mode exists but |
| 5698 |
is damped by the </span><i style='mso-bidi-font-style:normal'><span |
| 5699 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 5700 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 5701 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 5702 |
mso-symbol-font-family:Symbol'>e</span></span></i><span style='font-size:12.0pt; |
| 5703 |
mso-bidi-font-size:10.0pt;font-family:Palatino'> factor.<span |
| 5704 |
style="mso-spacerun: yes"> </span>Furthermore it can be implemented by |
| 5705 |
evaluating the <b style='mso-bidi-font-weight:normal'>G</b>s only once and |
| 5706 |
storing them for use on the next time-step. The code is written in a |
| 5707 |
sufficiently flexible manner that other time-stepping schemes could be readily |
| 5708 |
implemented.<o:p></o:p></span></p> |
| 5709 |
|
| 5710 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5711 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5712 |
|
| 5713 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5714 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 5715 |
time-step is limited by the following condition (see for example Potter, 1976; |
| 5716 |
p.69):<o:p></o:p></span></p> |
| 5717 |
|
| 5718 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5719 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5720 |
|
| 5721 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 5722 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5723 |
id="_x0000_i1136" type="#_x0000_t75" style='width:48.75pt;height:33pt' o:ole=""> |
| 5724 |
<v:imagedata src="./fulldoc_files/image280.wmz" o:title=""/> |
| 5725 |
</v:shape><![endif]--><![if !vml]><img width=65 height=44 |
| 5726 |
src="./fulldoc_files/image281.gif" v:shapes="_x0000_i1136"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5727 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1136" |
| 5728 |
DrawAspect="Content" ObjectID="_1051901315"> |
| 5729 |
</o:OLEObject> |
| 5730 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>if <sub><!--[if gte vml 1]><v:shape |
| 5731 |
id="_x0000_i1137" type="#_x0000_t75" style='width:116.25pt;height:32.25pt' |
| 5732 |
o:ole=""> |
| 5733 |
<v:imagedata src="./fulldoc_files/image282.wmz" o:title=""/> |
| 5734 |
</v:shape><![endif]--><![if !vml]><img width=155 height=43 |
| 5735 |
src="./fulldoc_files/image283.gif" v:shapes="_x0000_i1137"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5736 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1137" |
| 5737 |
DrawAspect="Content" ObjectID="_1051901317"> |
| 5738 |
</o:OLEObject> |
| 5739 |
</xml><![endif]--><o:p></o:p></span></p> |
| 5740 |
|
| 5741 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5742 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5743 |
|
| 5744 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 5745 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where <b style='mso-bidi-font-weight: |
| 5746 |
normal'>v</b> is the fastest propagation velocity anywhere on the mesh of size </span><span |
| 5747 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 5748 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 5749 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 5750 |
mso-symbol-font-family:Symbol'>D</span></span><span style='font-size:12.0pt; |
| 5751 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>.<span style="mso-spacerun: |
| 5752 |
yes"> </span>Typically we set </span><i style='mso-bidi-font-style:normal'><span |
| 5753 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 5754 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 5755 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 5756 |
mso-symbol-font-family:Symbol'>e</span></span></i><b style='mso-bidi-font-weight: |
| 5757 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 5758 |
Palatino'> </span></b><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5759 |
font-family:Palatino'>to a value of 0.1.<span style="mso-spacerun: yes"> |
| 5760 |
</span>It should be noted that if </span><i style='mso-bidi-font-style:normal'><span |
| 5761 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 5762 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 5763 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 5764 |
mso-symbol-font-family:Symbol'>e</span></span></i><span style='font-size:12.0pt; |
| 5765 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>=0 then<b style='mso-bidi-font-weight: |
| 5766 |
normal'> </b>AB2 is unstable in the inviscid case.<o:p></o:p></span></p> |
| 5767 |
|
| 5768 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5769 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5770 |
|
| 5771 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 5772 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 5773 |
prognostic and diagnostic steps of our calculation in <b style='mso-bidi-font-weight: |
| 5774 |
normal'>HPE</b>, <b style='mso-bidi-font-weight:normal'>QH</b> and <b |
| 5775 |
style='mso-bidi-font-weight:normal'>NH</b> are outlined in the schematic |
| 5776 |
diagram below - Fig.4.<span style="mso-spacerun: yes"> </span>We now go on to |
| 5777 |
describe the spatial discretization employed and, in section 2.3, our Elliptic |
| 5778 |
inversion procedure.<o:p></o:p></span></p> |
| 5779 |
|
| 5780 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5781 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5782 |
|
| 5783 |
<div style='mso-element:frame;mso-element-frame-width:407.45pt;mso-element-frame-height: |
| 5784 |
324.05pt;mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5785 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'> |
| 5786 |
|
| 5787 |
<table cellspacing=0 cellpadding=0 hspace=0 vspace=0 width=555 height=432 |
| 5788 |
align=left> |
| 5789 |
<tr> |
| 5790 |
<td valign=top align=left height=432 style='padding-top:0pt;padding-right: |
| 5791 |
9.0pt;padding-bottom:0pt;padding-left:9.0pt'> |
| 5792 |
<div style='border:solid windowtext .75pt;padding:1.0pt 1.0pt 1.0pt 1.0pt'> |
| 5793 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5794 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5795 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5796 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5797 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5798 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5799 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5800 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5801 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5802 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5803 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><!--[if gte vml 1]><v:rect |
| 5804 |
id="_x0000_s1029" style='position:absolute;left:0;text-align:left; |
| 5805 |
margin-left:104.8pt;margin-top:10.35pt;width:259.25pt;height:50.45pt; |
| 5806 |
z-index:1;mso-position-horizontal-relative:text; |
| 5807 |
mso-position-vertical-relative:text' o:allowincell="f" filled="f"/><![endif]--><![if !vml]><span |
| 5808 |
style='mso-ignore:vglayout'> |
| 5809 |
<table cellpadding=0 cellspacing=0 align=left> |
| 5810 |
<tr> |
| 5811 |
<td width=140 height=14></td> |
| 5812 |
</tr> |
| 5813 |
<tr> |
| 5814 |
<td></td> |
| 5815 |
<td><img width=346 height=68 src="./fulldoc_files/image284.gif" v:shapes="_x0000_s1029"></td> |
| 5816 |
</tr> |
| 5817 |
</table> |
| 5818 |
</span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5819 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5820 |
<br style='mso-ignore:vglayout' clear=ALL> |
| 5821 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5822 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5823 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5824 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5825 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5826 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 5827 |
style="mso-spacerun: yes"> </span></span><span |
| 5828 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1139" |
| 5829 |
type="#_x0000_t75" style='width:126.75pt;height:30.75pt' o:ole=""> |
| 5830 |
<v:imagedata src="./fulldoc_files/image285.wmz" o:title=""/> |
| 5831 |
</v:shape><![endif]--><![if !vml]><img width=169 height=41 |
| 5832 |
src="./fulldoc_files/image286.gif" v:shapes="_x0000_i1139"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5833 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1139" |
| 5834 |
DrawAspect="Content" ObjectID="_1051901318"> |
| 5835 |
</o:OLEObject> |
| 5836 |
</xml><![endif]--></span><span style='font-size:12.0pt;mso-bidi-font-size: |
| 5837 |
10.0pt;font-family:Palatino'>;<span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 5838 |
id="_x0000_i1140" type="#_x0000_t75" style='width:95.25pt;height:36pt' |
| 5839 |
o:ole=""> |
| 5840 |
<v:imagedata src="./fulldoc_files/image287.wmz" o:title=""/> |
| 5841 |
</v:shape><![endif]--><![if !vml]><img width=127 height=48 |
| 5842 |
src="./fulldoc_files/image288.gif" v:shapes="_x0000_i1140"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5843 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1140" |
| 5844 |
DrawAspect="Content" ObjectID="_1051901319"> |
| 5845 |
</o:OLEObject> |
| 5846 |
</xml><![endif]--><span style='mso-tab-count:1'> </span><o:p></o:p></span></p> |
| 5847 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5848 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5849 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5850 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5851 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><!--[if gte vml 1]><v:line |
| 5852 |
id="_x0000_s1030" style='position:absolute;left:0;text-align:left;z-index:2; |
| 5853 |
mso-position-horizontal-relative:text;mso-position-vertical-relative:text' |
| 5854 |
from="176.9pt,7.2pt" to="263.35pt,57.65pt" o:allowincell="f"> |
| 5855 |
<v:stroke startarrowwidth="narrow" startarrowlength="short" endarrow="block" |
| 5856 |
endarrowwidth="narrow" endarrowlength="short"/> |
| 5857 |
</v:line><v:line id="_x0000_s1031" style='position:absolute;left:0; |
| 5858 |
text-align:left;flip:x;z-index:3;mso-position-horizontal-relative:text; |
| 5859 |
mso-position-vertical-relative:text' from="112.1pt,7.2pt" to="176.95pt,57.65pt" |
| 5860 |
o:allowincell="f"> |
| 5861 |
<v:stroke startarrowwidth="narrow" startarrowlength="short" endarrow="block" |
| 5862 |
endarrowwidth="narrow" endarrowlength="short"/> |
| 5863 |
</v:line><![endif]--><![if !vml]><span style='mso-ignore:vglayout'> |
| 5864 |
<table cellpadding=0 cellspacing=0 align=left> |
| 5865 |
<tr> |
| 5866 |
<td width=148 height=9></td> |
| 5867 |
</tr> |
| 5868 |
<tr> |
| 5869 |
<td></td> |
| 5870 |
<td><img width=206 height=70 src="./fulldoc_files/image289.gif" v:shapes="_x0000_s1030 _x0000_s1031"></td> |
| 5871 |
</tr> |
| 5872 |
</table> |
| 5873 |
</span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 5874 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5875 |
<br style='mso-ignore:vglayout' clear=ALL> |
| 5876 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5877 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5878 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5879 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5880 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5881 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 5882 |
style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 5883 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5884 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5885 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5886 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5887 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5888 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 5889 |
style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 5890 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5891 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5892 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5893 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5894 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5895 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5896 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5897 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5898 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5899 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5900 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5901 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 5902 |
style="mso-spacerun: yes"> </span><b style='mso-bidi-font-weight: |
| 5903 |
normal'>HPE</b> and <b style='mso-bidi-font-weight:normal'>QH</b><span |
| 5904 |
style="mso-spacerun: yes"> </span><b |
| 5905 |
style='mso-bidi-font-weight:normal'>NH</b><o:p></o:p></span></p> |
| 5906 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5907 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5908 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5909 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5910 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5911 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 5912 |
style="mso-spacerun: |
| 5913 |
yes"> </span><span |
| 5914 |
style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 5915 |
id="_x0000_i1141" type="#_x0000_t75" style='width:123.75pt;height:44.25pt' |
| 5916 |
o:ole=""> |
| 5917 |
<v:imagedata src="./fulldoc_files/image290.wmz" o:title=""/> |
| 5918 |
</v:shape><![endif]--><![if !vml]><img width=165 height=59 |
| 5919 |
src="./fulldoc_files/image291.gif" v:shapes="_x0000_i1141"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5920 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1141" |
| 5921 |
DrawAspect="Content" ObjectID="_1051901320"> |
| 5922 |
</o:OLEObject> |
| 5923 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 5924 |
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| 5925 |
o:ole=""> |
| 5926 |
<v:imagedata src="./fulldoc_files/image292.wmz" o:title=""/> |
| 5927 |
</v:shape><![endif]--><![if !vml]><img width=251 height=41 |
| 5928 |
src="./fulldoc_files/image293.gif" v:shapes="_x0000_i1142"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5929 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1142" |
| 5930 |
DrawAspect="Content" ObjectID="_1051901322"> |
| 5931 |
</o:OLEObject> |
| 5932 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 5933 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5934 |
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| 5935 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5936 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5937 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5938 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5939 |
<p class=MsoNormal align=right style='margin-left:72.0pt;text-align:right; |
| 5940 |
border:none;mso-border-alt:solid windowtext .75pt;padding:0pt;mso-padding-alt: |
| 5941 |
1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame;mso-element-frame-width:407.45pt; |
| 5942 |
mso-element-frame-height:324.05pt;mso-element-frame-hspace:9.0pt;mso-element-wrap: |
| 5943 |
around;mso-element-anchor-vertical:paragraph;mso-element-anchor-horizontal: |
| 5944 |
margin;mso-element-top:4.95pt'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 5945 |
10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1143" |
| 5946 |
type="#_x0000_t75" style='width:216.75pt;height:27.75pt' o:ole="" |
| 5947 |
fillcolor="window"> |
| 5948 |
<v:imagedata src="./fulldoc_files/image294.wmz" o:title=""/> |
| 5949 |
</v:shape><![endif]--><![if !vml]><img width=289 height=37 |
| 5950 |
src="./fulldoc_files/image295.gif" v:shapes="_x0000_i1143"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5951 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1143" |
| 5952 |
DrawAspect="Content" ObjectID="_1051901323"> |
| 5953 |
</o:OLEObject> |
| 5954 |
</xml><![endif]--><sub><!--[if gte vml 1]><v:shape id="_x0000_i1144" type="#_x0000_t75" |
| 5955 |
style='width:9pt;height:15.75pt' o:ole=""> |
| 5956 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 5957 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 5958 |
src="./fulldoc_files/image296.gif" v:shapes="_x0000_i1144"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5959 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1144" |
| 5960 |
DrawAspect="Content" ObjectID="_1051901324"> |
| 5961 |
</o:OLEObject> |
| 5962 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 5963 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5964 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5965 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5966 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5967 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5968 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 5969 |
id="_x0000_i1145" type="#_x0000_t75" style='width:104.25pt;height:30pt' |
| 5970 |
o:ole=""> |
| 5971 |
<v:imagedata src="./fulldoc_files/image297.wmz" o:title=""/> |
| 5972 |
</v:shape><![endif]--><![if !vml]><img width=139 height=40 |
| 5973 |
src="./fulldoc_files/image298.gif" v:shapes="_x0000_i1145"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5974 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1145" |
| 5975 |
DrawAspect="Content" ObjectID="_1051901325"> |
| 5976 |
</o:OLEObject> |
| 5977 |
</xml><![endif]--><span style='mso-tab-count:1'> </span><span |
| 5978 |
style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 5979 |
id="_x0000_i1146" type="#_x0000_t75" style='width:143.25pt;height:45.75pt' |
| 5980 |
o:ole=""> |
| 5981 |
<v:imagedata src="./fulldoc_files/image299.wmz" o:title=""/> |
| 5982 |
</v:shape><![endif]--><![if !vml]><img width=191 height=61 |
| 5983 |
src="./fulldoc_files/image300.gif" v:shapes="_x0000_i1146"><![endif]></sub><!--[if gte mso 9]><xml> |
| 5984 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1146" |
| 5985 |
DrawAspect="Content" ObjectID="_1051901327"> |
| 5986 |
</o:OLEObject> |
| 5987 |
</xml><![endif]--><o:p></o:p></span></p> |
| 5988 |
<p class=MsoNormal style='margin-left:72.0pt;border:none;mso-border-alt:solid windowtext .75pt; |
| 5989 |
padding:0pt;mso-padding-alt:1.0pt 1.0pt 1.0pt 1.0pt;mso-element:frame; |
| 5990 |
mso-element-frame-width:407.45pt;mso-element-frame-height:324.05pt; |
| 5991 |
mso-element-frame-hspace:9.0pt;mso-element-wrap:around;mso-element-anchor-vertical: |
| 5992 |
paragraph;mso-element-anchor-horizontal:margin;mso-element-top:4.95pt'><span |
| 5993 |
style='font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 5994 |
</div> |
| 5995 |
</td> |
| 5996 |
</tr> |
| 5997 |
</table> |
| 5998 |
|
| 5999 |
</div> |
| 6000 |
|
| 6001 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6002 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6003 |
|
| 6004 |
<p class=MsoBodyText align=center style='margin-left:0pt;text-align:center; |
| 6005 |
mso-outline-level:1'><b style='mso-bidi-font-weight:normal'><span |
| 6006 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Fig.4.</span></b><span |
| 6007 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 6008 |
style="mso-spacerun: yes"> </span>Outline of the <b style='mso-bidi-font-weight: |
| 6009 |
normal'>HPE</b>, <b style='mso-bidi-font-weight:normal'>QH</b> and <b |
| 6010 |
style='mso-bidi-font-weight:normal'>NH </b>algorithms.<o:p></o:p></span></p> |
| 6011 |
|
| 6012 |
<p class=MsoBodyText align=center style='margin-left:0pt;text-align:center; |
| 6013 |
mso-outline-level:1'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6014 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6015 |
|
| 6016 |
<h2 style='text-align:justify'><a name="_Toc407078233"></a><a |
| 6017 |
name="_Toc407090387"></a><a name="_Toc407090590"></a><a name="_Toc407169619"><span |
| 6018 |
style='mso-bookmark:_Toc407090590'><span style='mso-bookmark:_Toc407090387'><span |
| 6019 |
style='mso-bookmark:_Toc407078233'>2.2 Spatial discretization.</span></span></span></a></h2> |
| 6020 |
|
| 6021 |
<p class=MsoBodyText><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 6022 |
|
| 6023 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6024 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The ocean is carved up in to a |
| 6025 |
large number of volumes which can be called zones or cells - see |
| 6026 |
Fig.5.<span style="mso-spacerun: yes"> </span>They take on a regular shape |
| 6027 |
over the interior of the ocean but can be modified in shape when they abut a |
| 6028 |
solid boundary - see Fig.5.<span style="mso-spacerun: yes"> </span>We |
| 6029 |
associate tracer quantities with these cells; the cells have a volume <sub><!--[if gte vml 1]><v:shape |
| 6030 |
id="_x0000_i1138" type="#_x0000_t75" style='width:18pt;height:15pt' o:ole="" |
| 6031 |
fillcolor="window"> |
| 6032 |
<v:imagedata src="./fulldoc_files/image301.wmz" o:title=""/> |
| 6033 |
</v:shape><![endif]--><![if !vml]><img width=24 height=20 |
| 6034 |
src="./fulldoc_files/image302.gif" v:shapes="_x0000_i1138"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6035 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1138" |
| 6036 |
DrawAspect="Content" ObjectID="_1051901328"> |
| 6037 |
</o:OLEObject> |
| 6038 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and six faces <sub><!--[if gte vml 1]><v:shape |
| 6039 |
id="_x0000_i1147" type="#_x0000_t75" style='width:17.25pt;height:15pt' o:ole="" |
| 6040 |
fillcolor="window"> |
| 6041 |
<v:imagedata src="./fulldoc_files/image303.wmz" o:title=""/> |
| 6042 |
</v:shape><![endif]--><![if !vml]><img width=23 height=20 |
| 6043 |
src="./fulldoc_files/image304.gif" v:shapes="_x0000_i1147"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6044 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1147" |
| 6045 |
DrawAspect="Content" ObjectID="_1051901329"> |
| 6046 |
</o:OLEObject> |
| 6047 |
</xml><![endif]-->, where </span><span style='font-size:12.0pt;mso-bidi-font-size: |
| 6048 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 6049 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 6050 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>J</span></span><span |
| 6051 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> |
| 6052 |
denotes a generic tracer (such as <i style='mso-bidi-font-style:normal'>T</i> |
| 6053 |
and <i style='mso-bidi-font-style:normal'>S</i>).<span style="mso-spacerun: |
| 6054 |
yes"> </span>Except where they abut a solid boundary, the faces must be chosen |
| 6055 |
to coincide with our (orthogonal) coordinate system.<span style="mso-spacerun: |
| 6056 |
yes"> </span>If <i style='mso-bidi-font-style:normal'>x</i>, <i |
| 6057 |
style='mso-bidi-font-style:normal'>y</i> and <i style='mso-bidi-font-style: |
| 6058 |
normal'>z</i> are three orthogonal coordinates, increasing (nominally) |
| 6059 |
eastward, northward and upward - see Fig.5 - the faces normal to the <i |
| 6060 |
style='mso-bidi-font-style:normal'>x</i> axis have area <sub><!--[if gte vml 1]><v:shape |
| 6061 |
id="_x0000_i1148" type="#_x0000_t75" style='width:18pt;height:18.75pt' o:ole=""> |
| 6062 |
<v:imagedata src="./fulldoc_files/image305.wmz" o:title=""/> |
| 6063 |
</v:shape><![endif]--><![if !vml]><img width=24 height=25 |
| 6064 |
src="./fulldoc_files/image306.gif" v:shapes="_x0000_i1148"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6065 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1148" |
| 6066 |
DrawAspect="Content" ObjectID="_1051901330"> |
| 6067 |
</o:OLEObject> |
| 6068 |
</xml><![endif]-->, faces normal to the <i style='mso-bidi-font-style:normal'>y</i> |
| 6069 |
axis area <sub><!--[if gte vml 1]><v:shape id="_x0000_i1149" type="#_x0000_t75" |
| 6070 |
style='width:17.25pt;height:20.25pt' o:ole="" fillcolor="window"> |
| 6071 |
<v:imagedata src="./fulldoc_files/image307.wmz" o:title=""/> |
| 6072 |
</v:shape><![endif]--><![if !vml]><img width=23 height=27 |
| 6073 |
src="./fulldoc_files/image308.gif" v:shapes="_x0000_i1149"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6074 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1149" |
| 6075 |
DrawAspect="Content" ObjectID="_1051901331"> |
| 6076 |
</o:OLEObject> |
| 6077 |
</xml><![endif]-->, and faces normal to the <i style='mso-bidi-font-style: |
| 6078 |
normal'>z</i> axis area <sub><!--[if gte vml 1]><v:shape id="_x0000_i1150" |
| 6079 |
type="#_x0000_t75" style='width:17.25pt;height:18pt' o:ole="" fillcolor="window"> |
| 6080 |
<v:imagedata src="./fulldoc_files/image309.wmz" o:title=""/> |
| 6081 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 6082 |
src="./fulldoc_files/image310.gif" v:shapes="_x0000_i1150"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6083 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1150" |
| 6084 |
DrawAspect="Content" ObjectID="_1051901332"> |
| 6085 |
</o:OLEObject> |
| 6086 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>Velocity components |
| 6087 |
are always normal to the faces. The geometry of the computational domain, and |
| 6088 |
the coordinate system employed within it (whether, Cartesian, spherical-polar, |
| 6089 |
cylindrical etc), is set up by prescribing the volumes and surface areas of the |
| 6090 |
faces of all the cells of which it is comprised.<o:p></o:p></span></p> |
| 6091 |
|
| 6092 |
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;page-break-after: |
| 6093 |
avoid'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 6094 |
Palatino'><!--[if gte vml 1]><v:shape id="_x0000_i1151" type="#_x0000_t75" |
| 6095 |
style='width:6in;height:366.75pt' o:ole="" fillcolor="window"> |
| 6096 |
<v:imagedata src="./fulldoc_files/image311.wmz" o:title=""/> |
| 6097 |
</v:shape><![endif]--><![if !vml]><img width=576 height=489 |
| 6098 |
src="./fulldoc_files/image312.gif" v:shapes="_x0000_i1151"><![endif]><!--[if gte mso 9]><xml> |
| 6099 |
<o:OLEObject Type="Embed" ProgID="PowerPoint.Slide.8" ShapeID="_x0000_i1151" |
| 6100 |
DrawAspect="Content" ObjectID="_1051901334"> |
| 6101 |
</o:OLEObject> |
| 6102 |
</xml><![endif]--><b style='mso-bidi-font-weight:normal'>Fig.5</b> The faces of |
| 6103 |
the cells are coincident with three orthogonal coordinate axes, sketched here |
| 6104 |
for a Cartesian grid (except where the cells abut a solid boundary). Velocities |
| 6105 |
are face quantities defined normal to the faces of the cells; <i |
| 6106 |
style='mso-bidi-font-style:normal'>T</i>, <i style='mso-bidi-font-style:normal'>S</i> |
| 6107 |
and <i style='mso-bidi-font-style:normal'>p</i> are volume quantities.<o:p></o:p></span></p> |
| 6108 |
|
| 6109 |
<p class=MsoNormal style='text-align:justify;mso-outline-level:1'><span |
| 6110 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6111 |
|
| 6112 |
<p class=MsoNormal style='text-align:justify;mso-outline-level:1'><span |
| 6113 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In the |
| 6114 |
terminology of Arakawa and Lamb (1977), the grid used here is the 'C' grid.<o:p></o:p></span></p> |
| 6115 |
|
| 6116 |
<p class=MsoNormal style='text-align:justify;mso-outline-level:1'><span |
| 6117 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6118 |
|
| 6119 |
<h3><a name="_Toc407078234"></a><a name="_Toc407090388"></a><a |
| 6120 |
name="_Toc407090591"></a><a name="_Toc407169620"><span style='mso-bookmark: |
| 6121 |
_Toc407090591'><span style='mso-bookmark:_Toc407090388'><span style='mso-bookmark: |
| 6122 |
_Toc407078234'><u>2.2.1 Volume quantities</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6123 |
|
| 6124 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6125 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6126 |
|
| 6127 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6128 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The volume or cell quantities, <i |
| 6129 |
style='mso-bidi-font-style:normal'>p</i>, </span><i style='mso-bidi-font-style: |
| 6130 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 6131 |
Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 6132 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 6133 |
symbol;mso-symbol-font-family:Symbol'>r</span></span></i><span |
| 6134 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>, <i |
| 6135 |
style='mso-bidi-font-style:normal'>T</i> and <i style='mso-bidi-font-style: |
| 6136 |
normal'>S</i> are defined as <i style='mso-bidi-font-style:normal'>volume |
| 6137 |
averages</i> over the cells.<span style="mso-spacerun: yes"> </span>Prognostic |
| 6138 |
equations for these quantities are found using a `finite volume approach i.e. |
| 6139 |
by integration of the continuous equations over cells making use of Gauss |
| 6140 |
theorem. For example, applying Gauss theorem to the continuity equation |
| 6141 |
(1.1.2) over a cell it becomes:<o:p></o:p></span></p> |
| 6142 |
|
| 6143 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6144 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6145 |
|
| 6146 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6147 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6148 |
id="_x0000_i1152" type="#_x0000_t75" style='width:174.75pt;height:21.75pt' |
| 6149 |
o:ole=""> |
| 6150 |
<v:imagedata src="./fulldoc_files/image313.wmz" o:title=""/> |
| 6151 |
</v:shape><![endif]--><![if !vml]><img width=233 height=29 |
| 6152 |
src="./fulldoc_files/image314.gif" v:shapes="_x0000_i1152"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6153 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1152" |
| 6154 |
DrawAspect="Content" ObjectID="_1051901335"> |
| 6155 |
</o:OLEObject> |
| 6156 |
</xml><![endif]--><span style="mso-spacerun: |
| 6157 |
yes"> </span>(2.2.1)<o:p></o:p></span></p> |
| 6158 |
|
| 6159 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6160 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6161 |
|
| 6162 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6163 |
font-family:Palatino'>where<o:p></o:p></span></p> |
| 6164 |
|
| 6165 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6166 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6167 |
|
| 6168 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 6169 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6170 |
id="_x0000_i1153" type="#_x0000_t75" style='width:132pt;height:18.75pt' o:ole="" |
| 6171 |
fillcolor="window"> |
| 6172 |
<v:imagedata src="./fulldoc_files/image315.wmz" o:title=""/> |
| 6173 |
</v:shape><![endif]--><![if !vml]><img width=176 height=25 |
| 6174 |
src="./fulldoc_files/image316.gif" v:shapes="_x0000_i1153"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6175 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1153" |
| 6176 |
DrawAspect="Content" ObjectID="_1051901337"> |
| 6177 |
</o:OLEObject> |
| 6178 |
</xml><![endif]--><o:p></o:p></span></p> |
| 6179 |
|
| 6180 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6181 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6182 |
|
| 6183 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6184 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>and similarly for the </span><i |
| 6185 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 6186 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 6187 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 6188 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>d</span></span></i><i |
| 6189 |
style='mso-bidi-font-style:normal'><sub><span style='font-size:12.0pt; |
| 6190 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>y</span></sub></i><sub><span |
| 6191 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> </span></sub><span |
| 6192 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>and </span><i |
| 6193 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 6194 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 6195 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 6196 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>d</span></span></i><i |
| 6197 |
style='mso-bidi-font-style:normal'><sub><span style='font-size:12.0pt; |
| 6198 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>z</span></sub></i><span |
| 6199 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> terms. |
| 6200 |
The velocities are defined <i style='mso-bidi-font-style:normal'>perpendicular</i> |
| 6201 |
to the faces of the cells so ensuring that divergence and gradient operators |
| 6202 |
can always be naturally represented by symmetric operators. The divergence of |
| 6203 |
the flux of a quantity over the cell is:<o:p></o:p></span></p> |
| 6204 |
|
| 6205 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6206 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6207 |
|
| 6208 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6209 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6210 |
id="_x0000_i1154" type="#_x0000_t75" style='width:243pt;height:30pt' o:ole=""> |
| 6211 |
<v:imagedata src="./fulldoc_files/image317.wmz" o:title=""/> |
| 6212 |
</v:shape><![endif]--><![if !vml]><img width=324 height=40 |
| 6213 |
src="./fulldoc_files/image318.gif" v:shapes="_x0000_i1154"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6214 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1154" |
| 6215 |
DrawAspect="Content" ObjectID="_1051901338"> |
| 6216 |
</o:OLEObject> |
| 6217 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 6218 |
</span>(2.2.2)<o:p></o:p></span></p> |
| 6219 |
|
| 6220 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6221 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6222 |
|
| 6223 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6224 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 6225 |
id="_x0000_i1155" type="#_x0000_t75" style='width:71.25pt;height:21.75pt' |
| 6226 |
o:ole=""> |
| 6227 |
<v:imagedata src="./fulldoc_files/image319.wmz" o:title=""/> |
| 6228 |
</v:shape><![endif]--><![if !vml]><img width=95 height=29 |
| 6229 |
src="./fulldoc_files/image320.gif" v:shapes="_x0000_i1155"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6230 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1155" |
| 6231 |
DrawAspect="Content" ObjectID="_1051901339"> |
| 6232 |
</o:OLEObject> |
| 6233 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the flux with |
| 6234 |
components defined normal to the faces and <sub><!--[if gte vml 1]><v:shape |
| 6235 |
id="_x0000_i1156" type="#_x0000_t75" style='width:17.25pt;height:15.75pt' |
| 6236 |
o:ole="" fillcolor="window"> |
| 6237 |
<v:imagedata src="./fulldoc_files/image321.wmz" o:title=""/> |
| 6238 |
</v:shape><![endif]--><![if !vml]><img width=23 height=21 |
| 6239 |
src="./fulldoc_files/image322.gif" v:shapes="_x0000_i1156"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6240 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1156" |
| 6241 |
DrawAspect="Content" ObjectID="_1051901340"> |
| 6242 |
</o:OLEObject> |
| 6243 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the volume of the |
| 6244 |
cell.<span style="mso-spacerun: yes"> </span>The presence of a solid boundary |
| 6245 |
is indicated by setting the appropriate flux normal to the boundary to zero.<o:p></o:p></span></p> |
| 6246 |
|
| 6247 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6248 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6249 |
|
| 6250 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6251 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Let us now consider the |
| 6252 |
discrete evaluation of the <b style='mso-bidi-font-weight:normal'>G</b>s for |
| 6253 |
the volume quantities required for integration of (2.1.4).<span |
| 6254 |
style="mso-spacerun: yes"> </span>The flux of, say, the temperature <i |
| 6255 |
style='mso-bidi-font-style:normal'>T</i> through a u-face of a cell is:<o:p></o:p></span></p> |
| 6256 |
|
| 6257 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6258 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6259 |
|
| 6260 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 6261 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6262 |
id="_x0000_i1157" type="#_x0000_t75" style='width:38.25pt;height:21pt' o:ole=""> |
| 6263 |
<v:imagedata src="./fulldoc_files/image323.wmz" o:title=""/> |
| 6264 |
</v:shape><![endif]--><![if !vml]><img width=51 height=28 |
| 6265 |
src="./fulldoc_files/image324.gif" v:shapes="_x0000_i1157"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6266 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1157" |
| 6267 |
DrawAspect="Content" ObjectID="_1051901342"> |
| 6268 |
</o:OLEObject> |
| 6269 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 6270 |
|
| 6271 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6272 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6273 |
|
| 6274 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6275 |
font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape id="_x0000_i1158" |
| 6276 |
type="#_x0000_t75" style='width:17.25pt;height:17.25pt' o:ole=""> |
| 6277 |
<v:imagedata src="./fulldoc_files/image325.wmz" o:title=""/> |
| 6278 |
</v:shape><![endif]--><![if !vml]><img width=23 height=23 |
| 6279 |
src="./fulldoc_files/image326.gif" v:shapes="_x0000_i1158"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6280 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1158" |
| 6281 |
DrawAspect="Content" ObjectID="_1051901343"> |
| 6282 |
</o:OLEObject> |
| 6283 |
</xml><![endif]-->, the temperature on the face, is given by :<o:p></o:p></span></p> |
| 6284 |
|
| 6285 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6286 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6287 |
|
| 6288 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 6289 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6290 |
id="_x0000_i1159" type="#_x0000_t75" style='width:72.75pt;height:30.75pt' |
| 6291 |
o:ole=""> |
| 6292 |
<v:imagedata src="./fulldoc_files/image327.wmz" o:title=""/> |
| 6293 |
</v:shape><![endif]--><![if !vml]><img width=97 height=41 |
| 6294 |
src="./fulldoc_files/image328.gif" v:shapes="_x0000_i1159"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6295 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1159" |
| 6296 |
DrawAspect="Content" ObjectID="_1051901344"> |
| 6297 |
</o:OLEObject> |
| 6298 |
</xml><![endif]--><o:p></o:p></span></p> |
| 6299 |
|
| 6300 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6301 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6302 |
|
| 6303 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6304 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>the average of the temperature |
| 6305 |
in the two cells to which the face is common. The divergence of the flux of <i |
| 6306 |
style='mso-bidi-font-style:normal'>T</i> over a cell,<sub><!--[if gte vml 1]><v:shape |
| 6307 |
id="_x0000_i1160" type="#_x0000_t75" style='width:38.25pt;height:17.25pt' |
| 6308 |
o:ole=""> |
| 6309 |
<v:imagedata src="./fulldoc_files/image329.wmz" o:title=""/> |
| 6310 |
</v:shape><![endif]--><![if !vml]><img width=51 height=23 |
| 6311 |
src="./fulldoc_files/image330.gif" v:shapes="_x0000_i1160"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6312 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1160" |
| 6313 |
DrawAspect="Content" ObjectID="_1051901346"> |
| 6314 |
</o:OLEObject> |
| 6315 |
</xml><![endif]-->, required in the evaluation of <sub><!--[if gte vml 1]><v:shape |
| 6316 |
id="_x0000_i1161" type="#_x0000_t75" style='width:21pt;height:15.75pt' o:ole=""> |
| 6317 |
<v:imagedata src="./fulldoc_files/image331.wmz" o:title=""/> |
| 6318 |
</v:shape><![endif]--><![if !vml]><img width=28 height=21 |
| 6319 |
src="./fulldoc_files/image332.gif" v:shapes="_x0000_i1161"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6320 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1161" |
| 6321 |
DrawAspect="Content" ObjectID="_1051901347"> |
| 6322 |
</o:OLEObject> |
| 6323 |
</xml><![endif]-->, for example, is:<o:p></o:p></span></p> |
| 6324 |
|
| 6325 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6326 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6327 |
|
| 6328 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6329 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6330 |
id="_x0000_i1162" type="#_x0000_t75" style='width:275.25pt;height:30pt' o:ole=""> |
| 6331 |
<v:imagedata src="./fulldoc_files/image333.wmz" o:title=""/> |
| 6332 |
</v:shape><![endif]--><![if !vml]><img width=367 height=40 |
| 6333 |
src="./fulldoc_files/image334.gif" v:shapes="_x0000_i1162"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6334 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1162" |
| 6335 |
DrawAspect="Content" ObjectID="_1051901348"> |
| 6336 |
</o:OLEObject> |
| 6337 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 6338 |
</span>(2.2.3)<o:p></o:p></span></p> |
| 6339 |
|
| 6340 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6341 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6342 |
|
| 6343 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6344 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where the <sub><!--[if gte vml 1]><v:shape |
| 6345 |
id="_x0000_i1163" type="#_x0000_t75" style='width:12.75pt;height:20.25pt' |
| 6346 |
o:ole=""> |
| 6347 |
<v:imagedata src="./fulldoc_files/image335.wmz" o:title=""/> |
| 6348 |
</v:shape><![endif]--><![if !vml]><img width=17 height=27 |
| 6349 |
src="./fulldoc_files/image336.gif" v:shapes="_x0000_i1163"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6350 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1163" |
| 6351 |
DrawAspect="Content" ObjectID="_1051901349"> |
| 6352 |
</o:OLEObject> |
| 6353 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the spatial |
| 6354 |
operator in the <i style='mso-bidi-font-style:normal'>x</i> direction (and analogously |
| 6355 |
for <i style='mso-bidi-font-style:normal'>y</i> and <i style='mso-bidi-font-style: |
| 6356 |
normal'>z</i>).<span style="mso-spacerun: yes"> </span>It can be shown that |
| 6357 |
this simple average ensures that second moments of <i style='mso-bidi-font-style: |
| 6358 |
normal'>T</i> are conserved i.e. the identity <sub><!--[if gte vml 1]><v:shape |
| 6359 |
id="_x0000_i1164" type="#_x0000_t75" style='width:99.75pt;height:33pt' o:ole="" |
| 6360 |
fillcolor="window"> |
| 6361 |
<v:imagedata src="./fulldoc_files/image337.wmz" o:title=""/> |
| 6362 |
</v:shape><![endif]--><![if !vml]><img width=133 height=44 |
| 6363 |
src="./fulldoc_files/image338.gif" v:shapes="_x0000_i1164"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6364 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1164" |
| 6365 |
DrawAspect="Content" ObjectID="_1051901350"> |
| 6366 |
</o:OLEObject> |
| 6367 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is mimicked by the |
| 6368 |
discrete form (2.2.3) if <sub><!--[if gte vml 1]><v:shape id="_x0000_i1165" |
| 6369 |
type="#_x0000_t75" style='width:15.75pt;height:17.25pt' o:ole=""> |
| 6370 |
<v:imagedata src="./fulldoc_files/image339.wmz" o:title=""/> |
| 6371 |
</v:shape><![endif]--><![if !vml]><img width=21 height=23 |
| 6372 |
src="./fulldoc_files/image340.gif" v:shapes="_x0000_i1165"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6373 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1165" |
| 6374 |
DrawAspect="Content" ObjectID="_1051901352"> |
| 6375 |
</o:OLEObject> |
| 6376 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is chosen to be the |
| 6377 |
arithmetic mean. In (2.2.2) and (2.2.3), <sub><!--[if gte vml 1]><v:shape id="_x0000_i1166" |
| 6378 |
type="#_x0000_t75" style='width:17.25pt;height:15.75pt' o:ole="" fillcolor="window"> |
| 6379 |
<v:imagedata src="./fulldoc_files/image341.wmz" o:title=""/> |
| 6380 |
</v:shape><![endif]--><![if !vml]><img width=23 height=21 |
| 6381 |
src="./fulldoc_files/image342.gif" v:shapes="_x0000_i1166"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6382 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1166" |
| 6383 |
DrawAspect="Content" ObjectID="_1051901353"> |
| 6384 |
</o:OLEObject> |
| 6385 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the volume of the |
| 6386 |
cell in question.<o:p></o:p></span></p> |
| 6387 |
|
| 6388 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><i style='mso-bidi-font-style: |
| 6389 |
normal'><span style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 6390 |
Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></i></b></p> |
| 6391 |
|
| 6392 |
<h3><a name="_Toc407078235"></a><a name="_Toc407090389"></a><a |
| 6393 |
name="_Toc407090592"></a><a name="_Toc407169621"><span style='mso-bookmark: |
| 6394 |
_Toc407090592'><span style='mso-bookmark:_Toc407090389'><span style='mso-bookmark: |
| 6395 |
_Toc407078235'><u>2.2.2 Face quantities</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6396 |
|
| 6397 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6398 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6399 |
|
| 6400 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6401 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>It is clear from (2.2.3) that |
| 6402 |
velocities only appear as averages over faces of the cells and so we choose |
| 6403 |
only to define them there.<span style="mso-spacerun: yes"> </span>To deduce |
| 6404 |
appropriate discrete forms of the momentum equations, however, we associate |
| 6405 |
volumes with these face quantities - <sub><!--[if gte vml 1]><v:shape id="_x0000_i1826" |
| 6406 |
type="#_x0000_t75" style='width:56.25pt;height:17.25pt' o:ole=""> |
| 6407 |
<v:imagedata src="./fulldoc_files/image343.wmz" o:title=""/> |
| 6408 |
</v:shape><![endif]--><![if !vml]><img width=75 height=23 |
| 6409 |
src="./fulldoc_files/image344.gif" v:shapes="_x0000_i1826"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6410 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1826" |
| 6411 |
DrawAspect="Content" ObjectID="_1051901354"> |
| 6412 |
</o:OLEObject> |
| 6413 |
</xml><![endif]-->- and again use Gauss theorem.<span style="mso-spacerun: |
| 6414 |
yes"> </span>Let us first consider the special case in which these volumes are |
| 6415 |
not shaved.<span style="mso-spacerun: yes"> </span>Then the advecting terms |
| 6416 |
that make up the <sub><!--[if gte vml 1]><v:shape id="_x0000_i1827" type="#_x0000_t75" |
| 6417 |
style='width:18pt;height:17.25pt' o:ole=""> |
| 6418 |
<v:imagedata src="./fulldoc_files/image345.wmz" o:title=""/> |
| 6419 |
</v:shape><![endif]--><![if !vml]><img width=24 height=23 |
| 6420 |
src="./fulldoc_files/image346.gif" v:shapes="_x0000_i1827"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6421 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1827" |
| 6422 |
DrawAspect="Content" ObjectID="_1051901356"> |
| 6423 |
</o:OLEObject> |
| 6424 |
</xml><![endif]-->s in Eqs. (1.3.2</span><span style='font-size:12.0pt; |
| 6425 |
mso-bidi-font-size:10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino; |
| 6426 |
mso-hansi-font-family:Palatino;mso-char-type:symbol;mso-symbol-font-family: |
| 6427 |
Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>®</span></span><span |
| 6428 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>1.3.4) |
| 6429 |
have the form (using continuity equation (1.1.2):<o:p></o:p></span></p> |
| 6430 |
|
| 6431 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6432 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6433 |
|
| 6434 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6435 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6436 |
id="_x0000_i1828" type="#_x0000_t75" style='width:303.75pt;height:33.75pt' |
| 6437 |
o:ole=""> |
| 6438 |
<v:imagedata src="./fulldoc_files/image347.wmz" o:title=""/> |
| 6439 |
</v:shape><![endif]--><![if !vml]><img width=405 height=45 |
| 6440 |
src="./fulldoc_files/image348.gif" v:shapes="_x0000_i1828"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6441 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1828" |
| 6442 |
DrawAspect="Content" ObjectID="_1051901357"> |
| 6443 |
</o:OLEObject> |
| 6444 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>(2.2.4)<o:p></o:p></span></p> |
| 6445 |
|
| 6446 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6447 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6448 |
|
| 6449 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6450 |
font-family:Palatino'>where<span style="mso-spacerun: yes"> </span></span><sup><span |
| 6451 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 6452 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 6453 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 6454 |
mso-symbol-font-family:Symbol'>¾</span></span></sup><span style='font-size: |
| 6455 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 6456 |
style="mso-spacerun: yes"> </span>is the spatial-averaging operator and<o:p></o:p></span></p> |
| 6457 |
|
| 6458 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6459 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6460 |
|
| 6461 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6462 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6463 |
id="_x0000_i1829" type="#_x0000_t75" style='width:53.25pt;height:21pt' o:ole=""> |
| 6464 |
<v:imagedata src="./fulldoc_files/image349.wmz" o:title=""/> |
| 6465 |
</v:shape><![endif]--><![if !vml]><img width=71 height=28 |
| 6466 |
src="./fulldoc_files/image350.gif" v:shapes="_x0000_i1829"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6467 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1829" |
| 6468 |
DrawAspect="Content" ObjectID="_1051901358"> |
| 6469 |
</o:OLEObject> |
| 6470 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><span |
| 6471 |
style="mso-spacerun: |
| 6472 |
yes"> </span>(2.2.5)<o:p></o:p></span></p> |
| 6473 |
|
| 6474 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6475 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6476 |
|
| 6477 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6478 |
font-family:Palatino'>the average of the volumes of the cells on either side of |
| 6479 |
the face in question.<o:p></o:p></span></p> |
| 6480 |
|
| 6481 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6482 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6483 |
|
| 6484 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6485 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Exactly analogous expressions |
| 6486 |
are written down for </span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6487 |
id="_x0000_i1830" type="#_x0000_t75" style='width:36pt;height:15.75pt' o:ole=""> |
| 6488 |
<v:imagedata src="./fulldoc_files/image351.wmz" o:title=""/> |
| 6489 |
</v:shape><![endif]--><![if !vml]><img width=48 height=21 |
| 6490 |
src="./fulldoc_files/image352.gif" v:shapes="_x0000_i1830"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6491 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1830" |
| 6492 |
DrawAspect="Content" ObjectID="_1051901360"> |
| 6493 |
</o:OLEObject> |
| 6494 |
</xml><![endif]--></span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6495 |
font-family:Palatino'>and </span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6496 |
id="_x0000_i1831" type="#_x0000_t75" style='width:38.25pt;height:15.75pt' |
| 6497 |
o:ole=""> |
| 6498 |
<v:imagedata src="./fulldoc_files/image353.wmz" o:title=""/> |
| 6499 |
</v:shape><![endif]--><![if !vml]><img width=51 height=21 |
| 6500 |
src="./fulldoc_files/image354.gif" v:shapes="_x0000_i1831"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6501 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1831" |
| 6502 |
DrawAspect="Content" ObjectID="_1051901361"> |
| 6503 |
</o:OLEObject> |
| 6504 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 6505 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>in |
| 6506 |
which the <sub><!--[if gte vml 1]><v:shape id="_x0000_i1832" type="#_x0000_t75" |
| 6507 |
style='width:14.25pt;height:20.25pt' o:ole=""> |
| 6508 |
<v:imagedata src="./fulldoc_files/image355.wmz" o:title=""/> |
| 6509 |
</v:shape><![endif]--><![if !vml]><img width=19 height=27 |
| 6510 |
src="./fulldoc_files/image356.gif" v:shapes="_x0000_i1832"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6511 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1832" |
| 6512 |
DrawAspect="Content" ObjectID="_1051901362"> |
| 6513 |
</o:OLEObject> |
| 6514 |
</xml><![endif]-->average of the area <i style='mso-bidi-font-style:normal'>times</i> |
| 6515 |
velocity terms is replaced by, respectively, <sub><!--[if gte vml 1]><v:shape |
| 6516 |
id="_x0000_i1833" type="#_x0000_t75" style='width:14.25pt;height:20.25pt' |
| 6517 |
o:ole=""> |
| 6518 |
<v:imagedata src="./fulldoc_files/image357.wmz" o:title=""/> |
| 6519 |
</v:shape><![endif]--><![if !vml]><img width=19 height=27 |
| 6520 |
src="./fulldoc_files/image358.gif" v:shapes="_x0000_i1833"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6521 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1833" |
| 6522 |
DrawAspect="Content" ObjectID="_1051901364"> |
| 6523 |
</o:OLEObject> |
| 6524 |
</xml><![endif]-->and <sub><!--[if gte vml 1]><v:shape id="_x0000_i1834" |
| 6525 |
type="#_x0000_t75" style='width:12.75pt;height:20.25pt' o:ole=""> |
| 6526 |
<v:imagedata src="./fulldoc_files/image359.wmz" o:title=""/> |
| 6527 |
</v:shape><![endif]--><![if !vml]><img width=17 height=27 |
| 6528 |
src="./fulldoc_files/image360.gif" v:shapes="_x0000_i1834"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6529 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1834" |
| 6530 |
DrawAspect="Content" ObjectID="_1051901365"> |
| 6531 |
</o:OLEObject> |
| 6532 |
</xml><![endif]-->.The forms (2.2.4, 2.2.5) guarantees:<o:p></o:p></span></p> |
| 6533 |
|
| 6534 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6535 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6536 |
|
| 6537 |
<p class=MsoNormal style='text-align:justify;tab-stops:list 54.0pt'><span |
| 6538 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>-conservation |
| 6539 |
of the first moment because it is written in flux form,<o:p></o:p></span></p> |
| 6540 |
|
| 6541 |
<p class=MsoNormal style='text-align:justify;tab-stops:list 54.0pt'><span |
| 6542 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>-conservation |
| 6543 |
of the second moment because the fluxing velocities satisfy a non-divergence |
| 6544 |
condition:<o:p></o:p></span></p> |
| 6545 |
|
| 6546 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6547 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6548 |
|
| 6549 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 6550 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6551 |
id="_x0000_i1835" type="#_x0000_t75" style='width:206.25pt;height:32.25pt' |
| 6552 |
o:ole=""> |
| 6553 |
<v:imagedata src="./fulldoc_files/image361.wmz" o:title=""/> |
| 6554 |
</v:shape><![endif]--><![if !vml]><img width=275 height=43 |
| 6555 |
src="./fulldoc_files/image362.gif" v:shapes="_x0000_i1835"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6556 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1835" |
| 6557 |
DrawAspect="Content" ObjectID="_1051901366"> |
| 6558 |
</o:OLEObject> |
| 6559 |
</xml><![endif]--><o:p></o:p></span></p> |
| 6560 |
|
| 6561 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6562 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6563 |
|
| 6564 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6565 |
font-family:Palatino'>exactly analogous to (2.2.1).<o:p></o:p></span></p> |
| 6566 |
|
| 6567 |
<p class=MsoNormal style='mso-outline-level:1'><span style='font-size:12.0pt; |
| 6568 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6569 |
|
| 6570 |
<h3><a name="_Toc407078236"></a><a name="_Toc407090390"></a><a |
| 6571 |
name="_Toc407090593"></a><a name="_Toc407169622"><span style='mso-bookmark: |
| 6572 |
_Toc407090593'><span style='mso-bookmark:_Toc407090390'><span style='mso-bookmark: |
| 6573 |
_Toc407078236'><u>2.2.3 Coriolis terms</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6574 |
|
| 6575 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6576 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6577 |
|
| 6578 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6579 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Velocity components are |
| 6580 |
staggered in space and so the evaluation of Coriolis terms in (1.3.2</span><span |
| 6581 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 6582 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 6583 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 6584 |
mso-symbol-font-family:Symbol'>®</span></span><span style='font-size:12.0pt; |
| 6585 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>1.3.4) involves spatial |
| 6586 |
averaging: <o:p></o:p></span></p> |
| 6587 |
|
| 6588 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6589 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6590 |
|
| 6591 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6592 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6593 |
id="_x0000_i1836" type="#_x0000_t75" style='width:359.25pt;height:39.75pt' |
| 6594 |
o:ole="" fillcolor="window"> |
| 6595 |
<v:imagedata src="./fulldoc_files/image363.wmz" o:title=""/> |
| 6596 |
</v:shape><![endif]--><![if !vml]><img width=479 height=53 |
| 6597 |
src="./fulldoc_files/image364.gif" v:shapes="_x0000_i1836"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6598 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1836" |
| 6599 |
DrawAspect="Content" ObjectID="_1051901368"> |
| 6600 |
</o:OLEObject> |
| 6601 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>(2.2.6)<o:p></o:p></span></p> |
| 6602 |
|
| 6603 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6604 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6605 |
|
| 6606 |
<p class=MsoNormal style='text-align:justify;tab-stops:9.0pt'><span |
| 6607 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 6608 |
id="_x0000_i1167" type="#_x0000_t75" style='width:146.25pt;height:15.75pt' |
| 6609 |
o:ole=""> |
| 6610 |
<v:imagedata src="./fulldoc_files/image365.wmz" o:title=""/> |
| 6611 |
</v:shape><![endif]--><![if !vml]><img width=195 height=21 |
| 6612 |
src="./fulldoc_files/image366.gif" v:shapes="_x0000_i1167"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6613 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1167" |
| 6614 |
DrawAspect="Content" ObjectID="_1051901369"> |
| 6615 |
</o:OLEObject> |
| 6616 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>The above form |
| 6617 |
ensures energy conservation; see, for example, Arakawa and Lamb (1977).<o:p></o:p></span></p> |
| 6618 |
|
| 6619 |
<p class=MsoNormal style='text-align:justify;tab-stops:9.0pt'><span |
| 6620 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6621 |
|
| 6622 |
<p class=MsoNormal style='text-align:justify;tab-stops:9.0pt'><span |
| 6623 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Spatial |
| 6624 |
averaging of Coriolis has undesirable consequences - at coarse resolution the |
| 6625 |
w-field can be prone to grid-scale noise.<span style="mso-spacerun: yes"> |
| 6626 |
</span>Considerable attempts have been made to ameliorate this problem - see |
| 6627 |
section 2.2.6 where the 'C-D' scheme, devised by Alistair Adcroft, is described.<o:p></o:p></span></p> |
| 6628 |
|
| 6629 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6630 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6631 |
|
| 6632 |
<h3><a name="_Toc407078237"></a><a name="_Toc407090391"></a><a |
| 6633 |
name="_Toc407090594"></a><a name="_Toc407169623"><span style='mso-bookmark: |
| 6634 |
_Toc407090594'><span style='mso-bookmark:_Toc407090391'><span style='mso-bookmark: |
| 6635 |
_Toc407078237'><u>2.2.4 Pressure gradient force</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6636 |
|
| 6637 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6638 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6639 |
|
| 6640 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6641 |
font-family:Palatino'>The three components of the pressure gradient force are:<o:p></o:p></span></p> |
| 6642 |
|
| 6643 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6644 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6645 |
|
| 6646 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6647 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6648 |
id="_x0000_i1168" type="#_x0000_t75" style='width:168pt;height:42pt' o:ole=""> |
| 6649 |
<v:imagedata src="./fulldoc_files/image367.wmz" o:title=""/> |
| 6650 |
</v:shape><![endif]--><![if !vml]><img width=224 height=56 |
| 6651 |
src="./fulldoc_files/image368.gif" v:shapes="_x0000_i1168"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6652 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1168" |
| 6653 |
DrawAspect="Content" ObjectID="_1051901370"> |
| 6654 |
</o:OLEObject> |
| 6655 |
</xml><![endif]--><span style="mso-spacerun: |
| 6656 |
yes"> </span>(2.2.7)<o:p></o:p></span></p> |
| 6657 |
|
| 6658 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6659 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6660 |
|
| 6661 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6662 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The form (2.2.7) ensures that |
| 6663 |
the discrete operator representing <sub><!--[if gte vml 1]><v:shape id="_x0000_i1169" |
| 6664 |
type="#_x0000_t75" style='width:30pt;height:15.75pt' o:ole=""> |
| 6665 |
<v:imagedata src="./fulldoc_files/image369.wmz" o:title=""/> |
| 6666 |
</v:shape><![endif]--><![if !vml]><img width=40 height=21 |
| 6667 |
src="./fulldoc_files/image370.gif" v:shapes="_x0000_i1169"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6668 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1169" |
| 6669 |
DrawAspect="Content" ObjectID="_1051901371"> |
| 6670 |
</o:OLEObject> |
| 6671 |
</xml><![endif]-->, which must be inverted to find the pressure field, is a <u>symmetric</u> |
| 6672 |
operator facilitating the use of conjugate-gradient methods - see section |
| 6673 |
2.3.<span style="mso-spacerun: yes"> </span>It also leads to an appropriate |
| 6674 |
discrete analogue of energy conservation - see section 2.2.7 and, in |
| 6675 |
particular, Adcroft et al.(1997).<o:p></o:p></span></p> |
| 6676 |
|
| 6677 |
<p class=MsoNormal><u><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6678 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 6679 |
|
| 6680 |
<h3><a name="_Toc407078238"></a><a name="_Toc407090392"></a><a |
| 6681 |
name="_Toc407090595"></a><a name="_Toc407169624"><span style='mso-bookmark: |
| 6682 |
_Toc407090595'><span style='mso-bookmark:_Toc407090392'><span style='mso-bookmark: |
| 6683 |
_Toc407078238'><u>2.2.5 Forcing and dissipation</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6684 |
|
| 6685 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 6686 |
|
| 6687 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6688 |
font-family:Palatino'>Laplacian diffusion terms are represented for cell |
| 6689 |
quantities thus:<o:p></o:p></span></p> |
| 6690 |
|
| 6691 |
<p class=MsoNormal><u><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6692 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 6693 |
|
| 6694 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6695 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6696 |
id="_x0000_i1170" type="#_x0000_t75" style='width:218.25pt;height:30.75pt' |
| 6697 |
o:ole="" fillcolor="window"> |
| 6698 |
<v:imagedata src="./fulldoc_files/image371.wmz" o:title=""/> |
| 6699 |
</v:shape><![endif]--><![if !vml]><img width=291 height=41 |
| 6700 |
src="./fulldoc_files/image372.gif" v:shapes="_x0000_i1170"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6701 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1170" |
| 6702 |
DrawAspect="Content" ObjectID="_1051901373"> |
| 6703 |
</o:OLEObject> |
| 6704 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 6705 |
</span>(2.2.8a)<o:p></o:p></span></p> |
| 6706 |
|
| 6707 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6708 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6709 |
|
| 6710 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6711 |
font-family:Palatino'>and for face quantities:<o:p></o:p></span></p> |
| 6712 |
|
| 6713 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6714 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6715 |
|
| 6716 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6717 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6718 |
id="_x0000_i1171" type="#_x0000_t75" style='width:237pt;height:33.75pt' o:ole="" |
| 6719 |
fillcolor="window"> |
| 6720 |
<v:imagedata src="./fulldoc_files/image373.wmz" o:title=""/> |
| 6721 |
</v:shape><![endif]--><![if !vml]><img width=316 height=45 |
| 6722 |
src="./fulldoc_files/image374.gif" v:shapes="_x0000_i1171"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6723 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1171" |
| 6724 |
DrawAspect="Content" ObjectID="_1051901374"> |
| 6725 |
</o:OLEObject> |
| 6726 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 6727 |
</span>(2.2.8b)<o:p></o:p></span></p> |
| 6728 |
|
| 6729 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6730 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6731 |
|
| 6732 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6733 |
font-family:Palatino'>where</span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6734 |
id="_x0000_i1172" type="#_x0000_t75" style='width:15.75pt;height:15.75pt' |
| 6735 |
o:ole=""> |
| 6736 |
<v:imagedata src="./fulldoc_files/image375.wmz" o:title=""/> |
| 6737 |
</v:shape><![endif]--><![if !vml]><img width=21 height=21 |
| 6738 |
src="./fulldoc_files/image376.gif" v:shapes="_x0000_i1172"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6739 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1172" |
| 6740 |
DrawAspect="Content" ObjectID="_1051901375"> |
| 6741 |
</o:OLEObject> |
| 6742 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 6743 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>is |
| 6744 |
given by (2.2.5).<o:p></o:p></span></p> |
| 6745 |
|
| 6746 |
<p class=MsoNormal><u><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6747 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 6748 |
|
| 6749 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6750 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Higher order dissipative forms |
| 6751 |
are obtained by repeated application of the <sub><!--[if gte vml 1]><v:shape |
| 6752 |
id="_x0000_i1173" type="#_x0000_t75" style='width:17.25pt;height:15.75pt' |
| 6753 |
o:ole=""> |
| 6754 |
<v:imagedata src="./fulldoc_files/image377.wmz" o:title=""/> |
| 6755 |
</v:shape><![endif]--><![if !vml]><img width=23 height=21 |
| 6756 |
src="./fulldoc_files/image378.gif" v:shapes="_x0000_i1173"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6757 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1173" |
| 6758 |
DrawAspect="Content" ObjectID="_1051901376"> |
| 6759 |
</o:OLEObject> |
| 6760 |
</xml><![endif]-->operators defined above.<o:p></o:p></span></p> |
| 6761 |
|
| 6762 |
<p class=MsoBodyText style='margin-left:0pt'><u><span style='font-size:12.0pt; |
| 6763 |
mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 6764 |
|
| 6765 |
<p class=MsoBodyText style='margin-left:0pt'><b style='mso-bidi-font-weight: |
| 6766 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 6767 |
Palatino'>Include form of discrete forcing terms here.<o:p></o:p></span></b></p> |
| 6768 |
|
| 6769 |
<p class=MsoNormalIndent style='margin-left:0pt'><u><span style='font-size: |
| 6770 |
12.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 6771 |
|
| 6772 |
<h3><a name="_Toc407078239"></a><a name="_Toc407090393"></a><a |
| 6773 |
name="_Toc407090596"></a><a name="_Toc407169625"><span style='mso-bookmark: |
| 6774 |
_Toc407090596'><span style='mso-bookmark:_Toc407090393'><span style='mso-bookmark: |
| 6775 |
_Toc407078239'><u>2.2.6 The C-D scheme</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6776 |
|
| 6777 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6778 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6779 |
|
| 6780 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6781 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The spatial averaging required |
| 6782 |
in the evaluation of Coriolis terms on the C grid is a significant |
| 6783 |
disadvantage when the model is used at resolutions which are coarse relative to |
| 6784 |
the Rossby radius of deformation.<span style="mso-spacerun: yes"> </span>A |
| 6785 |
checkerboard mode in the horizontal divergence field can readily be excited and |
| 6786 |
implicit treatment of Coriolis terms is significantly more complicated than on |
| 6787 |
unstaggered grids (such as the B grid, for example).<span |
| 6788 |
style="mso-spacerun: yes"> </span>As shown in Adcroft (1995), however, both of |
| 6789 |
these difficulties can be significantly ameliorated by use of a C-D grid in |
| 6790 |
which a D grid is used to step forward velocity components used in the |
| 6791 |
evaluation of Coriolis terms.<o:p></o:p></span></p> |
| 6792 |
|
| 6793 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6794 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6795 |
|
| 6796 |
<p class=MsoNormal style='text-align:justify'><b style='mso-bidi-font-weight: |
| 6797 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 6798 |
Palatino'>Include the discrete equations here.<o:p></o:p></span></b></p> |
| 6799 |
|
| 6800 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6801 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6802 |
|
| 6803 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6804 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The scheme has been |
| 6805 |
particularly useful in coarse-resolution studies of ocean circulation in which |
| 6806 |
the horizontal resolution is many times the Rossby radius of deformation.<o:p></o:p></span></p> |
| 6807 |
|
| 6808 |
<p class=MsoNormal style='text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 6809 |
|
| 6810 |
<h3><a name="_Toc407078240"></a><a name="_Toc407090394"></a><a |
| 6811 |
name="_Toc407090597"></a><a name="_Toc407169626"><span style='mso-bookmark: |
| 6812 |
_Toc407090597'><span style='mso-bookmark:_Toc407090394'><span style='mso-bookmark: |
| 6813 |
_Toc407078240'><u>2.2.7 Conservation properties</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6814 |
|
| 6815 |
<p class=MsoNormal><u><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6816 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 6817 |
|
| 6818 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6819 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The above discrete forms give |
| 6820 |
the model excellent integral conservation properties.<span style="mso-spacerun: |
| 6821 |
yes"> </span>They conserve integrals of mass, heat, salt, variance of |
| 6822 |
temperature and salinity and total energy, when effects of mixing and transfer |
| 6823 |
across boundaries are absent.<span style="mso-spacerun: yes"> </span>The |
| 6824 |
discrete analogue of kinetic energy is:<o:p></o:p></span></p> |
| 6825 |
|
| 6826 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6827 |
font-family:Palatino'><span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 6828 |
|
| 6829 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 6830 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6831 |
id="_x0000_i1837" type="#_x0000_t75" style='width:167.25pt;height:38.25pt' |
| 6832 |
o:ole=""> |
| 6833 |
<v:imagedata src="./fulldoc_files/image379.wmz" o:title=""/> |
| 6834 |
</v:shape><![endif]--><![if !vml]><img width=223 height=51 |
| 6835 |
src="./fulldoc_files/image380.gif" v:shapes="_x0000_i1837"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6836 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1837" |
| 6837 |
DrawAspect="Content" ObjectID="_1051901378"> |
| 6838 |
</o:OLEObject> |
| 6839 |
</xml><![endif]--><o:p></o:p></span></p> |
| 6840 |
|
| 6841 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6842 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6843 |
|
| 6844 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6845 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>These integral properties are |
| 6846 |
not compromised by the use of shaved cells provided care is taken in the definition |
| 6847 |
of control volumes for variables adjacent to the boundary (see appendix).<span |
| 6848 |
style="mso-spacerun: yes"> </span>The model does not conserve enstrophy, |
| 6849 |
however.</span><span style='font-family:Palatino'><o:p></o:p></span></p> |
| 6850 |
|
| 6851 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6852 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6853 |
|
| 6854 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span |
| 6855 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Include |
| 6856 |
section on shaved cells (maybe in appendix?)<o:p></o:p></span></b></p> |
| 6857 |
|
| 6858 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 6859 |
|
| 6860 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 6861 |
|
| 6862 |
<h2><a name="_Toc407078241"></a><a name="_Toc407090395"></a><a |
| 6863 |
name="_Toc407090598"></a><a name="_Toc407169627"><span style='mso-bookmark: |
| 6864 |
_Toc407090598'><span style='mso-bookmark:_Toc407090395'><span style='mso-bookmark: |
| 6865 |
_Toc407078241'>2.3<span style="mso-spacerun: yes"> </span>The Elliptic problem</span></span></span></a></h2> |
| 6866 |
|
| 6867 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6868 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6869 |
|
| 6870 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6871 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>We now formulate the discrete |
| 6872 |
analogues of the 2-d and 3-d elliptic problems for the pressure which |
| 6873 |
guarantees that the velocity fields evolving from <i style='mso-bidi-font-style: |
| 6874 |
normal'>n</i> to <i style='mso-bidi-font-style:normal'>n</i>+1 according to |
| 6875 |
(2.1.1) and (2.1.2) satisfy the non-divergence condition (2.1.3) at step <i |
| 6876 |
style='mso-bidi-font-style:normal'>n</i>+1.<span style="mso-spacerun: yes"> |
| 6877 |
</span>The parallel implementation of the preconditioned conjugate-gradient |
| 6878 |
methods used to invert them are discussed in section 2.3.2.<o:p></o:p></span></p> |
| 6879 |
|
| 6880 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6881 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6882 |
|
| 6883 |
<h3><a name="_Toc407078242"></a><a name="_Toc407090396"></a><a |
| 6884 |
name="_Toc407090599"></a><a name="_Toc407169628"><span style='mso-bookmark: |
| 6885 |
_Toc407090599'><span style='mso-bookmark:_Toc407090396'><span style='mso-bookmark: |
| 6886 |
_Toc407078242'><u>2.3.1 Discrete formulation</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 6887 |
|
| 6888 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6889 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6890 |
|
| 6891 |
<p class=MsoNormal><i style='mso-bidi-font-style:normal'><span |
| 6892 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Two-dimensional<o:p></o:p></span></i></p> |
| 6893 |
|
| 6894 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6895 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6896 |
|
| 6897 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6898 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Because of the finite volume |
| 6899 |
approach adopted in our treatment of volume quantities, in which velocities are |
| 6900 |
defined normal to the faces of the cells, the divergence operator has a natural |
| 6901 |
form leading to a local Elliptic operator which has a five-point stencil.<span |
| 6902 |
style="mso-spacerun: yes"> </span>By setting <i style='mso-bidi-font-style: |
| 6903 |
normal'>q</i>=0 in the momentum equations (2.1.1) and summing them over the |
| 6904 |
whole depth of the ocean, invoking the continuity equation (2.2.1) and applying |
| 6905 |
boundary conditions (1.2.1), the following equation for <sub><!--[if gte vml 1]><v:shape |
| 6906 |
id="_x0000_i1174" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 6907 |
<v:imagedata src="./fulldoc_files/image381.wmz" o:title=""/> |
| 6908 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 6909 |
src="./fulldoc_files/image382.gif" v:shapes="_x0000_i1174"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6910 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1174" |
| 6911 |
DrawAspect="Content" ObjectID="_1051901379"> |
| 6912 |
</o:OLEObject> |
| 6913 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>results<a |
| 6914 |
style='mso-footnote-id:ftn2' href="#_ftn2" name="_ftnref2" title=""><span |
| 6915 |
class=MsoFootnoteReference><span style='mso-special-character:footnote'><![if !supportFootnotes]>[2]<![endif]></span></span></a>:<o:p></o:p></span></p> |
| 6916 |
|
| 6917 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6918 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6919 |
|
| 6920 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6921 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6922 |
id="_x0000_i1175" type="#_x0000_t75" style='width:186.75pt;height:44.25pt' |
| 6923 |
o:ole="" fillcolor="window"> |
| 6924 |
<v:imagedata src="./fulldoc_files/image383.wmz" o:title=""/> |
| 6925 |
</v:shape><![endif]--><![if !vml]><img width=249 height=59 |
| 6926 |
src="./fulldoc_files/image384.gif" v:shapes="_x0000_i1175"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6927 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1175" |
| 6928 |
DrawAspect="Content" ObjectID="_1051901380"> |
| 6929 |
</o:OLEObject> |
| 6930 |
</xml><![endif]--><span style="mso-spacerun: |
| 6931 |
yes"> </span>(2.3.1)<o:p></o:p></span></p> |
| 6932 |
|
| 6933 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6934 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6935 |
|
| 6936 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6937 |
font-family:Palatino'>where<o:p></o:p></span></p> |
| 6938 |
|
| 6939 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 6940 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 6941 |
id="_x0000_i1176" type="#_x0000_t75" style='width:207.75pt;height:51.75pt' |
| 6942 |
o:ole=""> |
| 6943 |
<v:imagedata src="./fulldoc_files/image385.wmz" o:title=""/> |
| 6944 |
</v:shape><![endif]--><![if !vml]><img width=277 height=69 |
| 6945 |
src="./fulldoc_files/image386.gif" v:shapes="_x0000_i1176"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6946 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1176" |
| 6947 |
DrawAspect="Content" ObjectID="_1051901381"> |
| 6948 |
</o:OLEObject> |
| 6949 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 6950 |
</span>(2.3.2)<o:p></o:p></span></p> |
| 6951 |
|
| 6952 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6953 |
font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1177" |
| 6954 |
type="#_x0000_t75" style='width:9pt;height:15.75pt' o:ole=""> |
| 6955 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 6956 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 6957 |
src="./fulldoc_files/image387.gif" v:shapes="_x0000_i1177"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6958 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1177" |
| 6959 |
DrawAspect="Content" ObjectID="_1051901383"> |
| 6960 |
</o:OLEObject> |
| 6961 |
</xml><![endif]--><o:p></o:p></span></p> |
| 6962 |
|
| 6963 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 6964 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Here <sub><!--[if gte vml 1]><v:shape |
| 6965 |
id="_x0000_i1178" type="#_x0000_t75" style='width:15pt;height:20.25pt' o:ole=""> |
| 6966 |
<v:imagedata src="./fulldoc_files/image388.wmz" o:title=""/> |
| 6967 |
</v:shape><![endif]--><![if !vml]><img width=20 height=27 |
| 6968 |
src="./fulldoc_files/image389.gif" v:shapes="_x0000_i1178"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6969 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1178" |
| 6970 |
DrawAspect="Content" ObjectID="_1051901384"> |
| 6971 |
</o:OLEObject> |
| 6972 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is the discrete |
| 6973 |
analogue of <sub><!--[if gte vml 1]><v:shape id="_x0000_i1179" type="#_x0000_t75" |
| 6974 |
style='width:50.25pt;height:36.75pt' o:ole=""> |
| 6975 |
<v:imagedata src="./fulldoc_files/image390.wmz" o:title=""/> |
| 6976 |
</v:shape><![endif]--><![if !vml]><img width=67 height=49 |
| 6977 |
src="./fulldoc_files/image391.gif" v:shapes="_x0000_i1179"><![endif]></sub><!--[if gte mso 9]><xml> |
| 6978 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1179" |
| 6979 |
DrawAspect="Content" ObjectID="_1051901385"> |
| 6980 |
</o:OLEObject> |
| 6981 |
</xml><![endif]-->, a vertical integral over the whole depth of the ocean; we |
| 6982 |
sum over the vertical faces of the cells each of depth </span><i |
| 6983 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 6984 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 6985 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 6986 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>D</span></span></i><i |
| 6987 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 6988 |
10.0pt;font-family:Palatino'>z</span></i><span style='font-size:12.0pt; |
| 6989 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>|<sub>k</sub> making up the |
| 6990 |
column of ocean.<span style="mso-spacerun: yes"> </span>The div<sub>h</sub> |
| 6991 |
and grad<sub>h</sub> operators are horizontal components of (2.2.2) and |
| 6992 |
(2.2.7), respectively.<o:p></o:p></span></p> |
| 6993 |
|
| 6994 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6995 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 6996 |
|
| 6997 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 6998 |
font-family:Palatino'>Note that on the rhs of (2.3.1) we have retained a |
| 6999 |
term,<span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 7000 |
|
| 7001 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7002 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7003 |
|
| 7004 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7005 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7006 |
id="_x0000_i1180" type="#_x0000_t75" style='width:338.25pt;height:41.25pt' |
| 7007 |
o:ole=""> |
| 7008 |
<v:imagedata src="./fulldoc_files/image392.wmz" o:title=""/> |
| 7009 |
</v:shape><![endif]--><![if !vml]><img width=451 height=55 |
| 7010 |
src="./fulldoc_files/image393.gif" v:shapes="_x0000_i1180"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7011 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1180" |
| 7012 |
DrawAspect="Content" ObjectID="_1051901386"> |
| 7013 |
</o:OLEObject> |
| 7014 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7015 |
|
| 7016 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7017 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7018 |
|
| 7019 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7020 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>which ensures that </span><span |
| 7021 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1181" |
| 7022 |
type="#_x0000_t75" style='width:108.75pt;height:26.25pt' o:ole=""> |
| 7023 |
<v:imagedata src="./fulldoc_files/image394.wmz" o:title=""/> |
| 7024 |
</v:shape><![endif]--><![if !vml]><img width=145 height=35 |
| 7025 |
src="./fulldoc_files/image395.gif" v:shapes="_x0000_i1181"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7026 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1181" |
| 7027 |
DrawAspect="Content" ObjectID="_1051901388"> |
| 7028 |
</o:OLEObject> |
| 7029 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 7030 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>as the |
| 7031 |
model steps forward. This relaxation technique is often used in solving the |
| 7032 |
Navier-Stokes equations- (see, for example, Williams;1969).<span |
| 7033 |
style="mso-spacerun: yes"> </span>In the present context it obviates the need |
| 7034 |
to step forward barotropic equations for<sub><!--[if gte vml 1]><v:shape id="_x0000_i1182" |
| 7035 |
type="#_x0000_t75" style='width:23.25pt;height:20.25pt' o:ole=""> |
| 7036 |
<v:imagedata src="./fulldoc_files/image396.wmz" o:title=""/> |
| 7037 |
</v:shape><![endif]--><![if !vml]><img width=31 height=27 |
| 7038 |
src="./fulldoc_files/image397.gif" v:shapes="_x0000_i1182"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7039 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1182" |
| 7040 |
DrawAspect="Content" ObjectID="_1051901389"> |
| 7041 |
</o:OLEObject> |
| 7042 |
</xml><![endif]--> separately.<span style="mso-spacerun: yes"> </span>In our |
| 7043 |
method only the prognostic equations for interior velocities, Eq (4.1.1), are |
| 7044 |
stepped forward and the horizontal divergence of the depth-integrated |
| 7045 |
horizontal velocities at each time-step evaluated and used to modify the |
| 7046 |
source-function to the 2-d Elliptic problem accordingly, so tying together |
| 7047 |
the velocity and the pressure field.<o:p></o:p></span></p> |
| 7048 |
|
| 7049 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7050 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7051 |
|
| 7052 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7053 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The Elliptic problem |
| 7054 |
Eqs.(2.3.1) and (2.3.2) can be written in the concise matrix notation:<o:p></o:p></span></p> |
| 7055 |
|
| 7056 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7057 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7058 |
|
| 7059 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 7060 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7061 |
id="_x0000_i1183" type="#_x0000_t75" style='width:99.75pt;height:56.25pt' |
| 7062 |
o:ole="" fillcolor="window"> |
| 7063 |
<v:imagedata src="./fulldoc_files/image398.wmz" o:title=""/> |
| 7064 |
</v:shape><![endif]--><![if !vml]><img width=133 height=75 |
| 7065 |
src="./fulldoc_files/image399.gif" v:shapes="_x0000_i1183"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7066 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1183" |
| 7067 |
DrawAspect="Content" ObjectID="_1051901390"> |
| 7068 |
</o:OLEObject> |
| 7069 |
</xml><![endif]--><span style="mso-spacerun: |
| 7070 |
yes"> </span>(2.3.3)<o:p></o:p></span></p> |
| 7071 |
|
| 7072 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7073 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7074 |
|
| 7075 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7076 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where </span><span |
| 7077 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1184" |
| 7078 |
type="#_x0000_t75" style='width:21pt;height:17.25pt' o:ole=""> |
| 7079 |
<v:imagedata src="./fulldoc_files/image400.wmz" o:title=""/> |
| 7080 |
</v:shape><![endif]--><![if !vml]><img width=28 height=23 |
| 7081 |
src="./fulldoc_files/image401.gif" v:shapes="_x0000_i1184"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7082 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1184" |
| 7083 |
DrawAspect="Content" ObjectID="_1051901392"> |
| 7084 |
</o:OLEObject> |
| 7085 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 7086 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>is a |
| 7087 |
symmetric, positive-definite matrix<a style='mso-footnote-id:ftn3' href="#_ftn3" |
| 7088 |
name="_ftnref3" title=""><span class=MsoFootnoteReference><span |
| 7089 |
style='mso-special-character:footnote'><![if !supportFootnotes]>[3]<![endif]></span></span></a> |
| 7090 |
comprised of</span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7091 |
id="_x0000_i1185" type="#_x0000_t75" style='width:23.25pt;height:17.25pt' |
| 7092 |
o:ole=""> |
| 7093 |
<v:imagedata src="./fulldoc_files/image402.wmz" o:title=""/> |
| 7094 |
</v:shape><![endif]--><![if !vml]><img width=31 height=23 |
| 7095 |
src="./fulldoc_files/image403.gif" v:shapes="_x0000_i1185"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7096 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1185" |
| 7097 |
DrawAspect="Content" ObjectID="_1051901393"> |
| 7098 |
</o:OLEObject> |
| 7099 |
</xml><![endif]--> </span><span style='font-size:12.0pt;mso-bidi-font-size: |
| 7100 |
10.0pt;font-family:Palatino'>and</span><span style='font-family:Palatino'> <sub><!--[if gte vml 1]><v:shape |
| 7101 |
id="_x0000_i1186" type="#_x0000_t75" style='width:27.75pt;height:17.25pt' |
| 7102 |
o:ole=""> |
| 7103 |
<v:imagedata src="./fulldoc_files/image404.wmz" o:title=""/> |
| 7104 |
</v:shape><![endif]--><![if !vml]><img width=37 height=23 |
| 7105 |
src="./fulldoc_files/image405.gif" v:shapes="_x0000_i1186"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7106 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1186" |
| 7107 |
DrawAspect="Content" ObjectID="_1051901394"> |
| 7108 |
</o:OLEObject> |
| 7109 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 7110 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>(matrix |
| 7111 |
representations of the div and grad operators), <sub><!--[if gte vml 1]><v:shape |
| 7112 |
id="_x0000_i1187" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 7113 |
<v:imagedata src="./fulldoc_files/image406.wmz" o:title=""/> |
| 7114 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 7115 |
src="./fulldoc_files/image407.gif" v:shapes="_x0000_i1187"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7116 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1187" |
| 7117 |
DrawAspect="Content" ObjectID="_1051901395"> |
| 7118 |
</o:OLEObject> |
| 7119 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is a column vector of |
| 7120 |
surface pressure elements and <sub><!--[if gte vml 1]><v:shape id="_x0000_i1188" |
| 7121 |
type="#_x0000_t75" style='width:15.75pt;height:17.25pt' o:ole=""> |
| 7122 |
<v:imagedata src="./fulldoc_files/image408.wmz" o:title=""/> |
| 7123 |
</v:shape><![endif]--><![if !vml]><img width=21 height=23 |
| 7124 |
src="./fulldoc_files/image409.gif" v:shapes="_x0000_i1188"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7125 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1188" |
| 7126 |
DrawAspect="Content" ObjectID="_1051901396"> |
| 7127 |
</o:OLEObject> |
| 7128 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>a column vector |
| 7129 |
containing the elements of the rhs of (2.3.1).<span style="mso-spacerun: yes"> |
| 7130 |
</span>The system can thus be solved using a standard conjugate-gradient |
| 7131 |
method, preconditioned for efficient solution on a parallel computer - see |
| 7132 |
section 2.3.2.<o:p></o:p></span></p> |
| 7133 |
|
| 7134 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7135 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7136 |
|
| 7137 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7138 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>In summary, then, because (i) |
| 7139 |
the divergence constraint on the evolving velocities is applied in integral |
| 7140 |
form employing Gauss theorem and (ii) the kinematic boundary condition <b |
| 7141 |
style='mso-bidi-font-weight:normal'>v.n</b>=0 (where <b style='mso-bidi-font-weight: |
| 7142 |
normal'>n</b> is a unit vector normal to a solid boundary) is applied at the face |
| 7143 |
of a cell, then the form of (2.3.3) is unchanged, <i style='mso-bidi-font-style: |
| 7144 |
normal'>even if the face of a cell which abuts the solid boundary is inclined |
| 7145 |
to coordinate surfaces</i>.<span style="mso-spacerun: yes"> </span>This |
| 7146 |
property enables one to rather easily shave zones which abut boundaries to |
| 7147 |
improve the representation of flow over topography (see appendix).<o:p></o:p></span></p> |
| 7148 |
|
| 7149 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span |
| 7150 |
style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p> |
| 7151 |
|
| 7152 |
<p class=MsoNormal><i style='mso-bidi-font-style:normal'><span |
| 7153 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Three-dimensional<o:p></o:p></span></i></p> |
| 7154 |
|
| 7155 |
<p class=MsoNormal><i style='mso-bidi-font-style:normal'><u><span |
| 7156 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></i></p> |
| 7157 |
|
| 7158 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7159 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>In non-hydrostatic calculations |
| 7160 |
a three-dimensional elliptic equation must also be inverted for <sub><!--[if gte vml 1]><v:shape |
| 7161 |
id="_x0000_i1189" type="#_x0000_t75" style='width:21.75pt;height:17.25pt' |
| 7162 |
o:ole=""> |
| 7163 |
<v:imagedata src="./fulldoc_files/image410.wmz" o:title=""/> |
| 7164 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7165 |
src="./fulldoc_files/image411.gif" v:shapes="_x0000_i1189"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7166 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1189" |
| 7167 |
DrawAspect="Content" ObjectID="_1051901398"> |
| 7168 |
</o:OLEObject> |
| 7169 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>to ensure that the <u>local</u> |
| 7170 |
divergence vanishes.<span style="mso-spacerun: yes"> </span>The appropriate |
| 7171 |
discrete form can be deduced in a manner that exactly parallels that which was |
| 7172 |
used to deduce (2.3.1).<span style="mso-spacerun: yes"> </span>Taking </span><span |
| 7173 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 7174 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 7175 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 7176 |
mso-symbol-font-family:Symbol'>Ñ</span></span><i style='mso-bidi-font-style: |
| 7177 |
normal'><sub><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7178 |
font-family:Palatino'>h</span></sub></i><span style='font-size:12.0pt; |
| 7179 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>.(2.1.1)+<sub><!--[if gte vml 1]><v:shape |
| 7180 |
id="_x0000_i1190" type="#_x0000_t75" style='width:50.25pt;height:30.75pt' |
| 7181 |
o:ole="" fillcolor="window"> |
| 7182 |
<v:imagedata src="./fulldoc_files/image412.wmz" o:title=""/> |
| 7183 |
</v:shape><![endif]--><![if !vml]><img width=67 height=41 |
| 7184 |
src="./fulldoc_files/image413.gif" v:shapes="_x0000_i1190"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7185 |
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1190" |
| 7186 |
DrawAspect="Content" ObjectID="_1051901399"> |
| 7187 |
</o:OLEObject> |
| 7188 |
</xml><![endif]-->, invoking (2.1.3) and boundary conditions (1.2.1), the |
| 7189 |
resulting elliptic equation can be written:<o:p></o:p></span></p> |
| 7190 |
|
| 7191 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7192 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7193 |
|
| 7194 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 7195 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7196 |
id="_x0000_i1191" type="#_x0000_t75" style='width:90pt;height:56.25pt' o:ole=""> |
| 7197 |
<v:imagedata src="./fulldoc_files/image414.wmz" o:title=""/> |
| 7198 |
</v:shape><![endif]--><![if !vml]><img width=120 height=75 |
| 7199 |
src="./fulldoc_files/image415.gif" v:shapes="_x0000_i1191"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7200 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1191" |
| 7201 |
DrawAspect="Content" ObjectID="_1051901400"> |
| 7202 |
</o:OLEObject> |
| 7203 |
</xml><![endif]--><span style="mso-spacerun: |
| 7204 |
yes"> </span>(2.3.4)<o:p></o:p></span></p> |
| 7205 |
|
| 7206 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7207 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7208 |
|
| 7209 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7210 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 7211 |
id="_x0000_i1192" type="#_x0000_t75" style='width:21pt;height:17.25pt' o:ole=""> |
| 7212 |
<v:imagedata src="./fulldoc_files/image416.wmz" o:title=""/> |
| 7213 |
</v:shape><![endif]--><![if !vml]><img width=28 height=23 |
| 7214 |
src="./fulldoc_files/image417.gif" v:shapes="_x0000_i1192"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7215 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1192" |
| 7216 |
DrawAspect="Content" ObjectID="_1051901401"> |
| 7217 |
</o:OLEObject> |
| 7218 |
</xml><![endif]-->, like </span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7219 |
id="_x0000_i1193" type="#_x0000_t75" style='width:21pt;height:17.25pt' o:ole=""> |
| 7220 |
<v:imagedata src="./fulldoc_files/image400.wmz" o:title=""/> |
| 7221 |
</v:shape><![endif]--><![if !vml]><img width=28 height=23 |
| 7222 |
src="./fulldoc_files/image418.gif" v:shapes="_x0000_i1193"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7223 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1193" |
| 7224 |
DrawAspect="Content" ObjectID="_1051901402"> |
| 7225 |
</o:OLEObject> |
| 7226 |
</xml><![endif]-->, </span><span style='font-size:12.0pt;mso-bidi-font-size: |
| 7227 |
10.0pt;font-family:Palatino'>is</span><span style='font-family:Palatino'> </span><span |
| 7228 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>a |
| 7229 |
symmetric<a style='mso-footnote-id:ftn4' href="#_ftn4" name="_ftnref4" title=""><span |
| 7230 |
class=MsoFootnoteReference><span style='mso-special-character:footnote'><![if !supportFootnotes]>[4]<![endif]></span></span></a>, |
| 7231 |
positive-definite matrix representing the discrete representation of <sub><!--[if gte vml 1]><v:shape |
| 7232 |
id="_x0000_i1194" type="#_x0000_t75" style='width:17.25pt;height:15.75pt' |
| 7233 |
o:ole=""> |
| 7234 |
<v:imagedata src="./fulldoc_files/image419.wmz" o:title=""/> |
| 7235 |
</v:shape><![endif]--><![if !vml]><img width=23 height=21 |
| 7236 |
src="./fulldoc_files/image420.gif" v:shapes="_x0000_i1194"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7237 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1194" |
| 7238 |
DrawAspect="Content" ObjectID="_1051901404"> |
| 7239 |
</o:OLEObject> |
| 7240 |
</xml><![endif]-->, but now in three dimensions.<span style="mso-spacerun: |
| 7241 |
yes"> </span>Here <sub><!--[if gte vml 1]><v:shape id="_x0000_i1195" type="#_x0000_t75" |
| 7242 |
style='width:15.75pt;height:17.25pt' o:ole=""> |
| 7243 |
<v:imagedata src="./fulldoc_files/image421.wmz" o:title=""/> |
| 7244 |
</v:shape><![endif]--><![if !vml]><img width=21 height=23 |
| 7245 |
src="./fulldoc_files/image422.gif" v:shapes="_x0000_i1195"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7246 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1195" |
| 7247 |
DrawAspect="Content" ObjectID="_1051901405"> |
| 7248 |
</o:OLEObject> |
| 7249 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and <sub><!--[if gte vml 1]><v:shape |
| 7250 |
id="_x0000_i1196" type="#_x0000_t75" style='width:21.75pt;height:17.25pt' |
| 7251 |
o:ole=""> |
| 7252 |
<v:imagedata src="./fulldoc_files/image423.wmz" o:title=""/> |
| 7253 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7254 |
src="./fulldoc_files/image424.gif" v:shapes="_x0000_i1196"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7255 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1196" |
| 7256 |
DrawAspect="Content" ObjectID="_1051901406"> |
| 7257 |
</o:OLEObject> |
| 7258 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>are (1</span><span |
| 7259 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 7260 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 7261 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 7262 |
mso-symbol-font-family:Symbol'>´</span></span><i style='mso-bidi-font-style: |
| 7263 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 7264 |
Palatino'>N</span></i><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7265 |
font-family:Palatino'>) column vectors containing the source function (the |
| 7266 |
discrete form of Eq.(1.5.13)) and non-hydrostatic pressure, in each of the <sub><!--[if gte vml 1]><v:shape |
| 7267 |
id="_x0000_i1197" type="#_x0000_t75" style='width:66.75pt;height:18pt' o:ole=""> |
| 7268 |
<v:imagedata src="./fulldoc_files/image425.wmz" o:title=""/> |
| 7269 |
</v:shape><![endif]--><![if !vml]><img width=89 height=24 |
| 7270 |
src="./fulldoc_files/image426.gif" v:shapes="_x0000_i1197"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7271 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1197" |
| 7272 |
DrawAspect="Content" ObjectID="_1051901407"> |
| 7273 |
</o:OLEObject> |
| 7274 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>cells in to which |
| 7275 |
the fluid has been carved.<span style="mso-spacerun: yes"> </span>The column |
| 7276 |
vectors have singly subscripted elements<sub><!--[if gte vml 1]><v:shape id="_x0000_i1198" |
| 7277 |
type="#_x0000_t75" style='width:12.75pt;height:17.25pt' o:ole=""> |
| 7278 |
<v:imagedata src="./fulldoc_files/image427.wmz" o:title=""/> |
| 7279 |
</v:shape><![endif]--><![if !vml]><img width=17 height=23 |
| 7280 |
src="./fulldoc_files/image428.gif" v:shapes="_x0000_i1198"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7281 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1198" |
| 7282 |
DrawAspect="Content" ObjectID="_1051901409"> |
| 7283 |
</o:OLEObject> |
| 7284 |
</xml><![endif]--> in which the elements are first enumerated in each vertical |
| 7285 |
column, and only then in the horizontal directions thus: <o:p></o:p></span></p> |
| 7286 |
|
| 7287 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7288 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7289 |
|
| 7290 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7291 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7292 |
id="_x0000_i1199" type="#_x0000_t75" style='width:171.75pt;height:17.25pt' |
| 7293 |
o:ole=""> |
| 7294 |
<v:imagedata src="./fulldoc_files/image429.wmz" o:title=""/> |
| 7295 |
</v:shape><![endif]--><![if !vml]><img width=229 height=23 |
| 7296 |
src="./fulldoc_files/image430.gif" v:shapes="_x0000_i1199"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7297 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1199" |
| 7298 |
DrawAspect="Content" ObjectID="_1051901410"> |
| 7299 |
</o:OLEObject> |
| 7300 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7301 |
|
| 7302 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7303 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7304 |
|
| 7305 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7306 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where <i style='mso-bidi-font-style: |
| 7307 |
normal'>i</i> is an index increasing eastwards, <i style='mso-bidi-font-style: |
| 7308 |
normal'>j</i> is an index increasing southwards and <i style='mso-bidi-font-style: |
| 7309 |
normal'>k</i> increases downwards.<span style="mso-spacerun: yes"> |
| 7310 |
</span>Although huge, of size </span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7311 |
id="_x0000_i1200" type="#_x0000_t75" style='width:57.75pt;height:24pt' o:ole=""> |
| 7312 |
<v:imagedata src="./fulldoc_files/image431.wmz" o:title=""/> |
| 7313 |
</v:shape><![endif]--><![if !vml]><img width=77 height=32 |
| 7314 |
src="./fulldoc_files/image432.gif" v:shapes="_x0000_i1200"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7315 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1200" |
| 7316 |
DrawAspect="Content" ObjectID="_1051901412"> |
| 7317 |
</o:OLEObject> |
| 7318 |
</xml><![endif]--></span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7319 |
font-family:Palatino'>, <sub><!--[if gte vml 1]><v:shape id="_x0000_i1201" |
| 7320 |
type="#_x0000_t75" style='width:21.75pt;height:17.25pt' o:ole=""> |
| 7321 |
<v:imagedata src="./fulldoc_files/image433.wmz" o:title=""/> |
| 7322 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7323 |
src="./fulldoc_files/image434.gif" v:shapes="_x0000_i1201"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7324 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1201" |
| 7325 |
DrawAspect="Content" ObjectID="_1051901413"> |
| 7326 |
</o:OLEObject> |
| 7327 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>has a particularly |
| 7328 |
simple form which can be exploited to devise a highly efficient method of |
| 7329 |
inversion.<o:p></o:p></span></p> |
| 7330 |
|
| 7331 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7332 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7333 |
|
| 7334 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7335 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7336 |
id="_x0000_i1203" type="#_x0000_t75" style='width:21.75pt;height:17.25pt' |
| 7337 |
o:ole=""> |
| 7338 |
<v:imagedata src="./fulldoc_files/image433.wmz" o:title=""/> |
| 7339 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7340 |
src="./fulldoc_files/image435.gif" v:shapes="_x0000_i1203"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7341 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1203" |
| 7342 |
DrawAspect="Content" ObjectID="_1051901414"> |
| 7343 |
</o:OLEObject> |
| 7344 |
</xml><![endif]-->has 7 diagonals representing the coupling in the three space |
| 7345 |
dimensions. In any<span style="mso-spacerun: yes"> </span>particular row of |
| 7346 |
the matrix, the three leading diagonals are the coefficients multiplying the |
| 7347 |
pressure <i style='mso-bidi-font-style:normal'>in the same vertical column of |
| 7348 |
the fluid</i>; the four diagonals in the wings are the coefficients multiplying |
| 7349 |
pressures in cells <i style='mso-bidi-font-style:normal'>in the same horizontal |
| 7350 |
plane</i>.<span style="mso-spacerun: yes"> </span>The inner three diagonals |
| 7351 |
can usefully be blocked and arranged as shown below:<o:p></o:p></span></p> |
| 7352 |
|
| 7353 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7354 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7355 |
|
| 7356 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 7357 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7358 |
id="_x0000_i1202" type="#_x0000_t75" style='width:252.75pt;height:147.75pt' |
| 7359 |
o:ole=""> |
| 7360 |
<v:imagedata src="./fulldoc_files/image436.wmz" o:title=""/> |
| 7361 |
</v:shape><![endif]--><![if !vml]><img width=337 height=197 |
| 7362 |
src="./fulldoc_files/image437.gif" v:shapes="_x0000_i1202"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7363 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1202" |
| 7364 |
DrawAspect="Content" ObjectID="_1051901415"> |
| 7365 |
</o:OLEObject> |
| 7366 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 7367 |
</span>(2.3.5)<o:p></o:p></span></p> |
| 7368 |
|
| 7369 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7370 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7371 |
|
| 7372 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7373 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Here each block <sub><!--[if gte vml 1]><v:shape |
| 7374 |
id="_x0000_i1204" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole=""> |
| 7375 |
<v:imagedata src="./fulldoc_files/image438.wmz" o:title=""/> |
| 7376 |
</v:shape><![endif]--><![if !vml]><img width=20 height=23 |
| 7377 |
src="./fulldoc_files/image439.gif" v:shapes="_x0000_i1204"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7378 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1204" |
| 7379 |
DrawAspect="Content" ObjectID="_1051901417"> |
| 7380 |
</o:OLEObject> |
| 7381 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is a tri-diagonal |
| 7382 |
matrix representing <sub><!--[if gte vml 1]><v:shape id="_x0000_i1205" type="#_x0000_t75" |
| 7383 |
style='width:36.75pt;height:17.25pt' o:ole=""> |
| 7384 |
<v:imagedata src="./fulldoc_files/image440.wmz" o:title=""/> |
| 7385 |
</v:shape><![endif]--><![if !vml]><img width=49 height=23 |
| 7386 |
src="./fulldoc_files/image441.gif" v:shapes="_x0000_i1205"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7387 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1205" |
| 7388 |
DrawAspect="Content" ObjectID="_1051901418"> |
| 7389 |
</o:OLEObject> |
| 7390 |
</xml><![endif]-->and<b style='mso-bidi-font-weight:normal'> e </b>is a |
| 7391 |
diagonal matrix representing <sub><!--[if gte vml 1]><v:shape id="_x0000_i1206" |
| 7392 |
type="#_x0000_t75" style='width:21pt;height:18pt' o:ole=""> |
| 7393 |
<v:imagedata src="./fulldoc_files/image442.wmz" o:title=""/> |
| 7394 |
</v:shape><![endif]--><![if !vml]><img width=28 height=24 |
| 7395 |
src="./fulldoc_files/image443.gif" v:shapes="_x0000_i1206"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7396 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1206" |
| 7397 |
DrawAspect="Content" ObjectID="_1051901419"> |
| 7398 |
</o:OLEObject> |
| 7399 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span><b |
| 7400 |
style='mso-bidi-font-weight:normal'>D</b> and <b style='mso-bidi-font-weight: |
| 7401 |
normal'>e</b> are matrices of size <sub><!--[if gte vml 1]><v:shape id="_x0000_i1207" |
| 7402 |
type="#_x0000_t75" style='width:45pt;height:15.75pt' o:ole=""> |
| 7403 |
<v:imagedata src="./fulldoc_files/image444.wmz" o:title=""/> |
| 7404 |
</v:shape><![endif]--><![if !vml]><img width=60 height=21 |
| 7405 |
src="./fulldoc_files/image445.gif" v:shapes="_x0000_i1207"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7406 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1207" |
| 7407 |
DrawAspect="Content" ObjectID="_1051901420"> |
| 7408 |
</o:OLEObject> |
| 7409 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>if there are</span><span |
| 7410 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1208" |
| 7411 |
type="#_x0000_t75" style='width:18pt;height:15.75pt' o:ole=""> |
| 7412 |
<v:imagedata src="./fulldoc_files/image446.wmz" o:title=""/> |
| 7413 |
</v:shape><![endif]--><![if !vml]><img width=24 height=21 |
| 7414 |
src="./fulldoc_files/image447.gif" v:shapes="_x0000_i1208"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7415 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1208" |
| 7416 |
DrawAspect="Content" ObjectID="_1051901422"> |
| 7417 |
</o:OLEObject> |
| 7418 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 7419 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>cells |
| 7420 |
in each column of the ocean:- there are <sub><!--[if gte vml 1]><v:shape id="_x0000_i1209" |
| 7421 |
type="#_x0000_t75" style='width:45pt;height:15.75pt' o:ole=""> |
| 7422 |
<v:imagedata src="./fulldoc_files/image448.wmz" o:title=""/> |
| 7423 |
</v:shape><![endif]--><![if !vml]><img width=60 height=21 |
| 7424 |
src="./fulldoc_files/image449.gif" v:shapes="_x0000_i1209"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7425 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1209" |
| 7426 |
DrawAspect="Content" ObjectID="_1051901423"> |
| 7427 |
</o:OLEObject> |
| 7428 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>such blocks, one for |
| 7429 |
each column of the ocean.<o:p></o:p></span></p> |
| 7430 |
|
| 7431 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7432 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7433 |
|
| 7434 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7435 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>One further property of <sub><!--[if gte vml 1]><v:shape |
| 7436 |
id="_x0000_i1210" type="#_x0000_t75" style='width:21.75pt;height:17.25pt' |
| 7437 |
o:ole=""> |
| 7438 |
<v:imagedata src="./fulldoc_files/image450.wmz" o:title=""/> |
| 7439 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7440 |
src="./fulldoc_files/image451.gif" v:shapes="_x0000_i1210"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7441 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1210" |
| 7442 |
DrawAspect="Content" ObjectID="_1051901424"> |
| 7443 |
</o:OLEObject> |
| 7444 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>should be noted.<span |
| 7445 |
style="mso-spacerun: yes"> </span>If the vertical dimension of a cell is much |
| 7446 |
smaller than its horizontal extent (as is often the case because the ocean is |
| 7447 |
much shallower than it is wide) then the <sub><!--[if gte vml 1]><v:shape id="_x0000_i1211" |
| 7448 |
type="#_x0000_t75" style='width:21pt;height:18pt' o:ole=""> |
| 7449 |
<v:imagedata src="./fulldoc_files/image452.wmz" o:title=""/> |
| 7450 |
</v:shape><![endif]--><![if !vml]><img width=28 height=24 |
| 7451 |
src="./fulldoc_files/image453.gif" v:shapes="_x0000_i1211"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7452 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1211" |
| 7453 |
DrawAspect="Content" ObjectID="_1051901425"> |
| 7454 |
</o:OLEObject> |
| 7455 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 7456 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 7457 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 7458 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 7459 |
mso-symbol-font-family:Symbol'>»</span></span><span style='font-size:12.0pt; |
| 7460 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7461 |
id="_x0000_i1212" type="#_x0000_t75" style='width:36.75pt;height:17.25pt' |
| 7462 |
o:ole=""> |
| 7463 |
<v:imagedata src="./fulldoc_files/image440.wmz" o:title=""/> |
| 7464 |
</v:shape><![endif]--><![if !vml]><img width=49 height=23 |
| 7465 |
src="./fulldoc_files/image454.gif" v:shapes="_x0000_i1212"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7466 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1212" |
| 7467 |
DrawAspect="Content" ObjectID="_1051901427"> |
| 7468 |
</o:OLEObject> |
| 7469 |
</xml><![endif]--> and <sub><!--[if gte vml 1]><v:shape id="_x0000_i1213" |
| 7470 |
type="#_x0000_t75" style='width:21.75pt;height:17.25pt' o:ole=""> |
| 7471 |
<v:imagedata src="./fulldoc_files/image450.wmz" o:title=""/> |
| 7472 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7473 |
src="./fulldoc_files/image455.gif" v:shapes="_x0000_i1213"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7474 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1213" |
| 7475 |
DrawAspect="Content" ObjectID="_1051901428"> |
| 7476 |
</o:OLEObject> |
| 7477 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is dominated by the |
| 7478 |
blocks <b style='mso-bidi-font-weight:normal'>D</b> along its diagonal.<span |
| 7479 |
style="mso-spacerun: yes"> </span>The elements <b style='mso-bidi-font-weight: |
| 7480 |
normal'>e</b> are smaller than those of <b style='mso-bidi-font-weight:normal'>D</b> |
| 7481 |
by an amount <sub><!--[if gte vml 1]><v:shape id="_x0000_i1214" type="#_x0000_t75" |
| 7482 |
style='width:35.25pt;height:33.75pt' o:ole=""> |
| 7483 |
<v:imagedata src="./fulldoc_files/image456.wmz" o:title=""/> |
| 7484 |
</v:shape><![endif]--><![if !vml]><img width=47 height=45 |
| 7485 |
src="./fulldoc_files/image457.gif" v:shapes="_x0000_i1214"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7486 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1214" |
| 7487 |
DrawAspect="Content" ObjectID="_1051901429"> |
| 7488 |
</o:OLEObject> |
| 7489 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>Moreover, the |
| 7490 |
tracer parameter <i style='mso-bidi-font-style:normal'>q</i> always appears |
| 7491 |
as a multiplier of the <b style='mso-bidi-font-weight:normal'>e</b> matrix - |
| 7492 |
see (2.3.5); thus when <i style='mso-bidi-font-style:normal'>q</i> is set to |
| 7493 |
zero (corresponding to the hydrostatic limit), <sub><!--[if gte vml 1]><v:shape |
| 7494 |
id="_x0000_i1215" type="#_x0000_t75" style='width:21.75pt;height:17.25pt' |
| 7495 |
o:ole=""> |
| 7496 |
<v:imagedata src="./fulldoc_files/image450.wmz" o:title=""/> |
| 7497 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7498 |
src="./fulldoc_files/image458.gif" v:shapes="_x0000_i1215"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7499 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1215" |
| 7500 |
DrawAspect="Content" ObjectID="_1051901430"> |
| 7501 |
</o:OLEObject> |
| 7502 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>is comprised <i |
| 7503 |
style='mso-bidi-font-style:normal'>only</i> of the blocks <b style='mso-bidi-font-weight: |
| 7504 |
normal'>D </b>and so can readily be inverted.<span style="mso-spacerun: yes"> |
| 7505 |
</span>Thus if we precondition (2.3.4) by premultiplying it by a matrix which |
| 7506 |
is comprised of the inverse of these blocks, that preconditioner will be an |
| 7507 |
exact inverse of <sub><!--[if gte vml 1]><v:shape id="_x0000_i1216" type="#_x0000_t75" |
| 7508 |
style='width:21.75pt;height:17.25pt' o:ole=""> |
| 7509 |
<v:imagedata src="./fulldoc_files/image450.wmz" o:title=""/> |
| 7510 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7511 |
src="./fulldoc_files/image459.gif" v:shapes="_x0000_i1216"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7512 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1216" |
| 7513 |
DrawAspect="Content" ObjectID="_1051901431"> |
| 7514 |
</o:OLEObject> |
| 7515 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>in the hydrostatic |
| 7516 |
limit.<span style="mso-spacerun: yes"> </span>These properties of <sub><!--[if gte vml 1]><v:shape |
| 7517 |
id="_x0000_i1217" type="#_x0000_t75" style='width:21.75pt;height:17.25pt' |
| 7518 |
o:ole=""> |
| 7519 |
<v:imagedata src="./fulldoc_files/image450.wmz" o:title=""/> |
| 7520 |
</v:shape><![endif]--><![if !vml]><img width=29 height=23 |
| 7521 |
src="./fulldoc_files/image460.gif" v:shapes="_x0000_i1217"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7522 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1217" |
| 7523 |
DrawAspect="Content" ObjectID="_1051901432"> |
| 7524 |
</o:OLEObject> |
| 7525 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>will be exploited in |
| 7526 |
our chosen method of solution.<o:p></o:p></span></p> |
| 7527 |
|
| 7528 |
<p class=MsoNormalIndent style='margin-left:0pt'><u><span style='font-size: |
| 7529 |
14.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 7530 |
|
| 7531 |
<h3><a name="_Toc407078243"></a><a name="_Toc407090397"></a><a |
| 7532 |
name="_Toc407090600"></a><a name="_Toc407169629"><span style='mso-bookmark: |
| 7533 |
_Toc407090600'><span style='mso-bookmark:_Toc407090397'><span style='mso-bookmark: |
| 7534 |
_Toc407078243'><u>2.3.2 Preconditioned conjugate-gradient solution method</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 7535 |
|
| 7536 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7537 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7538 |
|
| 7539 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7540 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Many standard references to |
| 7541 |
preconditioned conjugate gradient methods exist - see, for example, Press et |
| 7542 |
al; 1988 and references therein.<span style="mso-spacerun: yes"> </span>We |
| 7543 |
briefly outline the nub of the method here, emphasising the use we make of |
| 7544 |
preconditioners.<o:p></o:p></span></p> |
| 7545 |
|
| 7546 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7547 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7548 |
|
| 7549 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7550 |
font-family:Palatino'>Our problem is to find <b style='mso-bidi-font-weight: |
| 7551 |
normal'>p</b> given <b style='mso-bidi-font-weight:normal'>A</b> and <b |
| 7552 |
style='mso-bidi-font-weight:normal'>f</b> (see (2.3.3) and (2.3.4)), where:<o:p></o:p></span></p> |
| 7553 |
|
| 7554 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7555 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7556 |
|
| 7557 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 7558 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 7559 |
style="mso-spacerun: yes"> </span><span |
| 7560 |
style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 7561 |
id="_x0000_i1218" type="#_x0000_t75" style='width:36.75pt;height:15.75pt' |
| 7562 |
o:ole=""> |
| 7563 |
<v:imagedata src="./fulldoc_files/image461.wmz" o:title=""/> |
| 7564 |
</v:shape><![endif]--><![if !vml]><img width=49 height=21 |
| 7565 |
src="./fulldoc_files/image462.gif" v:shapes="_x0000_i1218"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7566 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1218" |
| 7567 |
DrawAspect="Content" ObjectID="_1051901434"> |
| 7568 |
</o:OLEObject> |
| 7569 |
</xml><![endif]--><span style="mso-spacerun: |
| 7570 |
yes"> </span>(2.3.6)<o:p></o:p></span></p> |
| 7571 |
|
| 7572 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7573 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7574 |
|
| 7575 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7576 |
font-family:Palatino'>and <b style='mso-bidi-font-weight:normal'>A</b> is a |
| 7577 |
symmetric, positive-definite matrix.<o:p></o:p></span></p> |
| 7578 |
|
| 7579 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7580 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7581 |
|
| 7582 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7583 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>In serious modelling |
| 7584 |
applications the size of <b style='mso-bidi-font-weight:normal'>A</b> is too |
| 7585 |
large for direct methods to be useful in 3-dimensions and often in 2-dimensions |
| 7586 |
too.<span style="mso-spacerun: yes"> </span>Since <b style='mso-bidi-font-weight: |
| 7587 |
normal'>A</b> does not change in time, it could be inverted once and |
| 7588 |
stored.<span style="mso-spacerun: yes"> </span>However, although <b |
| 7589 |
style='mso-bidi-font-weight:normal'>A</b> is sparse, its inverse is dense and |
| 7590 |
so operating with its inverse would involve <i style='mso-bidi-font-style:normal'>N</i><sup>2</sup> |
| 7591 |
multiplications; an unrealistic task given that typically <i style='mso-bidi-font-style: |
| 7592 |
normal'>N</i> >> 100000.<span style="mso-spacerun: yes"> </span>So we |
| 7593 |
adopt an iterative procedure, preconditioned conjugate gradient iteration, |
| 7594 |
which exploits the sparseness of <b style='mso-bidi-font-weight:normal'>A</b> |
| 7595 |
and its diagonal dominance.<span style="mso-spacerun: yes"> </span>The |
| 7596 |
procedure involves repeated multiplication of the iterative solution by <b |
| 7597 |
style='mso-bidi-font-weight:normal'>A</b> and by another sparse matrix <b |
| 7598 |
style='mso-bidi-font-weight:normal'>K</b>, an approximate inverse of <b |
| 7599 |
style='mso-bidi-font-weight:normal'>A</b>; <b style='mso-bidi-font-weight:normal'>K</b> |
| 7600 |
is called the preconditioner.<o:p></o:p></span></p> |
| 7601 |
|
| 7602 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7603 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7604 |
|
| 7605 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7606 |
font-family:Palatino'>The algorithm can be understood thus:<o:p></o:p></span></p> |
| 7607 |
|
| 7608 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7609 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7610 |
|
| 7611 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7612 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Let us pre-multiply Eq.(2.3.6) |
| 7613 |
by a (carefully chosen) matrix <b style='mso-bidi-font-weight:normal'>K</b>, |
| 7614 |
which is an approximate inverse of <b style='mso-bidi-font-weight:normal'>A</b>, |
| 7615 |
so that<span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 7616 |
id="_x0000_i1219" type="#_x0000_t75" style='width:39.75pt;height:12.75pt' |
| 7617 |
o:ole=""> |
| 7618 |
<v:imagedata src="./fulldoc_files/image463.wmz" o:title=""/> |
| 7619 |
</v:shape><![endif]--><![if !vml]><img width=53 height=17 |
| 7620 |
src="./fulldoc_files/image464.gif" v:shapes="_x0000_i1219"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7621 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1219" |
| 7622 |
DrawAspect="Content" ObjectID="_1051901435"> |
| 7623 |
</o:OLEObject> |
| 7624 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>Then (2.3.6) can be |
| 7625 |
written:<o:p></o:p></span></p> |
| 7626 |
|
| 7627 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7628 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7629 |
|
| 7630 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7631 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7632 |
id="_x0000_i1220" type="#_x0000_t75" style='width:69.75pt;height:18pt' o:ole=""> |
| 7633 |
<v:imagedata src="./fulldoc_files/image465.wmz" o:title=""/> |
| 7634 |
</v:shape><![endif]--><![if !vml]><img width=93 height=24 |
| 7635 |
src="./fulldoc_files/image466.gif" v:shapes="_x0000_i1220"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7636 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1220" |
| 7637 |
DrawAspect="Content" ObjectID="_1051901436"> |
| 7638 |
</o:OLEObject> |
| 7639 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7640 |
|
| 7641 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7642 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7643 |
|
| 7644 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7645 |
font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape id="_x0000_i1221" |
| 7646 |
type="#_x0000_t75" style='width:60pt;height:14.25pt' o:ole=""> |
| 7647 |
<v:imagedata src="./fulldoc_files/image467.wmz" o:title=""/> |
| 7648 |
</v:shape><![endif]--><![if !vml]><img width=80 height=19 |
| 7649 |
src="./fulldoc_files/image468.gif" v:shapes="_x0000_i1221"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7650 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1221" |
| 7651 |
DrawAspect="Content" ObjectID="_1051901438"> |
| 7652 |
</o:OLEObject> |
| 7653 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>To the extent that |
| 7654 |
|<b style='mso-bidi-font-weight:normal'>C|</b> </span><span style='font-size: |
| 7655 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino; |
| 7656 |
mso-hansi-font-family:Palatino;mso-char-type:symbol;mso-symbol-font-family: |
| 7657 |
Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>®</span></span><b |
| 7658 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 7659 |
10.0pt;font-family:Palatino'>0</span></b><span style='font-size:12.0pt; |
| 7660 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>, the above suggests the |
| 7661 |
following iterative scheme -<span style="mso-spacerun: yes"> </span>'i' is the |
| 7662 |
iteration step:<o:p></o:p></span></p> |
| 7663 |
|
| 7664 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7665 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7666 |
|
| 7667 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7668 |
font-family:Palatino'><span style="mso-spacerun: |
| 7669 |
yes"> </span><span |
| 7670 |
style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1222" |
| 7671 |
type="#_x0000_t75" style='width:81pt;height:38.25pt' o:ole=""> |
| 7672 |
<v:imagedata src="./fulldoc_files/image469.wmz" o:title=""/> |
| 7673 |
</v:shape><![endif]--><![if !vml]><img width=108 height=51 |
| 7674 |
src="./fulldoc_files/image470.gif" v:shapes="_x0000_i1222"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7675 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1222" |
| 7676 |
DrawAspect="Content" ObjectID="_1051901439"> |
| 7677 |
</o:OLEObject> |
| 7678 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 7679 |
|
| 7680 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7681 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7682 |
|
| 7683 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7684 |
font-family:Palatino'>where<o:p></o:p></span></p> |
| 7685 |
|
| 7686 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7687 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7688 |
|
| 7689 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7690 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7691 |
id="_x0000_i1223" type="#_x0000_t75" style='width:45.75pt;height:15.75pt' |
| 7692 |
o:ole=""> |
| 7693 |
<v:imagedata src="./fulldoc_files/image471.wmz" o:title=""/> |
| 7694 |
</v:shape><![endif]--><![if !vml]><img width=61 height=21 |
| 7695 |
src="./fulldoc_files/image472.gif" v:shapes="_x0000_i1223"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7696 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1223" |
| 7697 |
DrawAspect="Content" ObjectID="_1051901440"> |
| 7698 |
</o:OLEObject> |
| 7699 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7700 |
|
| 7701 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7702 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7703 |
|
| 7704 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7705 |
font-family:Palatino'>is called the <i style='mso-bidi-font-style:normal'>search |
| 7706 |
direction</i><span style="mso-spacerun: yes"> </span>and <o:p></o:p></span></p> |
| 7707 |
|
| 7708 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7709 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7710 |
|
| 7711 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7712 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7713 |
id="_x0000_i1224" type="#_x0000_t75" style='width:62.25pt;height:18pt' o:ole=""> |
| 7714 |
<v:imagedata src="./fulldoc_files/image473.wmz" o:title=""/> |
| 7715 |
</v:shape><![endif]--><![if !vml]><img width=83 height=24 |
| 7716 |
src="./fulldoc_files/image474.gif" v:shapes="_x0000_i1224"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7717 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1224" |
| 7718 |
DrawAspect="Content" ObjectID="_1051901441"> |
| 7719 |
</o:OLEObject> |
| 7720 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7721 |
|
| 7722 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7723 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7724 |
|
| 7725 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7726 |
font-family:Palatino'>is the <i style='mso-bidi-font-style:normal'>residual |
| 7727 |
vector</i>.<span style="mso-spacerun: yes"> </span>The <b style='mso-bidi-font-weight: |
| 7728 |
normal'>r</b>'s and <b style='mso-bidi-font-weight:normal'>b</b>'s can be |
| 7729 |
deduced from the previous iteration using the relations:<o:p></o:p></span></p> |
| 7730 |
|
| 7731 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7732 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7733 |
|
| 7734 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7735 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7736 |
id="_x0000_i1225" type="#_x0000_t75" style='width:84pt;height:36pt' o:ole=""> |
| 7737 |
<v:imagedata src="./fulldoc_files/image475.wmz" o:title=""/> |
| 7738 |
</v:shape><![endif]--><![if !vml]><img width=112 height=48 |
| 7739 |
src="./fulldoc_files/image476.gif" v:shapes="_x0000_i1225"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7740 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1225" |
| 7741 |
DrawAspect="Content" ObjectID="_1051901442"> |
| 7742 |
</o:OLEObject> |
| 7743 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7744 |
|
| 7745 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7746 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7747 |
|
| 7748 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7749 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The above iterative procedure |
| 7750 |
can be accelerated by choosing those search directions that minimize the |
| 7751 |
magnitude of the residual vector as measured by the inner product <sub><!--[if gte vml 1]><v:shape |
| 7752 |
id="_x0000_i1226" type="#_x0000_t75" style='width:33.75pt;height:17.25pt' |
| 7753 |
o:ole=""> |
| 7754 |
<v:imagedata src="./fulldoc_files/image477.wmz" o:title=""/> |
| 7755 |
</v:shape><![endif]--><![if !vml]><img width=45 height=23 |
| 7756 |
src="./fulldoc_files/image478.gif" v:shapes="_x0000_i1226"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7757 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1226" |
| 7758 |
DrawAspect="Content" ObjectID="_1051901444"> |
| 7759 |
</o:OLEObject> |
| 7760 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>Our chosen method, |
| 7761 |
the conjugate gradient method<a style='mso-footnote-id:ftn5' href="#_ftn5" |
| 7762 |
name="_ftnref5" title=""><span class=MsoFootnoteReference><span |
| 7763 |
style='mso-special-character:footnote'><![if !supportFootnotes]>[5]<![endif]></span></span></a>,<span |
| 7764 |
style="mso-spacerun: yes"> </span>takes a form much like the simple scheme |
| 7765 |
outlined above, but the search directions are optimized.<span |
| 7766 |
style="mso-spacerun: yes"> </span>It can be written:<o:p></o:p></span></p> |
| 7767 |
|
| 7768 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7769 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7770 |
|
| 7771 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-family: |
| 7772 |
Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1227" type="#_x0000_t75" |
| 7773 |
style='width:204pt;height:261.75pt' o:ole=""> |
| 7774 |
<v:imagedata src="./fulldoc_files/image479.wmz" o:title=""/> |
| 7775 |
</v:shape><![endif]--><![if !vml]><img width=272 height=349 |
| 7776 |
src="./fulldoc_files/image480.gif" v:shapes="_x0000_i1227"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7777 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1227" |
| 7778 |
DrawAspect="Content" ObjectID="_1051901445"> |
| 7779 |
</o:OLEObject> |
| 7780 |
</xml><![endif]--><span style="mso-spacerun: yes"> |
| 7781 |
</span></span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7782 |
font-family:Palatino'>(2.3.7)<o:p></o:p></span></p> |
| 7783 |
|
| 7784 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7785 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7786 |
|
| 7787 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7788 |
font-family:Palatino'>Here <b style='mso-bidi-font-weight:normal'>[<span |
| 7789 |
style="mso-spacerun: yes"> </span>,<span style="mso-spacerun: yes"> </span>]</b> |
| 7790 |
is the inner product of two vectors.<o:p></o:p></span></p> |
| 7791 |
|
| 7792 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7793 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7794 |
|
| 7795 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7796 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The conjugate-gradient |
| 7797 |
procedure involves, at each iteration, multiplication of vectors by<span |
| 7798 |
style="mso-spacerun: yes"> </span><b style='mso-bidi-font-weight:normal'>A</b> |
| 7799 |
and <b style='mso-bidi-font-weight:normal'>K</b> and the evaluation of two |
| 7800 |
global sums to form the inner product.<span style="mso-spacerun: yes"> |
| 7801 |
</span>The cost of the preconditioner is one operation by it per iteration.<o:p></o:p></span></p> |
| 7802 |
|
| 7803 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7804 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7805 |
|
| 7806 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7807 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>We have designed |
| 7808 |
preconditioners, <b style='mso-bidi-font-weight:normal'>K</b>, for both the 2-d |
| 7809 |
and 3-d problems, so that (i) it can be easily stored (ii) the number of |
| 7810 |
operations required when multiplying by it, is as small as possible and (iii) |
| 7811 |
it is a good approximation to <b style='mso-bidi-font-weight:normal'>A</b><sup>-1</sup> |
| 7812 |
so the iterative procedure converges rapidly.<span style="mso-spacerun: yes"> |
| 7813 |
</span>Because the true inverse is dense, our choice will be a compromise |
| 7814 |
between these, sometimes conflicting, ideal properties.<o:p></o:p></span></p> |
| 7815 |
|
| 7816 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7817 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7818 |
|
| 7819 |
<p class=MsoNormal><i style='mso-bidi-font-style:normal'><span |
| 7820 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Two-dimensional<o:p></o:p></span></i></p> |
| 7821 |
|
| 7822 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7823 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7824 |
|
| 7825 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7826 |
font-family:Palatino'>At each horizontal location (2.3.3) can be written:<o:p></o:p></span></p> |
| 7827 |
|
| 7828 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7829 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7830 |
|
| 7831 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7832 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7833 |
id="_x0000_i1229" type="#_x0000_t75" style='width:3in;height:18pt' o:ole=""> |
| 7834 |
<v:imagedata src="./fulldoc_files/image481.wmz" o:title=""/> |
| 7835 |
</v:shape><![endif]--><![if !vml]><img width=288 height=24 |
| 7836 |
src="./fulldoc_files/image482.gif" v:shapes="_x0000_i1229"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7837 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1229" |
| 7838 |
DrawAspect="Content" ObjectID="_1051901446"> |
| 7839 |
</o:OLEObject> |
| 7840 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7841 |
|
| 7842 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7843 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7844 |
|
| 7845 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 7846 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where the superscripts denote |
| 7847 |
the center, west, east, north and south locations in the operators five point |
| 7848 |
stencil.<span style="mso-spacerun: yes"> </span>The leading diagonal of <b |
| 7849 |
style='mso-bidi-font-weight:normal'>A<sub>2d</sub></b> will be comprised of the |
| 7850 |
<sub><!--[if gte vml 1]><v:shape id="_x0000_i1230" type="#_x0000_t75" style='width:15.75pt; |
| 7851 |
height:15.75pt' o:ole=""> |
| 7852 |
<v:imagedata src="./fulldoc_files/image483.wmz" o:title=""/> |
| 7853 |
</v:shape><![endif]--><![if !vml]><img width=21 height=21 |
| 7854 |
src="./fulldoc_files/image484.gif" v:shapes="_x0000_i1230"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7855 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1230" |
| 7856 |
DrawAspect="Content" ObjectID="_1051901448"> |
| 7857 |
</o:OLEObject> |
| 7858 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>and the four non-zero |
| 7859 |
off-diagonals will be comprised of the <sub><!--[if gte vml 1]><v:shape id="_x0000_i1231" |
| 7860 |
type="#_x0000_t75" style='width:38.25pt;height:15.75pt' o:ole=""> |
| 7861 |
<v:imagedata src="./fulldoc_files/image485.wmz" o:title=""/> |
| 7862 |
</v:shape><![endif]--><![if !vml]><img width=51 height=21 |
| 7863 |
src="./fulldoc_files/image486.gif" v:shapes="_x0000_i1231"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7864 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1231" |
| 7865 |
DrawAspect="Content" ObjectID="_1051901449"> |
| 7866 |
</o:OLEObject> |
| 7867 |
</xml><![endif]-->.<span style="mso-spacerun: yes"> </span>Because of the |
| 7868 |
dominance of the leading diagonal, to a first approximation:<o:p></o:p></span></p> |
| 7869 |
|
| 7870 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7871 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7872 |
|
| 7873 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7874 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7875 |
id="_x0000_i1232" type="#_x0000_t75" style='width:48pt;height:32.25pt' o:ole=""> |
| 7876 |
<v:imagedata src="./fulldoc_files/image487.wmz" o:title=""/> |
| 7877 |
</v:shape><![endif]--><![if !vml]><img width=64 height=43 |
| 7878 |
src="./fulldoc_files/image488.gif" v:shapes="_x0000_i1232"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7879 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1232" |
| 7880 |
DrawAspect="Content" ObjectID="_1051901450"> |
| 7881 |
</o:OLEObject> |
| 7882 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7883 |
|
| 7884 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7885 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7886 |
|
| 7887 |
<p class=MsoNormalIndent style='margin-left:0pt;text-align:justify'><span |
| 7888 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>One of |
| 7889 |
the simplest forms that could be chosen for <sub><!--[if gte vml 1]><v:shape |
| 7890 |
id="_x0000_i1233" type="#_x0000_t75" style='width:23.25pt;height:15.75pt' |
| 7891 |
o:ole=""> |
| 7892 |
<v:imagedata src="./fulldoc_files/image489.wmz" o:title=""/> |
| 7893 |
</v:shape><![endif]--><![if !vml]><img width=31 height=21 |
| 7894 |
src="./fulldoc_files/image490.gif" v:shapes="_x0000_i1233"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7895 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1233" |
| 7896 |
DrawAspect="Content" ObjectID="_1051901451"> |
| 7897 |
</o:OLEObject> |
| 7898 |
</xml><![endif]-->, then, is to suppose that it is a diagonal matrix comprised |
| 7899 |
of elements equal to the reciprocal of the corresponding elements along the |
| 7900 |
leading diagonal of <b style='mso-bidi-font-weight:normal'>A</b>.<span |
| 7901 |
style="mso-spacerun: yes"> </span>However, this can be improved by |
| 7902 |
constructing an approximate local inverse as follows.<o:p></o:p></span></p> |
| 7903 |
|
| 7904 |
<p class=MsoNormalIndent style='margin-left:0pt'><span style='font-size:12.0pt; |
| 7905 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7906 |
|
| 7907 |
<p class=MsoNormalIndent style='margin-left:0pt;text-align:justify'><span |
| 7908 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>At the |
| 7909 |
five points in the stencil surrounding c then, to the same level of |
| 7910 |
approximation, we may write:<o:p></o:p></span></p> |
| 7911 |
|
| 7912 |
<p class=MsoNormalIndent style='margin-left:0pt;text-align:justify'><span |
| 7913 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7914 |
|
| 7915 |
<p class=MsoNormalIndent align=center style='margin-left:0pt;text-align:center'><span |
| 7916 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7917 |
id="_x0000_i1234" type="#_x0000_t75" style='width:132.75pt;height:38.25pt' |
| 7918 |
o:ole=""> |
| 7919 |
<v:imagedata src="./fulldoc_files/image491.wmz" o:title=""/> |
| 7920 |
</v:shape><![endif]--><![if !vml]><img width=177 height=51 |
| 7921 |
src="./fulldoc_files/image492.gif" v:shapes="_x0000_i1234"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7922 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1234" |
| 7923 |
DrawAspect="Content" ObjectID="_1051901452"> |
| 7924 |
</o:OLEObject> |
| 7925 |
</xml><![endif]--><o:p></o:p></span></p> |
| 7926 |
|
| 7927 |
<p class=MsoNormalIndent style='margin-left:0pt'><span style='font-size:12.0pt; |
| 7928 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7929 |
|
| 7930 |
<p class=MsoNormalIndent style='margin-left:0pt'><span style='font-size:12.0pt; |
| 7931 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>where <sub><!--[if gte vml 1]><v:shape |
| 7932 |
id="_x0000_i1235" type="#_x0000_t75" style='width:18.75pt;height:23.25pt' |
| 7933 |
o:ole=""> |
| 7934 |
<v:imagedata src="./fulldoc_files/image493.wmz" o:title=""/> |
| 7935 |
</v:shape><![endif]--><![if !vml]><img width=25 height=31 |
| 7936 |
src="./fulldoc_files/image494.gif" v:shapes="_x0000_i1235"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7937 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1235" |
| 7938 |
DrawAspect="Content" ObjectID="_1051901454"> |
| 7939 |
</o:OLEObject> |
| 7940 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>denotes the point to |
| 7941 |
the west etc.<o:p></o:p></span></p> |
| 7942 |
|
| 7943 |
<p class=MsoNormalIndent style='margin-left:0pt'><span style='font-size:12.0pt; |
| 7944 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Hence we can make a better |
| 7945 |
approximation to </span><span style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7946 |
id="_x0000_i1236" type="#_x0000_t75" style='width:17.25pt;height:18pt' o:ole=""> |
| 7947 |
<v:imagedata src="./fulldoc_files/image495.wmz" o:title=""/> |
| 7948 |
</v:shape><![endif]--><![if !vml]><img width=23 height=24 |
| 7949 |
src="./fulldoc_files/image496.gif" v:shapes="_x0000_i1236"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7950 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1236" |
| 7951 |
DrawAspect="Content" ObjectID="_1051901455"> |
| 7952 |
</o:OLEObject> |
| 7953 |
</xml><![endif]--></span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7954 |
font-family:Palatino'>thus:<o:p></o:p></span></p> |
| 7955 |
|
| 7956 |
<p class=MsoNormalIndent style='margin-left:0pt'><span style='font-size:12.0pt; |
| 7957 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7958 |
|
| 7959 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7960 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7961 |
id="_x0000_i1237" type="#_x0000_t75" style='width:243.75pt;height:44.25pt' |
| 7962 |
o:ole=""> |
| 7963 |
<v:imagedata src="./fulldoc_files/image497.wmz" o:title=""/> |
| 7964 |
</v:shape><![endif]--><![if !vml]><img width=325 height=59 |
| 7965 |
src="./fulldoc_files/image498.gif" v:shapes="_x0000_i1237"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7966 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1237" |
| 7967 |
DrawAspect="Content" ObjectID="_1051901456"> |
| 7968 |
</o:OLEObject> |
| 7969 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 7970 |
|
| 7971 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7972 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7973 |
|
| 7974 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7975 |
font-family:Palatino'>To arrive at a symmetric preconditioner we replace </span><span |
| 7976 |
style='font-family:Palatino'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1238" |
| 7977 |
type="#_x0000_t75" style='width:26.25pt;height:21.75pt' o:ole=""> |
| 7978 |
<v:imagedata src="./fulldoc_files/image499.wmz" o:title=""/> |
| 7979 |
</v:shape><![endif]--><![if !vml]><img width=35 height=29 |
| 7980 |
src="./fulldoc_files/image500.gif" v:shapes="_x0000_i1238"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7981 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1238" |
| 7982 |
DrawAspect="Content" ObjectID="_1051901457"> |
| 7983 |
</o:OLEObject> |
| 7984 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span></span><span |
| 7985 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>etc |
| 7986 |
thus:<o:p></o:p></span></p> |
| 7987 |
|
| 7988 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 7989 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 7990 |
|
| 7991 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 7992 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 7993 |
id="_x0000_i1239" type="#_x0000_t75" style='width:111.75pt;height:30pt' o:ole=""> |
| 7994 |
<v:imagedata src="./fulldoc_files/image501.wmz" o:title=""/> |
| 7995 |
</v:shape><![endif]--><![if !vml]><img width=149 height=40 |
| 7996 |
src="./fulldoc_files/image502.gif" v:shapes="_x0000_i1239"><![endif]></sub><!--[if gte mso 9]><xml> |
| 7997 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1239" |
| 7998 |
DrawAspect="Content" ObjectID="_1051901459"> |
| 7999 |
</o:OLEObject> |
| 8000 |
</xml><![endif]--><o:p></o:p></span></p> |
| 8001 |
|
| 8002 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8003 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8004 |
|
| 8005 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8006 |
font-family:Palatino'>giving, finally, our local preconditioner for use in |
| 8007 |
(2.3.7):<o:p></o:p></span></p> |
| 8008 |
|
| 8009 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8010 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8011 |
|
| 8012 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8013 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 8014 |
id="_x0000_i1240" type="#_x0000_t75" style='width:9pt;height:15.75pt' o:ole=""> |
| 8015 |
<v:imagedata src="./fulldoc_files/image082.wmz" o:title=""/> |
| 8016 |
</v:shape><![endif]--><![if !vml]><img width=12 height=21 |
| 8017 |
src="./fulldoc_files/image503.gif" v:shapes="_x0000_i1240"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8018 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1240" |
| 8019 |
DrawAspect="Content" ObjectID="_1051901460"> |
| 8020 |
</o:OLEObject> |
| 8021 |
</xml><![endif]--><sub><!--[if gte vml 1]><v:shape id="_x0000_i1241" type="#_x0000_t75" |
| 8022 |
style='width:336.75pt;height:44.25pt' o:ole=""> |
| 8023 |
<v:imagedata src="./fulldoc_files/image504.wmz" o:title=""/> |
| 8024 |
</v:shape><![endif]--><![if !vml]><img width=449 height=59 |
| 8025 |
src="./fulldoc_files/image505.gif" v:shapes="_x0000_i1241"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8026 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1241" |
| 8027 |
DrawAspect="Content" ObjectID="_1051901461"> |
| 8028 |
</o:OLEObject> |
| 8029 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>(2.3.8)<o:p></o:p></span></p> |
| 8030 |
|
| 8031 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8032 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8033 |
|
| 8034 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8035 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Although simple, (2.3.8) is |
| 8036 |
highly effective, reducing the number of iterations required for convergence |
| 8037 |
by, typically, a factor of four.<o:p></o:p></span></p> |
| 8038 |
|
| 8039 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8040 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8041 |
|
| 8042 |
<p class=MsoNormal style='text-align:justify'><i style='mso-bidi-font-style: |
| 8043 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 8044 |
Palatino'>Three-dimensional<o:p></o:p></span></i></p> |
| 8045 |
|
| 8046 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8047 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8048 |
|
| 8049 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8050 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>After considerable |
| 8051 |
experimentation we have chosen a block-diagonal preconditioner, a matrix whose |
| 8052 |
diagonal is made up of the inverse of the tri-diagonal matrices <b |
| 8053 |
style='mso-bidi-font-weight:normal'>D</b> defined above:<o:p></o:p></span></p> |
| 8054 |
|
| 8055 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8056 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8057 |
|
| 8058 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8059 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 8060 |
style="mso-spacerun: yes"> </span><span style="mso-spacerun: |
| 8061 |
yes"> </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1242" |
| 8062 |
type="#_x0000_t75" style='width:267.75pt;height:146.25pt' o:ole=""> |
| 8063 |
<v:imagedata src="./fulldoc_files/image506.wmz" o:title=""/> |
| 8064 |
</v:shape><![endif]--><![if !vml]><img width=357 height=195 |
| 8065 |
src="./fulldoc_files/image507.gif" v:shapes="_x0000_i1242"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8066 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1242" |
| 8067 |
DrawAspect="Content" ObjectID="_1051901462"> |
| 8068 |
</o:OLEObject> |
| 8069 |
</xml><![endif]--><span style="mso-spacerun: |
| 8070 |
yes"> </span>(2.3.9)<o:p></o:p></span></p> |
| 8071 |
|
| 8072 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8073 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8074 |
|
| 8075 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8076 |
font-family:Palatino'>Evaluation of the inner products to compute </span><i |
| 8077 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 8078 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 8079 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 8080 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>a</span></span></i><span |
| 8081 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> and </span><i |
| 8082 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 8083 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 8084 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 8085 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>b</span></span></i><span |
| 8086 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> in |
| 8087 |
(2.3.7), involves forming the vector <b style='mso-bidi-font-weight:normal'>x</b>, |
| 8088 |
where <o:p></o:p></span></p> |
| 8089 |
|
| 8090 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8091 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8092 |
|
| 8093 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 8094 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 8095 |
id="_x0000_i1243" type="#_x0000_t75" style='width:38.25pt;height:12.75pt' |
| 8096 |
o:ole=""> |
| 8097 |
<v:imagedata src="./fulldoc_files/image508.wmz" o:title=""/> |
| 8098 |
</v:shape><![endif]--><![if !vml]><img width=51 height=17 |
| 8099 |
src="./fulldoc_files/image509.gif" v:shapes="_x0000_i1243"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8100 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1243" |
| 8101 |
DrawAspect="Content" ObjectID="_1051901464"> |
| 8102 |
</o:OLEObject> |
| 8103 |
</xml><![endif]--><o:p></o:p></span></p> |
| 8104 |
|
| 8105 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8106 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8107 |
|
| 8108 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8109 |
font-family:Palatino'>or, since <sub><!--[if gte vml 1]><v:shape id="_x0000_i1244" |
| 8110 |
type="#_x0000_t75" style='width:42.75pt;height:15pt' o:ole=""> |
| 8111 |
<v:imagedata src="./fulldoc_files/image510.wmz" o:title=""/> |
| 8112 |
</v:shape><![endif]--><![if !vml]><img width=57 height=20 |
| 8113 |
src="./fulldoc_files/image511.gif" v:shapes="_x0000_i1244"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8114 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1244" |
| 8115 |
DrawAspect="Content" ObjectID="_1051901465"> |
| 8116 |
</o:OLEObject> |
| 8117 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>, where <b |
| 8118 |
style='mso-bidi-font-weight:normal'>D</b> is the matrix of diagonal elements of |
| 8119 |
(2.3.5).<o:p></o:p></span></p> |
| 8120 |
|
| 8121 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8122 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8123 |
|
| 8124 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 8125 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 8126 |
id="_x0000_i1245" type="#_x0000_t75" style='width:47.25pt;height:15pt' o:ole=""> |
| 8127 |
<v:imagedata src="./fulldoc_files/image512.wmz" o:title=""/> |
| 8128 |
</v:shape><![endif]--><![if !vml]><img width=63 height=20 |
| 8129 |
src="./fulldoc_files/image513.gif" v:shapes="_x0000_i1245"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8130 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1245" |
| 8131 |
DrawAspect="Content" ObjectID="_1051901466"> |
| 8132 |
</o:OLEObject> |
| 8133 |
</xml><![endif]--><o:p></o:p></span></p> |
| 8134 |
|
| 8135 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8136 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8137 |
|
| 8138 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8139 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If our ocean model has many |
| 8140 |
levels, then <b style='mso-bidi-font-weight:normal'>D</b><sup>-1</sup> will be |
| 8141 |
dense and so storing and multiplying by <b style='mso-bidi-font-weight:normal'>D</b><sup>-1</sup> |
| 8142 |
is also demanding of resources.<span style="mso-spacerun: yes"> |
| 8143 |
</span>Instead, we exploit the fact that <b style='mso-bidi-font-weight:normal'>D</b> |
| 8144 |
is tri-diagonal, and use LU decomposition to solve the preconditioning |
| 8145 |
equations for <b style='mso-bidi-font-weight:normal'>x</b> in the form:<o:p></o:p></span></p> |
| 8146 |
|
| 8147 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8148 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8149 |
|
| 8150 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 8151 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 8152 |
id="_x0000_i1246" type="#_x0000_t75" style='width:36.75pt;height:12.75pt' |
| 8153 |
o:ole=""> |
| 8154 |
<v:imagedata src="./fulldoc_files/image514.wmz" o:title=""/> |
| 8155 |
</v:shape><![endif]--><![if !vml]><img width=49 height=17 |
| 8156 |
src="./fulldoc_files/image515.gif" v:shapes="_x0000_i1246"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8157 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1246" |
| 8158 |
DrawAspect="Content" ObjectID="_1051901467"> |
| 8159 |
</o:OLEObject> |
| 8160 |
</xml><![endif]--><o:p></o:p></span></p> |
| 8161 |
|
| 8162 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8163 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8164 |
|
| 8165 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8166 |
font-family:Palatino'>We write <b style='mso-bidi-font-weight:normal'>D=LU</b><span |
| 8167 |
style="mso-spacerun: yes"> </span>where <b style='mso-bidi-font-weight:normal'>L</b> |
| 8168 |
is a lower-triangular matrix and <b style='mso-bidi-font-weight:normal'>U</b> |
| 8169 |
an upper triangular matrix which have the form:<o:p></o:p></span></p> |
| 8170 |
|
| 8171 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8172 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8173 |
|
| 8174 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8175 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><span style="mso-spacerun: |
| 8176 |
yes"> </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1247" type="#_x0000_t75" |
| 8177 |
style='width:110.25pt;height:1in' o:ole=""> |
| 8178 |
<v:imagedata src="./fulldoc_files/image516.wmz" o:title=""/> |
| 8179 |
</v:shape><![endif]--><![if !vml]><img width=147 height=96 |
| 8180 |
src="./fulldoc_files/image517.gif" v:shapes="_x0000_i1247"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8181 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1247" |
| 8182 |
DrawAspect="Content" ObjectID="_1051901469"> |
| 8183 |
</o:OLEObject> |
| 8184 |
</xml><![endif]-->,<span style="mso-spacerun: yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 8185 |
id="_x0000_i1248" type="#_x0000_t75" style='width:105pt;height:1in' o:ole=""> |
| 8186 |
<v:imagedata src="./fulldoc_files/image518.wmz" o:title=""/> |
| 8187 |
</v:shape><![endif]--><![if !vml]><img width=140 height=96 |
| 8188 |
src="./fulldoc_files/image519.gif" v:shapes="_x0000_i1248"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8189 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1248" |
| 8190 |
DrawAspect="Content" ObjectID="_1051901470"> |
| 8191 |
</o:OLEObject> |
| 8192 |
</xml><![endif]--><span style='mso-tab-count:1'> </span>and <sub><!--[if gte vml 1]><v:shape |
| 8193 |
id="_x0000_i1249" type="#_x0000_t75" style='width:108pt;height:1in' o:ole=""> |
| 8194 |
<v:imagedata src="./fulldoc_files/image520.wmz" o:title=""/> |
| 8195 |
</v:shape><![endif]--><![if !vml]><img width=144 height=96 |
| 8196 |
src="./fulldoc_files/image521.gif" v:shapes="_x0000_i1249"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8197 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1249" |
| 8198 |
DrawAspect="Content" ObjectID="_1051901471"> |
| 8199 |
</o:OLEObject> |
| 8200 |
</xml><![endif]--><o:p></o:p></span></p> |
| 8201 |
|
| 8202 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8203 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8204 |
|
| 8205 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8206 |
font-family:Palatino'>It is easy to see, that if <sub><!--[if gte vml 1]><v:shape |
| 8207 |
id="_x0000_i1250" type="#_x0000_t75" style='width:32.25pt;height:17.25pt' |
| 8208 |
o:ole=""> |
| 8209 |
<v:imagedata src="./fulldoc_files/image522.wmz" o:title=""/> |
| 8210 |
</v:shape><![endif]--><![if !vml]><img width=43 height=23 |
| 8211 |
src="./fulldoc_files/image523.gif" v:shapes="_x0000_i1250"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8212 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1250" |
| 8213 |
DrawAspect="Content" ObjectID="_1051901472"> |
| 8214 |
</o:OLEObject> |
| 8215 |
</xml><![endif]--><span style="mso-spacerun: yes"> </span>we have a system of |
| 8216 |
simple equations:<o:p></o:p></span></p> |
| 8217 |
|
| 8218 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8219 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8220 |
|
| 8221 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 8222 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><sub><!--[if gte vml 1]><v:shape |
| 8223 |
id="_x0000_i1251" type="#_x0000_t75" style='width:324pt;height:18.75pt' o:ole=""> |
| 8224 |
<v:imagedata src="./fulldoc_files/image524.wmz" o:title=""/> |
| 8225 |
</v:shape><![endif]--><![if !vml]><img width=432 height=25 |
| 8226 |
src="./fulldoc_files/image525.gif" v:shapes="_x0000_i1251"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8227 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1251" |
| 8228 |
DrawAspect="Content" ObjectID="_1051901474"> |
| 8229 |
</o:OLEObject> |
| 8230 |
</xml><![endif]--><o:p></o:p></span></p> |
| 8231 |
|
| 8232 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8233 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8234 |
|
| 8235 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8236 |
font-family:Palatino'>and so on.<span style="mso-spacerun: yes"> </span><o:p></o:p></span></p> |
| 8237 |
|
| 8238 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8239 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8240 |
|
| 8241 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8242 |
font-family:Palatino'>Finding the inverse of <b style='mso-bidi-font-weight: |
| 8243 |
normal'>D</b>, or solving problem <b style='mso-bidi-font-weight:normal'>Dx=r</b> |
| 8244 |
is equivalent to solving the two sets of equations:<o:p></o:p></span></p> |
| 8245 |
|
| 8246 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8247 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8248 |
|
| 8249 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8250 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><span |
| 8251 |
style="mso-spacerun: yes"> </span><span style="mso-spacerun: |
| 8252 |
yes"> </span><sub><!--[if gte vml 1]><v:shape |
| 8253 |
id="_x0000_i1252" type="#_x0000_t75" style='width:36.75pt;height:32.25pt' |
| 8254 |
o:ole=""> |
| 8255 |
<v:imagedata src="./fulldoc_files/image526.wmz" o:title=""/> |
| 8256 |
</v:shape><![endif]--><![if !vml]><img width=49 height=43 |
| 8257 |
src="./fulldoc_files/image527.gif" v:shapes="_x0000_i1252"><![endif]></sub><!--[if gte mso 9]><xml> |
| 8258 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1252" |
| 8259 |
DrawAspect="Content" ObjectID="_1051901475"> |
| 8260 |
</o:OLEObject> |
| 8261 |
</xml><![endif]--><span style="mso-spacerun: |
| 8262 |
yes"> </span>(2.3.10)<o:p></o:p></span></p> |
| 8263 |
|
| 8264 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8265 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8266 |
|
| 8267 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8268 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>first for <b style='mso-bidi-font-weight: |
| 8269 |
normal'>z</b> and then for <b style='mso-bidi-font-weight:normal'>x</b>.<span |
| 8270 |
style="mso-spacerun: yes"> </span>This is straightforward because of the |
| 8271 |
triangular structure of <b style='mso-bidi-font-weight:normal'>L</b> and <b |
| 8272 |
style='mso-bidi-font-weight:normal'>U</b>.<span style="mso-spacerun: yes"> |
| 8273 |
</span>Importantly the number of operations required to solve (2.3.10) for <b |
| 8274 |
style='mso-bidi-font-weight:normal'>x</b> scales as <i style='mso-bidi-font-style: |
| 8275 |
normal'>N<sub>Z</sub></i> compared to <i style='mso-bidi-font-style:normal'>N<sub>Z</sub></i><sup>2</sup><span |
| 8276 |
style="mso-spacerun: yes"> </span>if we had used the inverse of <b |
| 8277 |
style='mso-bidi-font-weight:normal'>D</b> directly.<o:p></o:p></span></p> |
| 8278 |
|
| 8279 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8280 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8281 |
|
| 8282 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8283 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The resulting preconditioner |
| 8284 |
was found to be a good compromise; its use significantly reduces the number of |
| 8285 |
iterations required to find a solution to (2.3.6) because it is an acceptable |
| 8286 |
approximation to the inverse of <b style='mso-bidi-font-weight:normal'>A</b>, |
| 8287 |
it is sparse and, most importantly, its application requires no communication |
| 8288 |
across the network in the data-parallel implementation of the algorithm.<o:p></o:p></span></p> |
| 8289 |
|
| 8290 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8291 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8292 |
|
| 8293 |
</div> |
| 8294 |
|
| 8295 |
<span style='font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family: |
| 8296 |
"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US; |
| 8297 |
mso-bidi-language:AR-SA'><br clear=all style='page-break-before:always; |
| 8298 |
mso-break-type:section-break'> |
| 8299 |
</span> |
| 8300 |
|
| 8301 |
<div class=Section4> |
| 8302 |
|
| 8303 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 8304 |
|
| 8305 |
<h1><a name="_Toc407078244"></a><a name="_Toc407090398"></a><a |
| 8306 |
name="_Toc407090601"></a><a name="_Toc407169630"><span style='mso-bookmark: |
| 8307 |
_Toc407090601'><span style='mso-bookmark:_Toc407090398'><span style='mso-bookmark: |
| 8308 |
_Toc407078244'>CHAPTER 3 PARALLEL IMPLEMENTATION</span></span></span></a><span |
| 8309 |
style='mso-bookmark:_Toc407078244'></span></h1> |
| 8310 |
|
| 8311 |
</div> |
| 8312 |
|
| 8313 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078244'><span |
| 8314 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 8315 |
|
| 8316 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078244'><span |
| 8317 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 8318 |
|
| 8319 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078244'><b |
| 8320 |
style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 8321 |
10.0pt;font-family:Palatino'>Not complete yet<o:p></o:p></span></b></span></p> |
| 8322 |
|
| 8323 |
<p class=MsoBodyText style='margin-left:0pt'><span style='mso-bookmark:_Toc407078244'><span |
| 8324 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 8325 |
|
| 8326 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify'><span |
| 8327 |
style='mso-bookmark:_Toc407078244'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 8328 |
10.0pt;font-family:Palatino'>The current model implementation uses a |
| 8329 |
conservative form of Fortran 90. The array syntax notation feature of Fortran |
| 8330 |
90 is heavily used, however, the more elaborate features of Fortran 90 such as |
| 8331 |
overloading of operators, modules, array valued functions are avoided (the |
| 8332 |
performance of these constructs varies widely from one compiler to another). |
| 8333 |
Apart from the array notation, the only new syntax elements that experienced |
| 8334 |
Fortran 77 or C programmers need to understand to work with the model, are the |
| 8335 |
Fortran 90 <b style='mso-bidi-font-weight:normal'>SHIFT </b>primitives.<o:p></o:p></span></span></p> |
| 8336 |
|
| 8337 |
<p class=MsoBodyText style='text-align:justify'><span style='mso-bookmark:_Toc407078244'><span |
| 8338 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 8339 |
|
| 8340 |
<p class=MsoBodyText style='text-align:justify'><span style='mso-bookmark:_Toc407078244'><span |
| 8341 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 8342 |
|
| 8343 |
<h2><span style='mso-bookmark:_Toc407078244'><a name="_Toc407169631">2.1 |
| 8344 |
Enumeration of arrays.</a></span></h2> |
| 8345 |
|
| 8346 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078244'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8347 |
|
| 8348 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify;mso-outline-level: |
| 8349 |
1'><span style='mso-bookmark:_Toc407078244'><span style='font-size:12.0pt; |
| 8350 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>In the model implementation the |
| 8351 |
grid cells are mapped to regular three-dimensional arrays. As shown in Fig.6 |
| 8352 |
the index <i style='mso-bidi-font-style:normal'>i</i> is used to index the <i |
| 8353 |
style='mso-bidi-font-style:normal'>x</i>-axis, <i style='mso-bidi-font-style: |
| 8354 |
normal'>j</i> to index the <i style='mso-bidi-font-style:normal'>y</i>-axis and |
| 8355 |
<i style='mso-bidi-font-style:normal'>k</i> to index the <i style='mso-bidi-font-style: |
| 8356 |
normal'>z</i>-axis. The rule that coordinate (<i style='mso-bidi-font-style: |
| 8357 |
normal'>i</i>=1,<i style='mso-bidi-font-style:normal'>j</i>=1,<i |
| 8358 |
style='mso-bidi-font-style:normal'>k</i>=1) of any variable must fall within |
| 8359 |
the western most, southern most and upper most cell and be as far toward the |
| 8360 |
west, south and top of that cell is used throughout the code. This is illustrated |
| 8361 |
in Fig.6. <o:p></o:p></span></span></p> |
| 8362 |
|
| 8363 |
<p class=MsoBodyText style='text-align:justify;mso-outline-level:1'><!--[if gte vml 1]><o:wrapblock><v:shape |
| 8364 |
id="_x0000_s1037" type="#_x0000_t75" style='position:absolute;left:0; |
| 8365 |
text-align:left;margin-left:-11.55pt;margin-top:-58.5pt;width:492pt;height:656.45pt; |
| 8366 |
z-index:8;mso-position-horizontal-relative:text; |
| 8367 |
mso-position-vertical-relative:text' o:allowincell="f"> |
| 8368 |
<v:imagedata src="./fulldoc_files/image528.wmz" o:title=""/> |
| 8369 |
<v:textbox style='mso-next-textbox:#_x0000_s1037'/> |
| 8370 |
<w:wrap type="topAndBottom"/> |
| 8371 |
</v:shape><![if gte mso 9]><o:OLEObject Type="Embed" ProgID="PowerPoint.Show.8" |
| 8372 |
ShapeID="_x0000_s1037" DrawAspect="Content" ObjectID="_1051901476"> |
| 8373 |
</o:OLEObject> |
| 8374 |
<![endif]><![endif]--><![if !vml]><span style='mso-ignore:vglayout;position: |
| 8375 |
relative;z-index:7;left:-15px;top:0px;width:656px;height:875px'><img |
| 8376 |
width=656 height=875 src="./fulldoc_files/image529.gif" v:shapes="_x0000_s1037"></span><![endif]><!--[if gte vml 1]></o:wrapblock><![endif]--><br |
| 8377 |
style='mso-ignore:vglayout' clear=ALL> |
| 8378 |
<span style='mso-bookmark:_Toc407078244'><b style='mso-bidi-font-weight:normal'><span |
| 8379 |
style='font-size:10.0pt;font-family:Palatino'>Fig 3</span></b></span><span |
| 8380 |
style='mso-bookmark:_Toc407078244'><span style='font-size:10.0pt;font-family: |
| 8381 |
Palatino'> .The discrete domain is mapped to multi-dimensional arrays using an |
| 8382 |
enumeration scheme that follows the two rules illustrated. Both the major |
| 8383 |
prognostic variables and the intermediate terms abide by this convention.<o:p></o:p></span></span></p> |
| 8384 |
|
| 8385 |
<span style='font-size:10.0pt;font-family:Palatino;mso-fareast-font-family: |
| 8386 |
"Times New Roman";mso-bidi-font-family:"Times New Roman";mso-ansi-language: |
| 8387 |
EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br clear=all |
| 8388 |
style='mso-special-character:line-break;page-break-before:always'> |
| 8389 |
</span> |
| 8390 |
|
| 8391 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078244'><span |
| 8392 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 8393 |
|
| 8394 |
<br style='mso-ignore:vglayout' clear=ALL> |
| 8395 |
|
| 8396 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 8397 |
|
| 8398 |
<h1 style='text-align:justify'><span style='mso-bookmark:_Toc407078244'><a |
| 8399 |
name="_Toc407090399"></a><a name="_Toc407090602"></a><a name="_Toc407169632"><span |
| 8400 |
style='mso-bookmark:_Toc407090602'><span style='mso-bookmark:_Toc407090399'>Chapter |
| 8401 |
4<span style="mso-spacerun: yes"> </span>Procedures and variables</span></span></a></span><u><o:p></o:p></u></h1> |
| 8402 |
|
| 8403 |
</div> |
| 8404 |
|
| 8405 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8406 |
|
| 8407 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8408 |
|
| 8409 |
<h2><a name="_Toc407078245"></a><a name="_Toc407090400"></a><a |
| 8410 |
name="_Toc407090603"></a><a name="_Toc407169633"><span style='mso-bookmark: |
| 8411 |
_Toc407090603'><span style='mso-bookmark:_Toc407090400'><span style='mso-bookmark: |
| 8412 |
_Toc407078245'>4.1 Procedures</span></span></span></a></h2> |
| 8413 |
|
| 8414 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8415 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8416 |
|
| 8417 |
<h3><a name="_Toc407078246"></a><a name="_Toc407090401"></a><a |
| 8418 |
name="_Toc407090604"></a><a name="_Toc407169634"><span style='mso-bookmark: |
| 8419 |
_Toc407090604'><span style='mso-bookmark:_Toc407090401'><span style='mso-bookmark: |
| 8420 |
_Toc407078246'><u>4.1.1 Flow chart</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 8421 |
|
| 8422 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8423 |
|
| 8424 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8425 |
font-family:Palatino'>See below a flow chart of the code. Some procedures are |
| 8426 |
not mentioned (diagnostic procedures for example).<o:p></o:p></span></p> |
| 8427 |
|
| 8428 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8429 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8430 |
|
| 8431 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8432 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8433 |
|
| 8434 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8435 |
font-family:Helvetica'>MAIN<o:p></o:p></span></p> |
| 8436 |
|
| 8437 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8438 |
font-family:Helvetica'>|----CONTROL<o:p></o:p></span></p> |
| 8439 |
|
| 8440 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8441 |
font-family:Helvetica'><span style='mso-tab-count:1'> </span>|<o:p></o:p></span></p> |
| 8442 |
|
| 8443 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8444 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|----SET_DEFAULTS<span |
| 8445 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8446 |
normal'>Set default values for model parameters</i><o:p></o:p></span></p> |
| 8447 |
|
| 8448 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8449 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span |
| 8450 |
style='mso-tab-count:1'> </span>|----DATE<span style="mso-spacerun: |
| 8451 |
yes"> </span><i |
| 8452 |
style='mso-bidi-font-style:normal'>Record date and time of run</i><o:p></o:p></span></p> |
| 8453 |
|
| 8454 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8455 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span |
| 8456 |
style='mso-tab-count:1'> </span>|----MACHINE<span |
| 8457 |
style="mso-spacerun: yes"> </span><i |
| 8458 |
style='mso-bidi-font-style:normal'>Record machine identifying string</i><o:p></o:p></span></p> |
| 8459 |
|
| 8460 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8461 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<o:p></o:p></span></p> |
| 8462 |
|
| 8463 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8464 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|----READ_DATA<span |
| 8465 |
style="mso-spacerun: yes"> </span><i |
| 8466 |
style='mso-bidi-font-style:normal'>Read file specifying model parameters</i><o:p></o:p></span></p> |
| 8467 |
|
| 8468 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8469 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8470 |
1'> </span>|----READ_TOPOGRAPHY<span style="mso-spacerun: |
| 8471 |
yes"> </span><i style='mso-bidi-font-style:normal'>Read |
| 8472 |
land/water map</i><o:p></o:p></span></p> |
| 8473 |
|
| 8474 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8475 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<o:p></o:p></span></p> |
| 8476 |
|
| 8477 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8478 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|----INITIALISE<o:p></o:p></span></p> |
| 8479 |
|
| 8480 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8481 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span |
| 8482 |
style='mso-tab-count:1'> </span>|----INITIALISE_MASKS<span |
| 8483 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8484 |
normal'>Set land/water masks arrays</i><o:p></o:p></span></p> |
| 8485 |
|
| 8486 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8487 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8488 |
1'> </span>|----INITIALISE_GRIDDING<span style="mso-spacerun: |
| 8489 |
yes"> </span><i style='mso-bidi-font-style:normal'>Set up arrays |
| 8490 |
expressing geometry</i><o:p></o:p></span></p> |
| 8491 |
|
| 8492 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8493 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8494 |
1'> </span>|<span style='mso-tab-count:1'> </span>|----INITIALISE_CARTESIAN_GRID<o:p></o:p></span></p> |
| 8495 |
|
| 8496 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8497 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8498 |
1'> </span>|<span style='mso-tab-count:1'> </span>|----INITIALISE_SPHERICAL_POLAR_GRID<o:p></o:p></span></p> |
| 8499 |
|
| 8500 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8501 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span |
| 8502 |
style='mso-tab-count:1'> </span>|----INITIALISE_OPERATORS<span |
| 8503 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8504 |
normal'>Set up differencing operators</i><o:p></o:p></span></p> |
| 8505 |
|
| 8506 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8507 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span |
| 8508 |
style='mso-tab-count:1'> </span>|----INITIALISE_FIELDS<span |
| 8509 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8510 |
normal'>Set initial values of model variables</i><o:p></o:p></span></p> |
| 8511 |
|
| 8512 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8513 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8514 |
1'> </span>|<span style='mso-tab-count:1'> </span>|----INITIALISE_U<o:p></o:p></span></p> |
| 8515 |
|
| 8516 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8517 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8518 |
1'> </span>|<span style='mso-tab-count:1'> </span>|----INITIALISE_V<o:p></o:p></span></p> |
| 8519 |
|
| 8520 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8521 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8522 |
1'> </span>|<span style='mso-tab-count:1'> </span>|----INITIALISE_S<o:p></o:p></span></p> |
| 8523 |
|
| 8524 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8525 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8526 |
1'> </span>|<span style='mso-tab-count:1'> </span>|----INITIALISE_T<o:p></o:p></span></p> |
| 8527 |
|
| 8528 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8529 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span |
| 8530 |
style='mso-tab-count:1'> </span>|----INITIALISE_CORIOLIS<span |
| 8531 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8532 |
normal'>Set Coriolis term operator</i><o:p></o:p></span></p> |
| 8533 |
|
| 8534 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8535 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8536 |
1'> </span>|----INITIALISE_METRIC<span style="mso-spacerun: |
| 8537 |
yes"> </span><i style='mso-bidi-font-style:normal'>Set |
| 8538 |
metric term operator<o:p></o:p></i></span></p> |
| 8539 |
|
| 8540 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8541 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8542 |
1'> </span>|----CG3DAI<span style="mso-spacerun: |
| 8543 |
yes"> </span><i style='mso-bidi-font-style:normal'>Define |
| 8544 |
3d laplacian "A matrix" operator</i><o:p></o:p></span></p> |
| 8545 |
|
| 8546 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8547 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8548 |
1'> </span>|----CG3DPI<span style="mso-spacerun: |
| 8549 |
yes"> </span><i style='mso-bidi-font-style:normal'>Define |
| 8550 |
3d "A matrix" preconditioner<o:p></o:p></i></span></p> |
| 8551 |
|
| 8552 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8553 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8554 |
1'> </span>|----CG2DAI<span style="mso-spacerun: |
| 8555 |
yes"> </span><i style='mso-bidi-font-style:normal'>Define |
| 8556 |
2d laplacian "A matrix" operator</i><o:p></o:p></span></p> |
| 8557 |
|
| 8558 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8559 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<span style='mso-tab-count: |
| 8560 |
1'> </span>|----CG2DPI<span style="mso-spacerun: |
| 8561 |
yes"> </span><i style='mso-bidi-font-style:normal'>Define |
| 8562 |
2d "A matrix" preconditioner</i><o:p></o:p></span></p> |
| 8563 |
|
| 8564 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8565 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<o:p></o:p></span></p> |
| 8566 |
|
| 8567 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8568 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|----CHECK_INPUT<span |
| 8569 |
style="mso-spacerun: |
| 8570 |
yes"> </span><i |
| 8571 |
style='mso-bidi-font-style:normal'>Validate input data</i><o:p></o:p></span></p> |
| 8572 |
|
| 8573 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8574 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<o:p></o:p></span></p> |
| 8575 |
|
| 8576 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8577 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>|----PRINT_HEADING<span |
| 8578 |
style="mso-spacerun: yes"> </span><i |
| 8579 |
style='mso-bidi-font-style:normal'>Print out run data summary page</i><o:p></o:p></span></p> |
| 8580 |
|
| 8581 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8582 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|<o:p></o:p></span></p> |
| 8583 |
|
| 8584 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8585 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>|----MODEL<span |
| 8586 |
style="mso-spacerun: |
| 8587 |
yes"> </span><span |
| 8588 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style:normal'>Perform |
| 8589 |
integration</i><o:p></o:p></span></p> |
| 8590 |
|
| 8591 |
<p class=MsoNormal align=right style='text-align:right;text-indent:36.0pt'><span |
| 8592 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span |
| 8593 |
style='mso-tab-count:1'> </span>|----RHO_WGRID_CALC<span |
| 8594 |
style="mso-spacerun: yes"> </span><i |
| 8595 |
style='mso-bidi-font-style:normal'>Evaluate initial density</i><o:p></o:p></span></p> |
| 8596 |
|
| 8597 |
<p class=MsoNormal style='text-indent:36.0pt'><span style='font-size:12.0pt; |
| 8598 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8599 |
1'> </span>|<o:p></o:p></span></p> |
| 8600 |
|
| 8601 |
<p class=MsoNormal><i style='mso-bidi-font-style:normal'><span |
| 8602 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>MAIN |
| 8603 |
LOOP</span></i><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8604 |
font-family:Helvetica'> =====><o:p></o:p></span></p> |
| 8605 |
|
| 8606 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8607 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8608 |
|
| 8609 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8610 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----FORWARD<span |
| 8611 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8612 |
normal'>Control explicit stepping of u, v, and w</i><o:p></o:p></span></p> |
| 8613 |
|
| 8614 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8615 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8616 |
2'> </span>|<span style='mso-tab-count:1'> </span>|----TERMS0<span |
| 8617 |
style="mso-spacerun: yes"> </span><i |
| 8618 |
style='mso-bidi-font-style:normal'>Set up temporary arrays</i><o:p></o:p></span></p> |
| 8619 |
|
| 8620 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8621 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8622 |
2'> </span>|<span style='mso-tab-count:1'> </span>|----TERMS1<span |
| 8623 |
style="mso-spacerun: yes"> </span><i |
| 8624 |
style='mso-bidi-font-style:normal'>needed throughout stepping</i><o:p></o:p></span></p> |
| 8625 |
|
| 8626 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8627 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8628 |
2'> </span>|<span style='mso-tab-count:1'> </span>|----GU_CALCULATE<span |
| 8629 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8630 |
normal'>Calculate explicit dU/dt</i><o:p></o:p></span></p> |
| 8631 |
|
| 8632 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8633 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8634 |
2'> </span>|<span style='mso-tab-count:1'> </span>|<span |
| 8635 |
style='mso-tab-count:1'> </span>|----EXTERNAL_FORCING_U<span |
| 8636 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8637 |
normal'>Add forcing</i><o:p></o:p></span></p> |
| 8638 |
|
| 8639 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8640 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8641 |
style='mso-tab-count:1'> </span>|----GV_CALCULATE<span |
| 8642 |
style="mso-spacerun: yes"> </span><span style="mso-spacerun: |
| 8643 |
yes"> </span><i style='mso-bidi-font-style:normal'>Calculate |
| 8644 |
explicit dV/dt</i><o:p></o:p></span></p> |
| 8645 |
|
| 8646 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8647 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8648 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|----EXTERNAL_FORCING_V<span |
| 8649 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8650 |
normal'>Add forcing</i><o:p></o:p></span></p> |
| 8651 |
|
| 8652 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8653 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8654 |
style='mso-tab-count:1'> </span>|----GW_CALCULATE<span |
| 8655 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8656 |
normal'>Calculate explicit dW/dt</i><o:p></o:p></span></p> |
| 8657 |
|
| 8658 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8659 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8660 |
|
| 8661 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8662 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----PFIND<span |
| 8663 |
style="mso-spacerun: yes"> |
| 8664 |
</span><i style='mso-bidi-font-style:normal'>Diagnose pressure field</i><o:p></o:p></span></p> |
| 8665 |
|
| 8666 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8667 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8668 |
style='mso-tab-count:1'> </span>|----PFIND_HSTATIC<span |
| 8669 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8670 |
normal'>Find hydrostatic pressure</i><o:p></o:p></span></p> |
| 8671 |
|
| 8672 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8673 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8674 |
style='mso-tab-count:1'> </span>|----PFIND_SURFACE<span |
| 8675 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8676 |
normal'>Find surface pressure</i><o:p></o:p></span></p> |
| 8677 |
|
| 8678 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8679 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8680 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|----CG2D<span |
| 8681 |
style="mso-spacerun: yes"> </span><i |
| 8682 |
style='mso-bidi-font-style:normal'>2d preconditioned conjgrad</i><o:p></o:p></span></p> |
| 8683 |
|
| 8684 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8685 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8686 |
2'> </span>|<span style='mso-tab-count:1'> </span>|<span |
| 8687 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|----CG2DMA<span |
| 8688 |
style="mso-spacerun: yes"> </span><span style="mso-spacerun: |
| 8689 |
yes"> </span><i style='mso-bidi-font-style:normal'>Multiply by 2d laplacian</i><o:p></o:p></span></p> |
| 8690 |
|
| 8691 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8692 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8693 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|<span |
| 8694 |
style='mso-tab-count:1'> </span>|----CG2DPC<span style="mso-spacerun: |
| 8695 |
yes"> </span><i style='mso-bidi-font-style: |
| 8696 |
normal'>Precondition</i><o:p></o:p></span></p> |
| 8697 |
|
| 8698 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8699 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8700 |
style='mso-tab-count:1'> </span>|----PFIND_3D<span |
| 8701 |
style="mso-spacerun: yes"> </span><i |
| 8702 |
style='mso-bidi-font-style:normal'>Find remaining pressure</i><o:p></o:p></span></p> |
| 8703 |
|
| 8704 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8705 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8706 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|----PFIND_RHS3D<span |
| 8707 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8708 |
normal'>Form right hand side</i><o:p></o:p></span></p> |
| 8709 |
|
| 8710 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8711 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8712 |
2'> </span>|<span style='mso-tab-count:1'> </span>|<span |
| 8713 |
style='mso-tab-count:1'> </span>|----CG3D<span style="mso-spacerun: |
| 8714 |
yes"> </span><span style="mso-spacerun: yes"> </span><i |
| 8715 |
style='mso-bidi-font-style:normal'>3d preconditioned conjgrad</i><o:p></o:p></span></p> |
| 8716 |
|
| 8717 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8718 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8719 |
2'> </span>|<span style='mso-tab-count:1'> </span>|<span |
| 8720 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|----CG3DMA<span |
| 8721 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8722 |
normal'>Multiply by 3d laplacian</i><o:p></o:p></span></p> |
| 8723 |
|
| 8724 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8725 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8726 |
style='mso-tab-count:1'> </span>|<span style='mso-tab-count:1'> </span>|<span |
| 8727 |
style='mso-tab-count:1'> </span>|----CG3DPC<span style="mso-spacerun: |
| 8728 |
yes"> </span><i style='mso-bidi-font-style: |
| 8729 |
normal'>Precondition</i><o:p></o:p></span></p> |
| 8730 |
|
| 8731 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8732 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8733 |
|
| 8734 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8735 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----UPDATE_VELOCITIES<o:p></o:p></span></p> |
| 8736 |
|
| 8737 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8738 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8739 |
|
| 8740 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8741 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----EPARAM_SET_MIXING<span |
| 8742 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8743 |
normal'>Computes 3d diffusion tensor<o:p></o:p></i></span></p> |
| 8744 |
|
| 8745 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8746 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8747 |
|
| 8748 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8749 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----INC_TRACER<span |
| 8750 |
style="mso-spacerun: yes"> </span><i |
| 8751 |
style='mso-bidi-font-style:normal'>Step forward temperarture</i><o:p></o:p></span></p> |
| 8752 |
|
| 8753 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8754 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8755 |
style='mso-tab-count:1'> </span>|----EXTERNAL_FORCING_TEMPERATURE<span |
| 8756 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style:normal'>Add |
| 8757 |
forcing</i><o:p></o:p></span></p> |
| 8758 |
|
| 8759 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8760 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8761 |
|
| 8762 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8763 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----INC_TRACER<span |
| 8764 |
style="mso-spacerun: yes"> </span><i |
| 8765 |
style='mso-bidi-font-style:normal'>Step forward salinity</i><o:p></o:p></span></p> |
| 8766 |
|
| 8767 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8768 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<span |
| 8769 |
style='mso-tab-count:1'> </span>|----EXTERNAL_FORCING_SALINITY<span |
| 8770 |
style="mso-spacerun: yes"> </span><i style='mso-bidi-font-style: |
| 8771 |
normal'>Add forcing</i><o:p></o:p></span></p> |
| 8772 |
|
| 8773 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8774 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8775 |
|
| 8776 |
<p class=MsoNormal align=right style='text-align:right'><span style='font-size: |
| 8777 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><span style='mso-tab-count: |
| 8778 |
2'> </span>|----CADJTRACE<span style="mso-spacerun: |
| 8779 |
yes"> </span><i style='mso-bidi-font-style: |
| 8780 |
normal'>Mix unstable water column</i><o:p></o:p></span></p> |
| 8781 |
|
| 8782 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8783 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8784 |
|
| 8785 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8786 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|----RHO_WGRID_CALC<span |
| 8787 |
style="mso-spacerun: yes"> </span><i |
| 8788 |
style='mso-bidi-font-style:normal'>Evaluate density field</i><o:p></o:p></span></p> |
| 8789 |
|
| 8790 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8791 |
font-family:Helvetica'><span style='mso-tab-count:2'> </span>|<o:p></o:p></span></p> |
| 8792 |
|
| 8793 |
<p class=MsoNormal align=right style='text-align:right'><i style='mso-bidi-font-style: |
| 8794 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 8795 |
Helvetica'>TO MAIN LOOP </span></i><span style='font-size:12.0pt;mso-bidi-font-size: |
| 8796 |
10.0pt;font-family:Helvetica'><=====|----OUT<span style="mso-spacerun: |
| 8797 |
yes"> </span><span style="mso-spacerun: |
| 8798 |
yes"> </span><i style='mso-bidi-font-style: |
| 8799 |
normal'>Dump out model fields</i><o:p></o:p></span></p> |
| 8800 |
|
| 8801 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8802 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8803 |
|
| 8804 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8805 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8806 |
|
| 8807 |
<h3><a name="_Toc407078247"></a><a name="_Toc407090402"></a><a |
| 8808 |
name="_Toc407090605"></a><a name="_Toc407169635"><span style='mso-bookmark: |
| 8809 |
_Toc407090605'><span style='mso-bookmark:_Toc407090402'><span style='mso-bookmark: |
| 8810 |
_Toc407078247'><u>4.1.2 </u></span></span></span><u>Alphabetical list of |
| 8811 |
procedures and 'include' files</u></a><u><o:p></o:p></u></h3> |
| 8812 |
|
| 8813 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8814 |
|
| 8815 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span |
| 8816 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Include |
| 8817 |
the list here with a brief description (indicate the 'parent' procedure).<o:p></o:p></span></b></p> |
| 8818 |
|
| 8819 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span |
| 8820 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p> |
| 8821 |
|
| 8822 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span |
| 8823 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p> |
| 8824 |
|
| 8825 |
<h2><a name="_Toc407090403"></a><a name="_Toc407090606"></a><a |
| 8826 |
name="_Toc407169636"><span style='mso-bookmark:_Toc407090606'><span |
| 8827 |
style='mso-bookmark:_Toc407090403'>4.2 Variables</span></span></a></h2> |
| 8828 |
|
| 8829 |
<p class=MsoBodyText style='margin-left:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8830 |
|
| 8831 |
<p class=MsoBodyText style='margin-left:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8832 |
|
| 8833 |
<p class=MsoBodyText style='margin-left:0pt'><b style='mso-bidi-font-weight: |
| 8834 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 8835 |
Palatino'>Include an alphabetical list of variables here with the following |
| 8836 |
information: type (integer, real, character etc
), units (for real variables), |
| 8837 |
brief description, first occurrence in the code. Use table.<o:p></o:p></span></b></p> |
| 8838 |
|
| 8839 |
<p class=MsoBodyText style='margin-left:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8840 |
|
| 8841 |
<p class=MsoBodyText><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8842 |
|
| 8843 |
</div> |
| 8844 |
|
| 8845 |
<span style='font-size:11.0pt;mso-bidi-font-size:10.0pt;font-family:Arial; |
| 8846 |
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; |
| 8847 |
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br |
| 8848 |
clear=all style='page-break-before:always;mso-break-type:section-break'> |
| 8849 |
</span> |
| 8850 |
|
| 8851 |
<div class=Section5> |
| 8852 |
|
| 8853 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8854 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8855 |
|
| 8856 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 8857 |
|
| 8858 |
<h1 style='text-align:justify'><a name="_Toc407078252"></a><a |
| 8859 |
name="_Toc407090404"></a><a name="_Toc407090607"></a><a name="_Toc407169637"><span |
| 8860 |
style='mso-bookmark:_Toc407090607'><span style='mso-bookmark:_Toc407090404'><span |
| 8861 |
style='mso-bookmark:_Toc407078252'>Chapter 5 Getting started: practical |
| 8862 |
considerations</span></span></span></a></h1> |
| 8863 |
|
| 8864 |
</div> |
| 8865 |
|
| 8866 |
<p class=MsoNormal style='text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8867 |
|
| 8868 |
<p class=MsoNormal style='text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 8869 |
|
| 8870 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8871 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Notation : Fortran variable names |
| 8872 |
of the code are written in <i style='mso-bidi-font-style:normal'>italic</i>. |
| 8873 |
Subroutine and file names are written in CAPITAL LETTERS.<o:p></o:p></span></p> |
| 8874 |
|
| 8875 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8876 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8877 |
|
| 8878 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8879 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8880 |
|
| 8881 |
<h2 style='text-align:justify'><a name="_Toc407078253"></a><a |
| 8882 |
name="_Toc407090405"></a><a name="_Toc407090608"></a><a name="_Toc407169638"><span |
| 8883 |
style='mso-bookmark:_Toc407090608'><span style='mso-bookmark:_Toc407090405'><span |
| 8884 |
style='mso-bookmark:_Toc407078253'>5.1 Accessing the code - directory structure</span></span></span></a></h2> |
| 8885 |
|
| 8886 |
<p class=MsoNormal style='text-align:justify'><b style='mso-bidi-font-weight: |
| 8887 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 8888 |
Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p> |
| 8889 |
|
| 8890 |
<p class=MsoNormal style='text-align:justify'><b style='mso-bidi-font-weight: |
| 8891 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 8892 |
Palatino'>leave for now<o:p></o:p></span></b></p> |
| 8893 |
|
| 8894 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8895 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8896 |
|
| 8897 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8898 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8899 |
|
| 8900 |
<h2 style='text-align:justify'><a name="_Toc407078254"></a><a |
| 8901 |
name="_Toc407090406"></a><a name="_Toc407090609"></a><a name="_Toc407169639"><span |
| 8902 |
style='mso-bookmark:_Toc407090609'><span style='mso-bookmark:_Toc407090406'><span |
| 8903 |
style='mso-bookmark:_Toc407078254'>5.2 Configuring the model and setting up a |
| 8904 |
run</span></span></span></a></h2> |
| 8905 |
|
| 8906 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8907 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8908 |
|
| 8909 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8910 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This section is meant to review |
| 8911 |
the parameters that need to be set up before one can run the model. Unless |
| 8912 |
noted otherwise, these parameters are Fortran variables declared in file |
| 8913 |
PARAMS.h and set up in routine SET_DEFAULTS. The default values can be changed |
| 8914 |
by means of a namelist. The list that follows is not exhaustive. For example, |
| 8915 |
parameters related to the forcing files are expected to be user specific and |
| 8916 |
are not mentioned here. Others are left to the appendices. However, we have |
| 8917 |
attempted to include all the ones that will need to be set up no matter what |
| 8918 |
configuration you use. For the parameters not described here, look into file |
| 8919 |
PARAMS.h and routine SET_DEFAULTS. In what follows, the parameters are grouped |
| 8920 |
into categories related to the geometry and the equations solved in the model.<o:p></o:p></span></p> |
| 8921 |
|
| 8922 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8923 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8924 |
|
| 8925 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8926 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>We start with some constants |
| 8927 |
describing the state of the ocean. The real variables <i style='mso-bidi-font-style: |
| 8928 |
normal'>g</i>, <i style='mso-bidi-font-style:normal'>Cp</i>, <i |
| 8929 |
style='mso-bidi-font-style:normal'>RoNil</i> represent respectively gravity (in |
| 8930 |
m s<sup>-2</sup>), the specific heat (in J K<sup>-1</sup> kg<sup>-1</sup>), and |
| 8931 |
the reference density (in kg m<sup>-3</sup>) of the ocean.<o:p></o:p></span></p> |
| 8932 |
|
| 8933 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8934 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8935 |
|
| 8936 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8937 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The vertical coordinate used in |
| 8938 |
the model is actually pressure so that the same code can be used to simulate |
| 8939 |
fluid motions in the atmosphere. In the namelist, variables depending on the |
| 8940 |
choice of vertical coordinate (such as vertical viscosity and diffusivity |
| 8941 |
coefficients) have their vertical length expressed in meters. Later in the |
| 8942 |
code, this vertical length is converted in pressure unit (this involves |
| 8943 |
typically a simple multiplication or division by <i style='mso-bidi-font-style: |
| 8944 |
normal'>RoNil</i></span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8945 |
font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 8946 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 8947 |
symbol;mso-symbol-font-family:Symbol'>*</span></span><i style='mso-bidi-font-style: |
| 8948 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 8949 |
Palatino'>g</span></i><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8950 |
font-family:Palatino'>).<o:p></o:p></span></p> |
| 8951 |
|
| 8952 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8953 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8954 |
|
| 8955 |
<h3 style='text-align:justify'><a name="_Toc407078255"></a><a |
| 8956 |
name="_Toc407090407"></a><a name="_Toc407090610"></a><a name="_Toc407169640"><span |
| 8957 |
style='mso-bookmark:_Toc407090610'><span style='mso-bookmark:_Toc407090407'><span |
| 8958 |
style='mso-bookmark:_Toc407078255'><u>5.2.1 domain, geometry</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 8959 |
|
| 8960 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8961 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8962 |
|
| 8963 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 8964 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 8965 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 8966 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8967 |
font-family:Palatino'>dimensions<o:p></o:p></span></p> |
| 8968 |
|
| 8969 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8970 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The dimensions of the domain <i |
| 8971 |
style='mso-bidi-font-style:normal'>Nx</i>, <i style='mso-bidi-font-style:normal'>Ny</i>, |
| 8972 |
<i style='mso-bidi-font-style:normal'>Nz</i>, are declared and set in file |
| 8973 |
SIZE.h. The integer variables <i style='mso-bidi-font-style:normal'>L</i>, <i |
| 8974 |
style='mso-bidi-font-style:normal'>M</i>, <i style='mso-bidi-font-style:normal'>N</i> |
| 8975 |
in the namelist must be set to the values of <i style='mso-bidi-font-style: |
| 8976 |
normal'>Nx</i>, <i style='mso-bidi-font-style:normal'>Ny</i>, <i |
| 8977 |
style='mso-bidi-font-style:normal'>Nz</i>, respectively.<o:p></o:p></span></p> |
| 8978 |
|
| 8979 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8980 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 8981 |
|
| 8982 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 8983 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 8984 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 8985 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 8986 |
font-family:Palatino'>grid<o:p></o:p></span></p> |
| 8987 |
|
| 8988 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 8989 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The character variable <i |
| 8990 |
style='mso-bidi-font-style:normal'>gridStyle</i> controls the type of grid. Two |
| 8991 |
versions are currently available. For a Cartesian grid, set <i |
| 8992 |
style='mso-bidi-font-style:normal'>gridStyle</i> to 'Cartesian'. Then set up |
| 8993 |
the horizontal grid spacing <i style='mso-bidi-font-style:normal'>dM</i> (in |
| 8994 |
m). For a spherical polar grid, set <i style='mso-bidi-font-style:normal'>gridStyle</i> |
| 8995 |
to 'Spherical Polar'. Then specify the resolution along latitude and longitude <i |
| 8996 |
style='mso-bidi-font-style:normal'>dPhi</i> and <i style='mso-bidi-font-style: |
| 8997 |
normal'>dTheta</i> (in degrees) and the minimum latitude <i style='mso-bidi-font-style: |
| 8998 |
normal'>phiMin</i> (in degrees). Whatever grid you choose, also specify the 1D |
| 8999 |
array representing the vertical layers thickness <i style='mso-bidi-font-style: |
| 9000 |
normal'>deltaz</i> (in m) in the namelist. Note that in the code, the layer |
| 9001 |
thicknesses are expressed in pressure units (Pa) and are represented by the variable |
| 9002 |
<i style='mso-bidi-font-style:normal'>delps</i> (equal to <i style='mso-bidi-font-style: |
| 9003 |
normal'>deltaz</i> multiplied by <i style='mso-bidi-font-style:normal'>RoNil</i></span><span |
| 9004 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 9005 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 9006 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 9007 |
mso-symbol-font-family:Symbol'>*</span></span><i style='mso-bidi-font-style: |
| 9008 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9009 |
Palatino'>g</span></i><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9010 |
font-family:Palatino'>).<o:p></o:p></span></p> |
| 9011 |
|
| 9012 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9013 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9014 |
|
| 9015 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9016 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9017 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9018 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9019 |
font-family:Palatino'>topography<o:p></o:p></span></p> |
| 9020 |
|
| 9021 |
<p class=MsoBodyText style='margin-left:0pt;text-align:justify;mso-outline-level: |
| 9022 |
1'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>The |
| 9023 |
model code applies without modification to enclosed, periodic (x or y) and |
| 9024 |
double periodic (x and y) domains. The geometry of the model is controlled by |
| 9025 |
the topography file. A real 3D array <i style='mso-bidi-font-style:normal'>pmask</i> |
| 9026 |
is defined having the value 1 on water and 0 on land. Periodicity is assumed by |
| 9027 |
default and is suppressed by defining zero open interface areas for cells at |
| 9028 |
the limits of the computational domain.<o:p></o:p></span></p> |
| 9029 |
|
| 9030 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9031 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Note: The present elliptic |
| 9032 |
solver procedures CG2D and CG3D assume that they are solving a single global |
| 9033 |
problem. This means that all cells with non-zero volumes must interconnect, |
| 9034 |
either directly or indirectly, through the surface. If disconnected basins are |
| 9035 |
defined, the results are unpredictable.<o:p></o:p></span></p> |
| 9036 |
|
| 9037 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9038 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9039 |
|
| 9040 |
<h3 style='text-align:justify'><a name="_Toc407078256"></a><a |
| 9041 |
name="_Toc407090408"></a><a name="_Toc407090611"></a><a name="_Toc407169641"><span |
| 9042 |
style='mso-bookmark:_Toc407090611'><span style='mso-bookmark:_Toc407090408'><span |
| 9043 |
style='mso-bookmark:_Toc407078256'><u>5.2.2 Equation of state</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9044 |
|
| 9045 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9046 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9047 |
|
| 9048 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9049 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Initial reference temperature |
| 9050 |
and salinity profiles need to be provided to compute the perturbation density |
| 9051 |
and are represented respectively by the 1D arrays <i style='mso-bidi-font-style: |
| 9052 |
normal'>ths</i> (in <sup>o</sup>C) and <i style='mso-bidi-font-style:normal'>ssppt</i> |
| 9053 |
(in ppt). Two forms of equation of state are available in the baseline |
| 9054 |
implementation and are controlled by the character variable <i |
| 9055 |
style='mso-bidi-font-style:normal'>equationofState</i>. If set to 'linear', |
| 9056 |
then specify the constant expansion coefficients <i style='mso-bidi-font-style: |
| 9057 |
normal'>tAlpha</i> (in K<sup>-1</sup>)<sup> </sup>and <i style='mso-bidi-font-style: |
| 9058 |
normal'>sBeta</i> (in ppt<sup>-1</sup>) (through the variables <i |
| 9059 |
style='mso-bidi-font-style:normal'>alphaTemperature</i> and <i |
| 9060 |
style='mso-bidi-font-style:normal'>alphaSalt</i> in file PARAMS.h). If you set <i |
| 9061 |
style='mso-bidi-font-style:normal'>equationofState</i> to 'polynomial', density |
| 9062 |
is evaluated from a third order polynomial expansion of the full state |
| 9063 |
equation. The polynomial coefficients are read from a file called |
| 9064 |
POLY3D.COEFFS. Any other arbitrary formulae for deriving density can readily be |
| 9065 |
plugged into the model.<o:p></o:p></span></p> |
| 9066 |
|
| 9067 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9068 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9069 |
|
| 9070 |
<h3 style='text-align:justify'><a name="_Toc407078257"></a><a |
| 9071 |
name="_Toc407090409"></a><a name="_Toc407090612"></a><a name="_Toc407169642"><span |
| 9072 |
style='mso-bookmark:_Toc407090612'><span style='mso-bookmark:_Toc407090409'><span |
| 9073 |
style='mso-bookmark:_Toc407078257'><u>5.2.3 Hydrostatic, quasi-hydrostatic, or |
| 9074 |
non-hydrostatic regime</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9075 |
|
| 9076 |
<p class=MsoNormal style='text-align:justify'><u><span style='font-size:12.0pt; |
| 9077 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 9078 |
|
| 9079 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9080 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The logical variable <i |
| 9081 |
style='mso-bidi-font-style:normal'>nonHydrostatic</i> controls whether or not |
| 9082 |
you want the model to run in a nonhydrostatic regime (<b style='mso-bidi-font-weight: |
| 9083 |
normal'>NH</b>) as described in the first two chapters of this manual. If <i |
| 9084 |
style='mso-bidi-font-style:normal'>nonHydrostatic</i> is set to .TRUE., the |
| 9085 |
model will step forward for the vertical velocity and solve a 3D elliptic |
| 9086 |
equation for the pressure. Note that the vertical velocity can still be |
| 9087 |
diagnosed from the continuity equation if the logical variable <i |
| 9088 |
style='mso-bidi-font-style:normal'>stepW</i> is set to .FALSE. In the |
| 9089 |
nonhydrostatic regime, you also need to set up the logical variable <i |
| 9090 |
style='mso-bidi-font-style:normal'>buoyancy</i> that controls whether or not |
| 9091 |
you want to include the buoyancy term in the vertical momentum equation. The |
| 9092 |
distinction between hydrostatic (<b style='mso-bidi-font-weight:normal'>HPE</b>) |
| 9093 |
and quasi-hydrostatic (<b style='mso-bidi-font-weight:normal'>QH</b>) regime is |
| 9094 |
controlled by the logical variable <i style='mso-bidi-font-style:normal'>verticalCoriolis</i> |
| 9095 |
(see next section, momentum equations).<u><o:p></o:p></u></span></p> |
| 9096 |
|
| 9097 |
<p class=MsoNormal style='text-align:justify'><u><span style='font-size:12.0pt; |
| 9098 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 9099 |
|
| 9100 |
<h3 style='text-align:justify'><a name="_Toc407078258"></a><a |
| 9101 |
name="_Toc407090410"></a><a name="_Toc407090613"></a><a name="_Toc407169643"><span |
| 9102 |
style='mso-bookmark:_Toc407090613'><span style='mso-bookmark:_Toc407090410'><span |
| 9103 |
style='mso-bookmark:_Toc407078258'><u>5.2.4 Momentum equations</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9104 |
|
| 9105 |
<p class=MsoNormal style='text-align:justify'><u><span style='font-size:12.0pt; |
| 9106 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 9107 |
|
| 9108 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9109 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Unless noted otherwise, what |
| 9110 |
follows is not applicable to the vertical velocity <i style='mso-bidi-font-style: |
| 9111 |
normal'>w</i> if the variable <i style='mso-bidi-font-style:normal'>nonHydrostatic</i> |
| 9112 |
has been set to .FALSE. (<b style='mso-bidi-font-weight:normal'>HPE</b> or <b |
| 9113 |
style='mso-bidi-font-weight:normal'>QH</b> regime).<o:p></o:p></span></p> |
| 9114 |
|
| 9115 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9116 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9117 |
|
| 9118 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9119 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The logical variable <i |
| 9120 |
style='mso-bidi-font-style:normal'>momentumStepping</i> controls whether or not |
| 9121 |
you want to step forward for the velocity components <i style='mso-bidi-font-style: |
| 9122 |
normal'>u</i>, <i style='mso-bidi-font-style:normal'>v</i> and <i |
| 9123 |
style='mso-bidi-font-style:normal'>w</i>. If set to .TRUE., the following |
| 9124 |
parameters have to be specified.<o:p></o:p></span></p> |
| 9125 |
|
| 9126 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9127 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9128 |
|
| 9129 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9130 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9131 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9132 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9133 |
font-family:Palatino'>advection terms<o:p></o:p></span></p> |
| 9134 |
|
| 9135 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9136 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9137 |
terms in the momentum equations, set the logical variable <i style='mso-bidi-font-style: |
| 9138 |
normal'>momentumAdvection</i> to .TRUE.. A centered second-order advection |
| 9139 |
scheme is then used.<o:p></o:p></span></p> |
| 9140 |
|
| 9141 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9142 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9143 |
|
| 9144 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9145 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9146 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9147 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9148 |
font-family:Palatino'>metric terms<o:p></o:p></span></p> |
| 9149 |
|
| 9150 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9151 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9152 |
terms in the momentum equations, set the logical variable <i style='mso-bidi-font-style: |
| 9153 |
normal'>metricTerms</i> to .TRUE.. Note that <u>all</u> the metric terms are |
| 9154 |
included. This choice is to be made only if the grid is spherical polar (the |
| 9155 |
variable is automatically set to .FALSE. if the grid is Cartesian).<o:p></o:p></span></p> |
| 9156 |
|
| 9157 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9158 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9159 |
|
| 9160 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9161 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9162 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9163 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9164 |
font-family:Palatino'>Coriolis terms<o:p></o:p></span></p> |
| 9165 |
|
| 9166 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9167 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9168 |
terms in the momentum equations, set the logical variable <i style='mso-bidi-font-style: |
| 9169 |
normal'>Coriolis</i> to .TRUE.. If this is the case, also set the real variable |
| 9170 |
<i style='mso-bidi-font-style:normal'>raja</i> and the logical variable <i |
| 9171 |
style='mso-bidi-font-style:normal'>verticalCoriolis</i>. The former is a number |
| 9172 |
between 0 and 1 that controls the "C-D scheme" (see chapter 2). If <i |
| 9173 |
style='mso-bidi-font-style:normal'>raja</i> is set to a value greater than 0., |
| 9174 |
horizontal velocity components stepped forward on a 'D' grid are used in the |
| 9175 |
evaluation of the Coriolis terms with a weight given by <i style='mso-bidi-font-style: |
| 9176 |
normal'>raja</i>. If <i style='mso-bidi-font-style:normal'>raja</i> is set to |
| 9177 |
0., the Coriolis terms are estimated using the 'C' grid velocity components |
| 9178 |
only. The variable <i style='mso-bidi-font-style:normal'>verticalCoriolis</i> |
| 9179 |
controls whether or not you want to include the cos (latitude) terms in the |
| 9180 |
zonal and vertical momentum equations <b style='mso-bidi-font-weight:normal'>(I |
| 9181 |
think the name verticalCoriolis is misleading. The additional terms appear both |
| 9182 |
in the zonal and vertical momentum equations. I would suggest to replace the |
| 9183 |
name verticalCoriolis by cosphiCoriolis)</b>. If <i style='mso-bidi-font-style: |
| 9184 |
normal'>verticalCoriolis</i> is set to .TRUE. and <i style='mso-bidi-font-style: |
| 9185 |
normal'>nonHydrostatic</i> to .FALSE., the model is in the quasi-hydrostatic (<b |
| 9186 |
style='mso-bidi-font-weight:normal'>QH</b>) regime. If the grid is Cartesian, |
| 9187 |
you have to specify the Coriolis parameter dependence on latitude with the |
| 9188 |
character variable <i style='mso-bidi-font-style:normal'>CoriolisPlane</i>. If |
| 9189 |
this variable is set to 'betaplane', set the reference Coriolis parameter <i |
| 9190 |
style='mso-bidi-font-style:normal'>fcori</i> (in s<sup>-1</sup>) and its |
| 9191 |
derivative with respect to latitude <i style='mso-bidi-font-style:normal'>beta</i> |
| 9192 |
(in m<sup>-1</sup> s<sup>-1</sup>)<b style='mso-bidi-font-weight:normal'> (Note |
| 9193 |
: the Beta plane formulation is not available yet)</b>. If <i style='mso-bidi-font-style: |
| 9194 |
normal'>CoriolisPlane</i> is set to 'fplane', only <i style='mso-bidi-font-style: |
| 9195 |
normal'>fcori</i> needs to be set. Note that you can set up a non-rotating |
| 9196 |
problem on a Cartesian grid by simply setting <i style='mso-bidi-font-style: |
| 9197 |
normal'>fcori</i> to 0. <o:p></o:p></span></p> |
| 9198 |
|
| 9199 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9200 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9201 |
|
| 9202 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9203 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9204 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9205 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9206 |
font-family:Palatino'>dissipation terms<o:p></o:p></span></p> |
| 9207 |
|
| 9208 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9209 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9210 |
terms in the momentum equations, set the logical variable <i style='mso-bidi-font-style: |
| 9211 |
normal'>momentumDiffusion</i> to .TRUE.. If this is the case, specify the |
| 9212 |
horizontal and vertical viscosity coefficients <i style='mso-bidi-font-style: |
| 9213 |
normal'>CAPUV </i>and <i style='mso-bidi-font-style:normal'>RKPUV</i> respectively |
| 9214 |
in the namelist (in m<sup>2</sup> s<sup>-1</sup>). Note that in the code, these |
| 9215 |
variables are called <i style='mso-bidi-font-style:normal'>a2MomXY</i> and <i |
| 9216 |
style='mso-bidi-font-style:normal'>a2MomZ</i> and that the unit of the latter |
| 9217 |
is Pa<sup>2</sup>.s<sup>-1</sup> (multiplication by [<i style='mso-bidi-font-style: |
| 9218 |
normal'>RoNil</i></span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9219 |
font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 9220 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 9221 |
symbol;mso-symbol-font-family:Symbol'>*</span></span><i style='mso-bidi-font-style: |
| 9222 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9223 |
Palatino'>g</span></i><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9224 |
font-family:Palatino'>]<sup>2</sup>). If you also want to include biharmonic |
| 9225 |
diffusion terms in the momentum equations, set the logical variable <i |
| 9226 |
style='mso-bidi-font-style:normal'>momBhDiffusion</i> to .TRUE.. Then, set the |
| 9227 |
value of the horizontal biharmonic diffusion coefficient <i style='mso-bidi-font-style: |
| 9228 |
normal'>C4PUV</i> (in m<sup>4</sup> s<sup>-1</sup>) in the namelist. Note that |
| 9229 |
in the code, this variable is called <i style='mso-bidi-font-style:normal'>a4MomXY</i>.<o:p></o:p></span></p> |
| 9230 |
|
| 9231 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9232 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9233 |
|
| 9234 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9235 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9236 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9237 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9238 |
font-family:Palatino'>forcing terms<o:p></o:p></span></p> |
| 9239 |
|
| 9240 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9241 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This section only applies to |
| 9242 |
the horizontal velocity components.<o:p></o:p></span></p> |
| 9243 |
|
| 9244 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9245 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9246 |
terms in the momentum equations, set the logical variable <i style='mso-bidi-font-style: |
| 9247 |
normal'>momentumForcing</i> to .TRUE.. Then, additional terms will be added to |
| 9248 |
the internally induced tendency terms calculated by the model. It is assumed |
| 9249 |
that you have wind data available (or that you have prescribed an analytical |
| 9250 |
forcing) and a routine that estimates the forcing terms at each time step.<o:p></o:p></span></p> |
| 9251 |
|
| 9252 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9253 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9254 |
|
| 9255 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9256 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9257 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9258 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9259 |
font-family:Palatino'>boundary conditions<o:p></o:p></span></p> |
| 9260 |
|
| 9261 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9262 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Slip or no-slip conditions on |
| 9263 |
side walls and at the bottom and top are controlled by logical variables <i |
| 9264 |
style='mso-bidi-font-style:normal'>freeslipSide</i>, <i style='mso-bidi-font-style: |
| 9265 |
normal'>freeSlipBottom</i> and <i style='mso-bidi-font-style:normal'>freeSlipTop</i>, |
| 9266 |
respectively. If these variables are set to .TRUE., free slip boundary |
| 9267 |
conditions are applied (otherwise no-slip conditions are applied).<o:p></o:p></span></p> |
| 9268 |
|
| 9269 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9270 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9271 |
|
| 9272 |
<h3 style='text-align:justify'><a name="_Toc407078259"></a><a |
| 9273 |
name="_Toc407090411"></a><a name="_Toc407090614"></a><a name="_Toc407169644"><span |
| 9274 |
style='mso-bookmark:_Toc407090614'><span style='mso-bookmark:_Toc407090411'><span |
| 9275 |
style='mso-bookmark:_Toc407078259'><u>5.2.5 Diagnosis of pressure</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9276 |
|
| 9277 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9278 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9279 |
|
| 9280 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9281 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The logical variable <i |
| 9282 |
style='mso-bidi-font-style:normal'>pressureStepping</i> controls whether or not |
| 9283 |
you want to solve for the pressure field. If you do, the following parameters |
| 9284 |
need to be specified :<o:p></o:p></span></p> |
| 9285 |
|
| 9286 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9287 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9288 |
|
| 9289 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9290 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9291 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9292 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9293 |
font-family:Palatino'>hydrostatic pressure<o:p></o:p></span></p> |
| 9294 |
|
| 9295 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9296 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The logical variable <i |
| 9297 |
style='mso-bidi-font-style:normal'>seperatePh</i> controls whether or not you |
| 9298 |
want to calculate the hydrostatic pressure anomaly. If you do, then specify the |
| 9299 |
surface boundary condition with the character variable <i style='mso-bidi-font-style: |
| 9300 |
normal'>phSurfBC</i>. Two options are available : the hydrostatic pressure |
| 9301 |
anomaly is set to zero at the surface (<i style='mso-bidi-font-style:normal'>phSurfBC</i>='zero') |
| 9302 |
or is set to the density of the first layer times half the layer depth (<i |
| 9303 |
style='mso-bidi-font-style:normal'>phSurfBC</i>='topBoxPhIntegralofRho').<o:p></o:p></span></p> |
| 9304 |
|
| 9305 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9306 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9307 |
|
| 9308 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9309 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9310 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9311 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9312 |
font-family:Palatino'>surface pressure<o:p></o:p></span></p> |
| 9313 |
|
| 9314 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9315 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The logical variable <i |
| 9316 |
style='mso-bidi-font-style:normal'>seperatePs</i> controls whether or not you |
| 9317 |
want to solve for the surface pressure. If you do, the real constant variables <i |
| 9318 |
style='mso-bidi-font-style:normal'>freeSurfFac</i>, <i style='mso-bidi-font-style: |
| 9319 |
normal'>psGam</i>, <i style='mso-bidi-font-style:normal'>uDivAlpha</i>, and <i |
| 9320 |
style='mso-bidi-font-style:normal'>gBaro</i> need to be set up and control |
| 9321 |
whether or not you want to have a rigid lid or an implicit free surface. For a |
| 9322 |
rigid lid, set <i style='mso-bidi-font-style:normal'>freeSurfFac</i>, <i |
| 9323 |
style='mso-bidi-font-style:normal'>psGam</i>, <i style='mso-bidi-font-style: |
| 9324 |
normal'>uDivAlpha</i>, and <i style='mso-bidi-font-style:normal'>gBaro</i> to |
| 9325 |
0., 1., 0., and <i style='mso-bidi-font-style:normal'>g</i> (gravity) |
| 9326 |
respectively. To control the operation of the 2D iterative solver routine CG2D, |
| 9327 |
specify the values of the variables <i style='mso-bidi-font-style:normal'>toler2d</i>, |
| 9328 |
<i style='mso-bidi-font-style:normal'>max2dIt</i>, <i style='mso-bidi-font-style: |
| 9329 |
normal'>freqCheckToler2d</i>, <i style='mso-bidi-font-style:normal'>divhMax</i>, |
| 9330 |
<i style='mso-bidi-font-style:normal'>divhMin</i>. Finally, the logical |
| 9331 |
variable <i style='mso-bidi-font-style:normal'>stericEffect</i> controls |
| 9332 |
whether or not you want to include a steric anomaly in surface elevation. If |
| 9333 |
you do, then specify the value of variable <i style='mso-bidi-font-style:normal'>rhorefSurf</i>, |
| 9334 |
reference density for surface layers.<o:p></o:p></span></p> |
| 9335 |
|
| 9336 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9337 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9338 |
|
| 9339 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9340 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9341 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9342 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9343 |
font-family:Palatino'>non hydrostatic pressure<o:p></o:p></span></p> |
| 9344 |
|
| 9345 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9346 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This part is relevant only if |
| 9347 |
the variable <i style='mso-bidi-font-style:normal'>nonHydrostatic</i> has been |
| 9348 |
set to .TRUE. (see section 5.2.3). Then specify the values of the variables <i |
| 9349 |
style='mso-bidi-font-style:normal'>toler3d</i>, <i style='mso-bidi-font-style: |
| 9350 |
normal'>max3dIt</i>, <i style='mso-bidi-font-style:normal'>freqCheckToler3d</i>, |
| 9351 |
<i style='mso-bidi-font-style:normal'>divMax</i>, <i style='mso-bidi-font-style: |
| 9352 |
normal'>divMin</i> that control the operation of the 3D iterative solver |
| 9353 |
routine CG3D. Furthermore, the logical variable <i style='mso-bidi-font-style: |
| 9354 |
normal'>findD2pnhDZ2</i> controls whether or not you want to solve the |
| 9355 |
Dirichlet problem for the vertical gradient of nonhydrostatic pressure.<o:p></o:p></span></p> |
| 9356 |
|
| 9357 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9358 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9359 |
|
| 9360 |
<h3 style='text-align:justify'><a name="_Toc407078260"></a><a |
| 9361 |
name="_Toc407090412"></a><a name="_Toc407090615"></a><a name="_Toc407169645"><span |
| 9362 |
style='mso-bookmark:_Toc407090615'><span style='mso-bookmark:_Toc407090412'><span |
| 9363 |
style='mso-bookmark:_Toc407078260'><u>5.2.6 Tracer equations (temperature and |
| 9364 |
salinity)</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9365 |
|
| 9366 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9367 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9368 |
|
| 9369 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9370 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This section also applies to |
| 9371 |
other tracers (if necessary). The logical variable <i style='mso-bidi-font-style: |
| 9372 |
normal'>tempStepping</i> (<i style='mso-bidi-font-style:normal'>saltStepping</i>) |
| 9373 |
controls whether or not you want to step forward for temperature (salinity). If |
| 9374 |
you do, it is assumed that you have data defining initial conditions (or you |
| 9375 |
can specify initial vertical profiles through the variables <i |
| 9376 |
style='mso-bidi-font-style:normal'>ths</i> and <i style='mso-bidi-font-style: |
| 9377 |
normal'>ssppt</i>, see section 5.2.3). Moreover, the following parameters need |
| 9378 |
to be specified.<o:p></o:p></span></p> |
| 9379 |
|
| 9380 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9381 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9382 |
|
| 9383 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9384 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9385 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9386 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9387 |
font-family:Palatino'>advection terms<o:p></o:p></span></p> |
| 9388 |
|
| 9389 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9390 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9391 |
terms in the temperature (salinity) equation, set the logical variable <i |
| 9392 |
style='mso-bidi-font-style:normal'>tempAdvection</i> (<i style='mso-bidi-font-style: |
| 9393 |
normal'>saltAdvection</i>) to .TRUE.. If this is the case, choose the tracer |
| 9394 |
advection scheme with the character variable <i style='mso-bidi-font-style: |
| 9395 |
normal'>TradvecScheme</i>. Two options are available : 'upstream' or |
| 9396 |
'centered'. <b style='mso-bidi-font-weight:normal'>(Note : in the current |
| 9397 |
version, TradvecScheme is not declared in PARAMS.h but is a local variable of |
| 9398 |
routine INC_TRACER)</b>. In the current version, the advection scheme is common |
| 9399 |
to all tracers.<o:p></o:p></span></p> |
| 9400 |
|
| 9401 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9402 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9403 |
|
| 9404 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9405 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9406 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9407 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9408 |
font-family:Palatino'>dissipation terms<o:p></o:p></span></p> |
| 9409 |
|
| 9410 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9411 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include |
| 9412 |
diffusion terms in the temperature (salinity) equation, set the logical |
| 9413 |
variable <i style='mso-bidi-font-style:normal'>tempDiffusion</i> (<i |
| 9414 |
style='mso-bidi-font-style:normal'>saltDiffusion</i>) to .TRUE.. Then, choose |
| 9415 |
the tracer diffusion scheme with the character variable <i style='mso-bidi-font-style: |
| 9416 |
normal'>TrdifScheme</i>. Several options are available. Here, we only consider |
| 9417 |
the case of constant horizontal and vertical diffusivity coefficients. For |
| 9418 |
other cases, see appendix to know what parameters need to be set up. So, if <i |
| 9419 |
style='mso-bidi-font-style:normal'>TrdifScheme</i> is set to 'constant', the |
| 9420 |
variables <i style='mso-bidi-font-style:normal'>CAPTH</i> (<i style='mso-bidi-font-style: |
| 9421 |
normal'>CAPS</i>) and <i style='mso-bidi-font-style:normal'>RKPTH</i> (<i |
| 9422 |
style='mso-bidi-font-style:normal'>RKPS</i>) in the namelist<i |
| 9423 |
style='mso-bidi-font-style:normal'> </i>need to be set and represent the |
| 9424 |
horizontal and vertical diffusivity coefficients, respectively (in m<sup>2 </sup><span |
| 9425 |
style="mso-spacerun: yes"> </span>s<sup>-1</sup>). Note that in the code, the |
| 9426 |
variables are named <i style='mso-bidi-font-style:normal'>a2TempXY</i> (<i |
| 9427 |
style='mso-bidi-font-style:normal'>a2SaltXY</i>) and <i style='mso-bidi-font-style: |
| 9428 |
normal'>a2TempZ</i> (<i style='mso-bidi-font-style:normal'>a2SaltZ</i>) and |
| 9429 |
that the latter is expressed in Pa<sup>2</sup> s<sup>-1</sup>. If you also want |
| 9430 |
to include biharmonic diffusion terms in the temperature (salinity) equation, |
| 9431 |
set the logical variable <i style='mso-bidi-font-style:normal'>tempBhdiffusion</i> |
| 9432 |
(<i style='mso-bidi-font-style:normal'>saltBhdiffusion</i>) to .TRUE.. Then, |
| 9433 |
set the value of the horizontal biharmonic diffusion coefficient <i |
| 9434 |
style='mso-bidi-font-style:normal'>C4PTH</i> (<i style='mso-bidi-font-style: |
| 9435 |
normal'>C4PS</i>) in the namelist (in m<sup>4 </sup><span style="mso-spacerun: |
| 9436 |
yes"> </span>s<sup>-1</sup>). Note that in the code, the variable is named <i |
| 9437 |
style='mso-bidi-font-style:normal'>a4TempXY</i> (<i style='mso-bidi-font-style: |
| 9438 |
normal'>a4SaltXY</i>).<o:p></o:p></span></p> |
| 9439 |
|
| 9440 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9441 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9442 |
|
| 9443 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9444 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9445 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9446 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9447 |
font-family:Palatino'>forcing terms<o:p></o:p></span></p> |
| 9448 |
|
| 9449 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9450 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to include these |
| 9451 |
terms in the momentum equations, set the logical variable <i style='mso-bidi-font-style: |
| 9452 |
normal'>tempForcing</i> (<i style='mso-bidi-font-style:normal'>saltForcing</i>) |
| 9453 |
to .TRUE.. Then, additional terms will be added to the internally induced |
| 9454 |
tendency terms calculated by the model. It is assumed that you have air-sea |
| 9455 |
heat and freshwater fluxes data available (or that you have prescribed an |
| 9456 |
analytical forcing) and a routine that estimates the forcing terms at each time |
| 9457 |
step.<o:p></o:p></span></p> |
| 9458 |
|
| 9459 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9460 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9461 |
|
| 9462 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9463 |
-18.0pt;mso-list:l36 level1 lfo33;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9464 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9465 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9466 |
font-family:Palatino'>convective adjustment<o:p></o:p></span></p> |
| 9467 |
|
| 9468 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9469 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The logical variable <i |
| 9470 |
style='mso-bidi-font-style:normal'>ConvectiveAdjustment</i> controls whether or |
| 9471 |
not you want the static instabilities to be dealt with by a convective |
| 9472 |
adjustment scheme. If you do, specify the value of variable <i |
| 9473 |
style='mso-bidi-font-style:normal'>CadjFreq</i>, frequency (in s) with which |
| 9474 |
the convective adjustment scheme is applied. For details about the scheme, see |
| 9475 |
appendix. <o:p></o:p></span></p> |
| 9476 |
|
| 9477 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9478 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9479 |
|
| 9480 |
<h3 style='text-align:justify'><a name="_Toc407078261"></a><a |
| 9481 |
name="_Toc407090413"></a><a name="_Toc407090616"></a><a name="_Toc407169646"><span |
| 9482 |
style='mso-bookmark:_Toc407090616'><span style='mso-bookmark:_Toc407090413'><span |
| 9483 |
style='mso-bookmark:_Toc407078261'><u>5.2.7 Run setup</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9484 |
|
| 9485 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9486 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9487 |
|
| 9488 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9489 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9490 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9491 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9492 |
font-family:Palatino'>run duration<o:p></o:p></span></p> |
| 9493 |
|
| 9494 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9495 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The starting time, ending time |
| 9496 |
and time step of an integration need to be set up with the integer variables <i |
| 9497 |
style='mso-bidi-font-style:normal'>IPUSTTTMP</i>, <i style='mso-bidi-font-style: |
| 9498 |
normal'>IENDSECTMP</i> and <i style='mso-bidi-font-style:normal'>IDELT</i> in |
| 9499 |
the namelist (in s). Note that in the code, these parameters are real variables |
| 9500 |
named <i style='mso-bidi-font-style:normal'>startTime</i>, <i style='mso-bidi-font-style: |
| 9501 |
normal'>endTime</i> and <i style='mso-bidi-font-style:normal'>delt</i>. If the |
| 9502 |
starting time is non-zero, the model will try to read in a set of checkpoint |
| 9503 |
files from a previous integration (see section 5.3 for a description of the |
| 9504 |
checkpoint files).<o:p></o:p></span></p> |
| 9505 |
|
| 9506 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9507 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9508 |
|
| 9509 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9510 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9511 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9512 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9513 |
font-family:Palatino'>forcing controls<o:p></o:p></span></p> |
| 9514 |
|
| 9515 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9516 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Certain parameters related to |
| 9517 |
the reading of the forcing files might need to be set up (for example after a |
| 9518 |
restart). In general, this will depend on the particular user configuration. |
| 9519 |
Therefore, this is not extended any further.<o:p></o:p></span></p> |
| 9520 |
|
| 9521 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9522 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9523 |
|
| 9524 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9525 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9526 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9527 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9528 |
font-family:Palatino'>output<o:p></o:p></span></p> |
| 9529 |
|
| 9530 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9531 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Real constant variables |
| 9532 |
defining frequencies (in s) with which output files are written on disk need to |
| 9533 |
be set up. <i style='mso-bidi-font-style:normal'>dStateFreq</i> is the |
| 9534 |
frequency with which the state of the model is saved. <i style='mso-bidi-font-style: |
| 9535 |
normal'>dPUFreq</i> is the frequency with which pick-up files (suitable to |
| 9536 |
restart an integration) are saved. <i style='mso-bidi-font-style:normal'>dCkptFreq</i> |
| 9537 |
is the frequency with which "rolling" checkpoint files are saved. See |
| 9538 |
section 5.3.3 for a description of the output files.<o:p></o:p></span></p> |
| 9539 |
|
| 9540 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9541 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9542 |
|
| 9543 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9544 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9545 |
|
| 9546 |
<h2><a name="_Toc407078262"></a><a name="_Toc407090414"></a><a |
| 9547 |
name="_Toc407090617"></a><a name="_Toc407169647"><span style='mso-bookmark: |
| 9548 |
_Toc407090617'><span style='mso-bookmark:_Toc407090414'><span style='mso-bookmark: |
| 9549 |
_Toc407078262'>5.3 Compiling, running, and restarting the code</span></span></span></a></h2> |
| 9550 |
|
| 9551 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9552 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9553 |
|
| 9554 |
<h3><a name="_Toc407078263"></a><a name="_Toc407090415"></a><a |
| 9555 |
name="_Toc407090618"></a><a name="_Toc407169648"><span style='mso-bookmark: |
| 9556 |
_Toc407090618'><span style='mso-bookmark:_Toc407090415'><span style='mso-bookmark: |
| 9557 |
_Toc407078263'><u>5.3.1 compilation</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9558 |
|
| 9559 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9560 |
font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9561 |
|
| 9562 |
<p class=MsoNormal style='text-align:justify;tab-stops:198.0pt'><span |
| 9563 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Type |
| 9564 |
make wherever you are. There is a good chance it will work! To set the |
| 9565 |
precision, look into utility r8 (in directory ProgUtils). This utility is |
| 9566 |
called by the makefile to "preprocess" the procedures of the code |
| 9567 |
converting all the 'REAL' statements into 'REAL*4' or 'REAL*8'. The makefile |
| 9568 |
will create an executable named MITGCM. Use the UNIX command 'size' to know how |
| 9569 |
much memory is required to execute the code on a single processor.<o:p></o:p></span></p> |
| 9570 |
|
| 9571 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9572 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9573 |
|
| 9574 |
<h3 style='text-align:justify'><a name="_Toc407078264"></a><a |
| 9575 |
name="_Toc407090416"></a><a name="_Toc407090619"></a><a name="_Toc407169649"><span |
| 9576 |
style='mso-bookmark:_Toc407090619'><span style='mso-bookmark:_Toc407090416'><span |
| 9577 |
style='mso-bookmark:_Toc407078264'><u>5.3.2 execution</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9578 |
|
| 9579 |
<p class=MsoNormal style='text-align:justify'><u><span style='font-size:12.0pt; |
| 9580 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></u></p> |
| 9581 |
|
| 9582 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9583 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>First, we review the input |
| 9584 |
files needed to run the model :<o:p></o:p></span></p> |
| 9585 |
|
| 9586 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9587 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9588 |
|
| 9589 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9590 |
-18.0pt;mso-list:l20 level1 lfo30;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9591 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9592 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9593 |
font-family:Palatino'>namelist (file named DATA),<o:p></o:p></span></p> |
| 9594 |
|
| 9595 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9596 |
-18.0pt;mso-list:l20 level1 lfo30;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9597 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9598 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9599 |
font-family:Palatino'>topography (file named PMASK.SUN.B),<o:p></o:p></span></p> |
| 9600 |
|
| 9601 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9602 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9603 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9604 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9605 |
font-family:Palatino'>polynomial coefficients (file named POLY3D.COEFFS) if the |
| 9606 |
full equation of state is used,<o:p></o:p></span></p> |
| 9607 |
|
| 9608 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9609 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9610 |
|
| 9611 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9612 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>and if necessary :<o:p></o:p></span></p> |
| 9613 |
|
| 9614 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9615 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9616 |
|
| 9617 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9618 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9619 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9620 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9621 |
font-family:Palatino'>initial temperature and salinity,<o:p></o:p></span></p> |
| 9622 |
|
| 9623 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9624 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9625 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9626 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9627 |
font-family:Palatino'>wind data,<o:p></o:p></span></p> |
| 9628 |
|
| 9629 |
<p class=MsoNormal style='margin-left:18.0pt;text-align:justify;text-indent: |
| 9630 |
-18.0pt;mso-list:l19 level1 lfo29;tab-stops:list 18.0pt'><![if !supportLists]><span |
| 9631 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>-<span style='font:7.0pt "Times New Roman"'> |
| 9632 |
</span></span><![endif]><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9633 |
font-family:Palatino'>heat and freshwater fluxes data.<o:p></o:p></span></p> |
| 9634 |
|
| 9635 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9636 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9637 |
|
| 9638 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9639 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>If you want to restart the |
| 9640 |
code, pick-up files are also needed (see next section). To run the code, type |
| 9641 |
MITGCM < DATA > OUTPUT. The building of scripts to make the submission |
| 9642 |
and execution of the code more automatic is left to the user at this point.<o:p></o:p></span></p> |
| 9643 |
|
| 9644 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9645 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9646 |
|
| 9647 |
<h3 style='text-align:justify'><a name="_Toc407078265"></a><a |
| 9648 |
name="_Toc407090417"></a><a name="_Toc407090620"></a><a name="_Toc407169650"><span |
| 9649 |
style='mso-bookmark:_Toc407090620'><span style='mso-bookmark:_Toc407090417'><span |
| 9650 |
style='mso-bookmark:_Toc407078265'><u>5.3.3 output and restart</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9651 |
|
| 9652 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9653 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9654 |
|
| 9655 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9656 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Depending upon the values of |
| 9657 |
the various frequencies mentioned in section 5.2.7, output files describing the |
| 9658 |
state of the model will be written on disk. The name of these files is written |
| 9659 |
in the following way : "XXX.0000nIter", where XXX is a capital letter |
| 9660 |
or a group of capital letters indicating the quantity being saved (for example |
| 9661 |
U for the zonal velocity) and nIter is a chain of figures indicating the instant |
| 9662 |
(in number of time steps) at which saving occurs. The maximum value for nIter |
| 9663 |
is 10<sup>9 </sup><span style="mso-spacerun: yes"> </span>and 0s will fill in |
| 9664 |
the space after XXX when nIter is less than its maximum value as shown above. |
| 9665 |
Below follows a list of the output files. Unless noted otherwise, the different |
| 9666 |
quantities are expressed in SI units.<o:p></o:p></span></p> |
| 9667 |
|
| 9668 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9669 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9670 |
|
| 9671 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9672 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>U<span style='mso-tab-count: |
| 9673 |
2'> </span>:<span style='mso-tab-count:1'> </span>zonal |
| 9674 |
component of velocity vector<o:p></o:p></span></p> |
| 9675 |
|
| 9676 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9677 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>V<span style='mso-tab-count: |
| 9678 |
2'> </span>:<span style='mso-tab-count:1'> </span>meridional |
| 9679 |
component of velocity vector<o:p></o:p></span></p> |
| 9680 |
|
| 9681 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9682 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>W<span style='mso-tab-count: |
| 9683 |
2'> </span>:<span style='mso-tab-count:1'> </span>vertical |
| 9684 |
component of velocity vector (in Pa s<sup>-1</sup>)<o:p></o:p></span></p> |
| 9685 |
|
| 9686 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9687 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>T<span style='mso-tab-count: |
| 9688 |
2'> </span>:<span style='mso-tab-count:1'> </span>potential |
| 9689 |
temperature (in <sup>o</sup>C)<o:p></o:p></span></p> |
| 9690 |
|
| 9691 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9692 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>S<span style='mso-tab-count: |
| 9693 |
2'> </span>:<span style='mso-tab-count:1'> </span>salinity |
| 9694 |
(in ppt)<o:p></o:p></span></p> |
| 9695 |
|
| 9696 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9697 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>PS<span style='mso-tab-count: |
| 9698 |
2'> </span>:<span style='mso-tab-count:1'> </span>surface |
| 9699 |
pressure (in m)<o:p></o:p></span></p> |
| 9700 |
|
| 9701 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9702 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>PH<span style='mso-tab-count: |
| 9703 |
2'> </span>:<span style='mso-tab-count:1'> </span>hydrostatic |
| 9704 |
pressure (in m)<o:p></o:p></span></p> |
| 9705 |
|
| 9706 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9707 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>PNH<span style='mso-tab-count: |
| 9708 |
2'> </span>:<span style='mso-tab-count:1'> </span>nonhydrostatic |
| 9709 |
pressure (in m)<o:p></o:p></span></p> |
| 9710 |
|
| 9711 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9712 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>PTOTAL<span style='mso-tab-count: |
| 9713 |
1'> </span>:<span style='mso-tab-count:1'> </span>total |
| 9714 |
pressure (PS+PH+PNH) (in m)<o:p></o:p></span></p> |
| 9715 |
|
| 9716 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9717 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>GTNM1<span style='mso-tab-count: |
| 9718 |
1'> </span>:<span style='mso-tab-count:1'> </span>temperature |
| 9719 |
tendency at time step n-1 (in <sup>o</sup>C s<sup>-1</sup>)<o:p></o:p></span></p> |
| 9720 |
|
| 9721 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9722 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>GSNM1<span style='mso-tab-count: |
| 9723 |
1'> </span>:<span style='mso-tab-count:1'> </span>salinity |
| 9724 |
tendency at time step n-1 (in ppt s<sup>-1</sup>)<o:p></o:p></span></p> |
| 9725 |
|
| 9726 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9727 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>GUNM1<span style='mso-tab-count: |
| 9728 |
1'> </span>:<span style='mso-tab-count:1'> </span>zonal velocity |
| 9729 |
tendency (except pressure term) at<o:p></o:p></span></p> |
| 9730 |
|
| 9731 |
<p class=MsoNormal style='margin-left:72.0pt;text-align:justify;text-indent: |
| 9732 |
36.0pt'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9733 |
Palatino'>time step n-1<o:p></o:p></span></p> |
| 9734 |
|
| 9735 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9736 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>GVNM1<span style='mso-tab-count: |
| 9737 |
1'> </span>:<span style='mso-tab-count:1'> </span>meridional |
| 9738 |
velocity tendency (except pressure term) at <o:p></o:p></span></p> |
| 9739 |
|
| 9740 |
<p class=MsoNormal style='margin-left:72.0pt;text-align:justify;text-indent: |
| 9741 |
36.0pt'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9742 |
Palatino'>time step n-1<o:p></o:p></span></p> |
| 9743 |
|
| 9744 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9745 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>GWNM1<span style='mso-tab-count: |
| 9746 |
1'> </span>:<span style='mso-tab-count:1'> </span>vertical |
| 9747 |
velocity tendency (except pressure term) at <o:p></o:p></span></p> |
| 9748 |
|
| 9749 |
<p class=MsoNormal style='margin-left:72.0pt;text-align:justify;text-indent: |
| 9750 |
36.0pt'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9751 |
Palatino'>time step n-1 (in Pa s<sup>-2</sup>)<o:p></o:p></span></p> |
| 9752 |
|
| 9753 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9754 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>PNM1<span style='mso-tab-count: |
| 9755 |
2'> </span>:<span style='mso-tab-count:1'> </span>total |
| 9756 |
pressure at time step n-1<o:p></o:p></span></p> |
| 9757 |
|
| 9758 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9759 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>UAJA<span style='mso-tab-count: |
| 9760 |
2'> </span>:<span style='mso-tab-count:1'> </span>'D' |
| 9761 |
grid zonal velocity (used in C-D scheme)<o:p></o:p></span></p> |
| 9762 |
|
| 9763 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9764 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>VAJA<span style='mso-tab-count: |
| 9765 |
2'> </span>:<span style='mso-tab-count:1'> </span>'D' |
| 9766 |
grid meridional velocity (used in C-D scheme)<o:p></o:p></span></p> |
| 9767 |
|
| 9768 |
<p class=MsoNormal style='margin-left:108.0pt;text-align:justify;text-indent: |
| 9769 |
-108.0pt'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9770 |
Palatino'>UBXBYNM1 :<span style='mso-tab-count:1'> </span>interpolated |
| 9771 |
'D' grid zonal velocity (from 'C' grid component) at time step n-1<o:p></o:p></span></p> |
| 9772 |
|
| 9773 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9774 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>VBYBXNM1<span style='mso-tab-count: |
| 9775 |
1'> </span>:<span style='mso-tab-count:1'> </span>interpolated 'D' |
| 9776 |
grid meridional velocity (from 'C' grid <o:p></o:p></span></p> |
| 9777 |
|
| 9778 |
<p class=MsoNormal style='margin-left:72.0pt;text-align:justify;text-indent: |
| 9779 |
36.0pt'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9780 |
Palatino'>component) at time step n-1<o:p></o:p></span></p> |
| 9781 |
|
| 9782 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9783 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9784 |
|
| 9785 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9786 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>These are the files needed to |
| 9787 |
restart an integration (pick-up files) and their output is controlled by the |
| 9788 |
variable <i style='mso-bidi-font-style:normal'>dPUFreq</i> (see section 5.2.7). |
| 9789 |
Of course, if you are stepping forward other quantities (other tracer, ice
), |
| 9790 |
they will need to be output along with the files above. The variable <i |
| 9791 |
style='mso-bidi-font-style:normal'>dStateFreq</i> controls the output of the |
| 9792 |
quantities U, V, W, T, S, PTOTAL only, from which most diagnostics can be made. |
| 9793 |
Rolling checkpoint files, the output of which are controlled by the variable <i |
| 9794 |
style='mso-bidi-font-style:normal'>dCkptFreq</i>, are the same as the ones |
| 9795 |
above (pick-up files) but are named differently. Their name end with the suffix |
| 9796 |
'ckptA' or 'ckptB' instead of '0000nIter'. They can be used to restart the |
| 9797 |
model but are overwritten every other time they are output to save disk space |
| 9798 |
during long integrations.<o:p></o:p></span></p> |
| 9799 |
|
| 9800 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9801 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9802 |
|
| 9803 |
<p class=MsoNormal><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9804 |
font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9805 |
|
| 9806 |
<h2><a name="_Toc407078266"></a><a name="_Toc407090418"></a><a |
| 9807 |
name="_Toc407090621"></a><a name="_Toc407169651"><span style='mso-bookmark: |
| 9808 |
_Toc407090621'><span style='mso-bookmark:_Toc407090418'><span style='mso-bookmark: |
| 9809 |
_Toc407078266'>5.4 Examples : description of test cases</span></span></span></a></h2> |
| 9810 |
|
| 9811 |
<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span |
| 9812 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></b></p> |
| 9813 |
|
| 9814 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9815 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>First, we describe briefly each |
| 9816 |
case. Refer to the references for more detail.<o:p></o:p></span></p> |
| 9817 |
|
| 9818 |
<h3 style='text-align:justify'><a name="_Toc407078267"></a><a |
| 9819 |
name="_Toc407090419"></a><a name="_Toc407090622"></a><a name="_Toc407169652"><span |
| 9820 |
style='mso-bookmark:_Toc407090622'><span style='mso-bookmark:_Toc407090419'><span |
| 9821 |
style='mso-bookmark:_Toc407078267'><u>5.4.1 Two-layer ocean in a rectangular |
| 9822 |
basin driven by a steady wind-stress</u></span></span></span></a></h3> |
| 9823 |
|
| 9824 |
<p class=MsoNormal style='text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 9825 |
|
| 9826 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9827 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This case corresponds to the |
| 9828 |
numerical experiments of Holland and Lin (1975). In this study, the authors |
| 9829 |
explore the generation of mesoscale eddies and their contribution to the |
| 9830 |
oceanic circulation. Their model has two homogeneous layers on a simple closed |
| 9831 |
rectangular basin 1000 km </span><span style='font-size:12.0pt;mso-bidi-font-size: |
| 9832 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 9833 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 9834 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>´</span></span><span |
| 9835 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> 1000 |
| 9836 |
km with a flat bottom at 5 km depth, and is forced by a steady wind-stress that |
| 9837 |
varies in a simple sinusoidal manner with latitude and has an amplitude of 0.1 |
| 9838 |
Pa. The horizontal resolution is 20 km on a </span><i style='mso-bidi-font-style: |
| 9839 |
normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9840 |
Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 9841 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 9842 |
symbol;mso-symbol-font-family:Symbol'>b</span></span></i><span |
| 9843 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>-plane. |
| 9844 |
For sufficiently small viscosity values, the model, spun up from rest, exhibits |
| 9845 |
mesoscale eddies and eventually reaches a statistical steady state. Analysis of |
| 9846 |
the energy budget shows that the eddies are generated by baroclinic |
| 9847 |
instability.<o:p></o:p></span></p> |
| 9848 |
|
| 9849 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9850 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9851 |
|
| 9852 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9853 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The configuration given in |
| 9854 |
5.4.5 corresponds to the preliminary experiment described in Holland and Lin |
| 9855 |
(1975). In our height-coordinate model, quasi reduced-gravity conditions can be |
| 9856 |
configurated by prescribing an initial temperature profile mimicking the |
| 9857 |
reduced-gravity used in Holland and Lin set-up.<o:p></o:p></span></p> |
| 9858 |
|
| 9859 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9860 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9861 |
|
| 9862 |
<h3 style='text-align:justify'><a name="_Toc407078268"></a><a |
| 9863 |
name="_Toc407090420"></a><a name="_Toc407090623"></a><a name="_Toc407169653"><span |
| 9864 |
style='mso-bookmark:_Toc407090623'><span style='mso-bookmark:_Toc407090420'><span |
| 9865 |
style='mso-bookmark:_Toc407078268'><u>5.4.2 Neutral ocean in a doubly periodic |
| 9866 |
domain driven by buoyancy forcing</u></span></span></span></a></h3> |
| 9867 |
|
| 9868 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9869 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9870 |
|
| 9871 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9872 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This case corresponds to the |
| 9873 |
numerical experiment of Jones and Marshall (1993) done with the present code. |
| 9874 |
In this study, the authors explore open ocean deep convection. The model has |
| 9875 |
dimensions 32 km </span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt; |
| 9876 |
font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 9877 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 9878 |
symbol;mso-symbol-font-family:Symbol'>´</span></span><span style='font-size: |
| 9879 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> 32 km </span><span |
| 9880 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 9881 |
mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino;mso-char-type: |
| 9882 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 9883 |
mso-symbol-font-family:Symbol'>´</span></span><span style='font-size:12.0pt; |
| 9884 |
mso-bidi-font-size:10.0pt;font-family:Palatino'> 2 km and 19 levels on the |
| 9885 |
vertical. Periodic boundary conditions are applied on the x and y directions. |
| 9886 |
The horizontal and vertical resolutions are 250 m and 100 m, respectively. The |
| 9887 |
model is initialized with a homogeneous, resting ocean governed by a linear |
| 9888 |
equation of state without salt. Constant cooling corresponding to a heat loss |
| 9889 |
of 800 W m<sup>-2</sup> is induced over a disk of radius 8 km at the center of |
| 9890 |
the domain and over a depth of 200 m from the surface. The model is run in the |
| 9891 |
nonhydrostatic mode and convective plumes develop. These plumes efficiently mix |
| 9892 |
the water column and generate a dense chimney of fluid, which subsequently |
| 9893 |
breaks up through the mechanism of baroclinic instability to form spinning |
| 9894 |
cones.<o:p></o:p></span></p> |
| 9895 |
|
| 9896 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9897 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9898 |
|
| 9899 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9900 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The configuration given |
| 9901 |
hereafter corresponds to the reference simulation of Jones and Marshall (1993).<o:p></o:p></span></p> |
| 9902 |
|
| 9903 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9904 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9905 |
|
| 9906 |
<h3 style='text-align:justify'><a name="_Toc407078269"></a><a |
| 9907 |
name="_Toc407090421"></a><a name="_Toc407090624"></a><a name="_Toc407169654"><span |
| 9908 |
style='mso-bookmark:_Toc407090624'><span style='mso-bookmark:_Toc407090421'><span |
| 9909 |
style='mso-bookmark:_Toc407078269'><u>5.4.3 Exponentially stratified ocean on a |
| 9910 |
wind-driven channel</u></span></span></span></a></h3> |
| 9911 |
|
| 9912 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9913 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9914 |
|
| 9915 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9916 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This case corresponds to the |
| 9917 |
wind-driven channel experiment of Visbeck et. al. (1997) done with the present |
| 9918 |
code. In this study, the authors compare eddy-resolving 3D simulations with 2D |
| 9919 |
simulations in which the eddies are parameterized in order to test and assess |
| 9920 |
different schemes for specifying eddy transfer coefficients. The model has |
| 9921 |
dimensions 1500 km </span><span style='font-size:12.0pt;mso-bidi-font-size: |
| 9922 |
10.0pt;font-family:Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family: |
| 9923 |
Palatino;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 9924 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>´</span></span><span |
| 9925 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> 500 km |
| 9926 |
</span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 9927 |
Symbol;mso-ascii-font-family:Palatino;mso-hansi-font-family:Palatino; |
| 9928 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 9929 |
symbol;mso-symbol-font-family:Symbol'>´</span></span><span style='font-size: |
| 9930 |
12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'> 4.5 km on a <i |
| 9931 |
style='mso-bidi-font-style:normal'>f</i>-plane. The grid spacing is 10 km on |
| 9932 |
the horizontal and varies on the vertical from 25 m in the upper layers to 400 |
| 9933 |
m at depth (20 vertical levels). Periodic conditions are applied at the |
| 9934 |
meridional boundaries. The model is initialized with an exponential temperature |
| 9935 |
profile of scale depth 900 m and is forced by a cosine wind stress of maximum |
| 9936 |
strength 0.2 Pa at the channel center. After six years or so, a steady state is |
| 9937 |
reached where the input of potential energy by the wind is balanced by release |
| 9938 |
of potential energy due to baroclinic eddies.<o:p></o:p></span></p> |
| 9939 |
|
| 9940 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9941 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9942 |
|
| 9943 |
<h3 style='text-align:justify'><a name="_Toc407078270"></a><a |
| 9944 |
name="_Toc407090422"></a><a name="_Toc407090625"></a><a name="_Toc407169655"><span |
| 9945 |
style='mso-bookmark:_Toc407090625'><span style='mso-bookmark:_Toc407090422'><span |
| 9946 |
style='mso-bookmark:_Toc407078270'><u>5.4.4 Global ocean driven by realistic |
| 9947 |
wind and buoyancy forcing</u></span></span></span></a></h3> |
| 9948 |
|
| 9949 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9950 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9951 |
|
| 9952 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9953 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>This case corresponds to |
| 9954 |
an-going study of the large-scale global ocean circulation. The spherical |
| 9955 |
domain extends from 80<sup>o</sup>S to 80<sup>o</sup>N in latitude and a |
| 9956 |
realistic topography is used. The horizontal resolution is 4<sup> o</sup> and |
| 9957 |
the vertical grid spacing varies from 25 m in the upper layers to 500 m at |
| 9958 |
depth (20 vertical levels). The full equation of state is employed. The model |
| 9959 |
is initialized with the Levitus climatology and forced by climatological |
| 9960 |
forcing, namely the
.<o:p></o:p></span></p> |
| 9961 |
|
| 9962 |
<h3 style='text-align:justify'><a name="_Toc407078271"></a><a |
| 9963 |
name="_Toc407090423"></a><a name="_Toc407090626"></a><a name="_Toc407169656"><span |
| 9964 |
style='mso-bookmark:_Toc407090626'><span style='mso-bookmark:_Toc407090423'><span |
| 9965 |
style='mso-bookmark:_Toc407078271'><u>5.4.5 Model configuration for the test |
| 9966 |
cases</u></span></span></span></a><u><o:p></o:p></u></h3> |
| 9967 |
|
| 9968 |
<p class=MsoNormal style='text-align:justify'><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 9969 |
|
| 9970 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9971 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>The parameter values are |
| 9972 |
summarized on Table 5.1.<o:p></o:p></span></p> |
| 9973 |
|
| 9974 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9975 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9976 |
|
| 9977 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 9978 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9979 |
|
| 9980 |
<p class=MsoNormal align=center style='text-align:center'><b style='mso-bidi-font-weight: |
| 9981 |
normal'>Table 5.<span style='mso-field-code:"SEQ Table \\* ARABIC \\s 1"'>1</span></b> |
| 9982 |
Model configuration for the test cases. "<span style='font-family:Symbol; |
| 9983 |
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; |
| 9984 |
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type: |
| 9985 |
symbol;mso-symbol-font-family:Symbol'>-</span></span>" indicate not |
| 9986 |
applicable or that the model results are not sensitive to the values chosen.</p> |
| 9987 |
|
| 9988 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 9989 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 9990 |
|
| 9991 |
<table border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse; |
| 9992 |
border:none;mso-border-alt:solid windowtext .5pt;mso-padding-alt:0pt 5.4pt 0pt 5.4pt'> |
| 9993 |
<tr style='height:26.95pt'> |
| 9994 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 9995 |
padding:0pt 5.4pt 0pt 5.4pt;height:26.95pt'> |
| 9996 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 9997 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 9998 |
</td> |
| 9999 |
<td width=96 valign=top style='width:72.0pt;border:solid windowtext 3.0pt; |
| 10000 |
border-left:none;padding:0pt 5.4pt 0pt 5.4pt;height:26.95pt'> |
| 10001 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10002 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>2-layer<o:p></o:p></span></p> |
| 10003 |
</td> |
| 10004 |
<td width=96 valign=top style='width:72.0pt;border:solid windowtext 3.0pt; |
| 10005 |
border-left:none;padding:0pt 5.4pt 0pt 5.4pt;height:26.95pt'> |
| 10006 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10007 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>convection<o:p></o:p></span></p> |
| 10008 |
</td> |
| 10009 |
<td width=114 valign=top style='width:85.5pt;border:solid windowtext 3.0pt; |
| 10010 |
border-left:none;padding:0pt 5.4pt 0pt 5.4pt;height:26.95pt'> |
| 10011 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10012 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>Channel<o:p></o:p></span></p> |
| 10013 |
</td> |
| 10014 |
<td width=109 valign=top style='width:81.85pt;border:solid windowtext 3.0pt; |
| 10015 |
border-left:none;padding:0pt 5.4pt 0pt 5.4pt;height:26.95pt'> |
| 10016 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10017 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>Global |
| 10018 |
4 deg<o:p></o:p></span></p> |
| 10019 |
</td> |
| 10020 |
</tr> |
| 10021 |
<tr style='height:18.3pt'> |
| 10022 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10023 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10024 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10025 |
height:18.3pt'> |
| 10026 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10027 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10028 |
10.0pt;font-family:Helvetica'>Nx<o:p></o:p></span></i></p> |
| 10029 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10030 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10031 |
10.0pt;font-family:Helvetica'>Ny<o:p></o:p></span></i></p> |
| 10032 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10033 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10034 |
10.0pt;font-family:Helvetica'>Nz-1</span></i><span style='font-size:12.0pt; |
| 10035 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10036 |
</td> |
| 10037 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10038 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10039 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10040 |
height:18.3pt'> |
| 10041 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10042 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>100<o:p></o:p></span></p> |
| 10043 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10044 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>100<o:p></o:p></span></p> |
| 10045 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10046 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>2<o:p></o:p></span></p> |
| 10047 |
</td> |
| 10048 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10049 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10050 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10051 |
height:18.3pt'> |
| 10052 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10053 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>132<o:p></o:p></span></p> |
| 10054 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10055 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>132<o:p></o:p></span></p> |
| 10056 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10057 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>19<o:p></o:p></span></p> |
| 10058 |
</td> |
| 10059 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10060 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10061 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10062 |
height:18.3pt'> |
| 10063 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10064 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>150<o:p></o:p></span></p> |
| 10065 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10066 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>50<o:p></o:p></span></p> |
| 10067 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10068 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>20<o:p></o:p></span></p> |
| 10069 |
</td> |
| 10070 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10071 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10072 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10073 |
height:18.3pt'> |
| 10074 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10075 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>90<o:p></o:p></span></p> |
| 10076 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10077 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>40<o:p></o:p></span></p> |
| 10078 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10079 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>20<o:p></o:p></span></p> |
| 10080 |
</td> |
| 10081 |
</tr> |
| 10082 |
<tr> |
| 10083 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10084 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10085 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10086 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10087 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10088 |
10.0pt;font-family:Helvetica'>gridStyle<o:p></o:p></span></i></p> |
| 10089 |
</td> |
| 10090 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10091 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10092 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10093 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10094 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'cartesian'<o:p></o:p></span></p> |
| 10095 |
</td> |
| 10096 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10097 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10098 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10099 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10100 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'cartesian'<o:p></o:p></span></p> |
| 10101 |
</td> |
| 10102 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10103 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10104 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10105 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10106 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'cartesian'<o:p></o:p></span></p> |
| 10107 |
</td> |
| 10108 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10109 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10110 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10111 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10112 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'spherical<o:p></o:p></span></p> |
| 10113 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10114 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>polar'<o:p></o:p></span></p> |
| 10115 |
</td> |
| 10116 |
</tr> |
| 10117 |
<tr> |
| 10118 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10119 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10120 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10121 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10122 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10123 |
10.0pt;font-family:Helvetica'>dm</span></i><span style='font-size:12.0pt; |
| 10124 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (km)<o:p></o:p></span></p> |
| 10125 |
</td> |
| 10126 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10127 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10128 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10129 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10130 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>20<o:p></o:p></span></p> |
| 10131 |
</td> |
| 10132 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10133 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10134 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10135 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10136 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0.25<o:p></o:p></span></p> |
| 10137 |
</td> |
| 10138 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10139 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10140 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10141 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10142 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>10<o:p></o:p></span></p> |
| 10143 |
</td> |
| 10144 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10145 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10146 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10147 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10148 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10149 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10150 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10151 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10152 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10153 |
</td> |
| 10154 |
</tr> |
| 10155 |
<tr style='height:15.7pt'> |
| 10156 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10157 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10158 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10159 |
height:15.7pt'> |
| 10160 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10161 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10162 |
10.0pt;font-family:Helvetica'>dphi<o:p></o:p></span></i></p> |
| 10163 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10164 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10165 |
10.0pt;font-family:Helvetica'>dTheta<o:p></o:p></span></i></p> |
| 10166 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10167 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10168 |
10.0pt;font-family:Helvetica'>phiMin</span></i><span style='font-size:12.0pt; |
| 10169 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (deg)<o:p></o:p></span></p> |
| 10170 |
</td> |
| 10171 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10172 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10173 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10174 |
height:15.7pt'> |
| 10175 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10176 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 10177 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10178 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10179 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10180 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10181 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10182 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10183 |
</td> |
| 10184 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10185 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10186 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10187 |
height:15.7pt'> |
| 10188 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10189 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 10190 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10191 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10192 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10193 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10194 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10195 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10196 |
</td> |
| 10197 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10198 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10199 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10200 |
height:15.7pt'> |
| 10201 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10202 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 10203 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10204 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10205 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10206 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10207 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10208 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10209 |
</td> |
| 10210 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10211 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10212 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10213 |
height:15.7pt'> |
| 10214 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10215 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>4<o:p></o:p></span></p> |
| 10216 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10217 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>4<o:p></o:p></span></p> |
| 10218 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10219 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>-80<o:p></o:p></span></p> |
| 10220 |
</td> |
| 10221 |
</tr> |
| 10222 |
<tr> |
| 10223 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10224 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10225 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10226 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10227 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10228 |
10.0pt;font-family:Helvetica'>deltaz </span></i><span style='font-size:12.0pt; |
| 10229 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(min)<o:p></o:p></span></p> |
| 10230 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10231 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>(max) |
| 10232 |
(m)<o:p></o:p></span></p> |
| 10233 |
</td> |
| 10234 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10235 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10236 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10237 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10238 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>1000<o:p></o:p></span></p> |
| 10239 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10240 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>4000<o:p></o:p></span></p> |
| 10241 |
</td> |
| 10242 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10243 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10244 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10245 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10246 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>100<o:p></o:p></span></p> |
| 10247 |
</td> |
| 10248 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10249 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10250 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10251 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10252 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>25<o:p></o:p></span></p> |
| 10253 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10254 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>400<o:p></o:p></span></p> |
| 10255 |
</td> |
| 10256 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10257 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10258 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10259 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10260 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>25<o:p></o:p></span></p> |
| 10261 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10262 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>500<o:p></o:p></span></p> |
| 10263 |
</td> |
| 10264 |
</tr> |
| 10265 |
<tr> |
| 10266 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 10267 |
border-top:none;mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10268 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10269 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>Geometry<o:p></o:p></span></p> |
| 10270 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10271 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 10272 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10273 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>Topography<o:p></o:p></span></p> |
| 10274 |
</td> |
| 10275 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10276 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10277 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10278 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10279 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>rectangular |
| 10280 |
box<o:p></o:p></span></p> |
| 10281 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10282 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>flat |
| 10283 |
bottom<o:p></o:p></span></p> |
| 10284 |
</td> |
| 10285 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10286 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10287 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10288 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10289 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>squareboxd-periodic<o:p></o:p></span></p> |
| 10290 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10291 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>flat |
| 10292 |
bottom<o:p></o:p></span></p> |
| 10293 |
</td> |
| 10294 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10295 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10296 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10297 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10298 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>channel<o:p></o:p></span></p> |
| 10299 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10300 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>s-periodic<o:p></o:p></span></p> |
| 10301 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10302 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>flat |
| 10303 |
bottom<o:p></o:p></span></p> |
| 10304 |
</td> |
| 10305 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10306 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10307 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10308 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10309 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>sphere<o:p></o:p></span></p> |
| 10310 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10311 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 10312 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10313 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>realistic |
| 10314 |
topo<o:p></o:p></span></p> |
| 10315 |
</td> |
| 10316 |
</tr> |
| 10317 |
<tr> |
| 10318 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 10319 |
border-top:none;mso-border-top-alt:solid windowtext 1.5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10320 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10321 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10322 |
10.0pt;font-family:Helvetica'>EquationofState<o:p></o:p></span></i></p> |
| 10323 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10324 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10325 |
10.0pt;font-family:Helvetica'>ths</span></i><span style='font-size:12.0pt; |
| 10326 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (<sup>o</sup>C)<o:p></o:p></span></p> |
| 10327 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10328 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10329 |
10.0pt;font-family:Helvetica'>ssppt</span></i><span style='font-size:12.0pt; |
| 10330 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (ppt)<o:p></o:p></span></p> |
| 10331 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10332 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10333 |
10.0pt;font-family:Helvetica'>tAlpha</span></i><span style='font-size:12.0pt; |
| 10334 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (K<sup>-1</sup>)<o:p></o:p></span></p> |
| 10335 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10336 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10337 |
10.0pt;font-family:Helvetica'>sBeta</span></i><span style='font-size:12.0pt; |
| 10338 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (ppt<sup>-1</sup>)<o:p></o:p></span></p> |
| 10339 |
</td> |
| 10340 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10341 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10342 |
mso-border-top-alt:solid windowtext 1.5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10343 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10344 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'linear'<o:p></o:p></span></p> |
| 10345 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10346 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>20 - |
| 10347 |
10<o:p></o:p></span></p> |
| 10348 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10349 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10350 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10351 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10352 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10353 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10354 |
</td> |
| 10355 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10356 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10357 |
mso-border-top-alt:solid windowtext 1.5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10358 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10359 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'linear'<o:p></o:p></span></p> |
| 10360 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10361 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<sup><o:p></o:p></sup></span></p> |
| 10362 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10363 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10364 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10365 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>2 </span><span |
| 10366 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10367 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10368 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10369 |
mso-symbol-font-family:Symbol'>´</span></span><span style='font-size:12.0pt; |
| 10370 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> 10<sup>-4<o:p></o:p></sup></span></p> |
| 10371 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10372 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10373 |
</td> |
| 10374 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10375 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10376 |
mso-border-top-alt:solid windowtext 1.5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10377 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10378 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'linear'<o:p></o:p></span></p> |
| 10379 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10380 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>exponential<o:p></o:p></span></p> |
| 10381 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10382 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10383 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10384 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>2 </span><span |
| 10385 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10386 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10387 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10388 |
mso-symbol-font-family:Symbol'>´</span></span><span style='font-size:12.0pt; |
| 10389 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> 10<sup>-4<o:p></o:p></sup></span></p> |
| 10390 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10391 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10392 |
</td> |
| 10393 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10394 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10395 |
mso-border-top-alt:solid windowtext 1.5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10396 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10397 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'polynomial'<o:p></o:p></span></p> |
| 10398 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10399 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10400 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10401 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10402 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10403 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10404 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10405 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10406 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10407 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10408 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10409 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10410 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10411 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10412 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10413 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10414 |
</td> |
| 10415 |
</tr> |
| 10416 |
<tr> |
| 10417 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 10418 |
border-top:none;mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10419 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10420 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10421 |
10.0pt;font-family:Helvetica'>nonHydrostatic<o:p></o:p></span></i></p> |
| 10422 |
</td> |
| 10423 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10424 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10425 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10426 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10427 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10428 |
</td> |
| 10429 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10430 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10431 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10432 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10433 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10434 |
</td> |
| 10435 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10436 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10437 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10438 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10439 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10440 |
</td> |
| 10441 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10442 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 10443 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10444 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10445 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10446 |
</td> |
| 10447 |
</tr> |
| 10448 |
<tr> |
| 10449 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10450 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10451 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10452 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10453 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10454 |
10.0pt;font-family:Helvetica'>momentumStepping<o:p></o:p></span></i></p> |
| 10455 |
</td> |
| 10456 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10457 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10458 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10459 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10460 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10461 |
</td> |
| 10462 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10463 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10464 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10465 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10466 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10467 |
</td> |
| 10468 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10469 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10470 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10471 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10472 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10473 |
</td> |
| 10474 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10475 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10476 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10477 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10478 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10479 |
</td> |
| 10480 |
</tr> |
| 10481 |
<tr> |
| 10482 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10483 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10484 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10485 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10486 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10487 |
10.0pt;font-family:Helvetica'>momentumAdvection<o:p></o:p></span></i></p> |
| 10488 |
</td> |
| 10489 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10490 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10491 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10492 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10493 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10494 |
</td> |
| 10495 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10496 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10497 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10498 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10499 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10500 |
</td> |
| 10501 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10502 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10503 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10504 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10505 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10506 |
</td> |
| 10507 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10508 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10509 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10510 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10511 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10512 |
</td> |
| 10513 |
</tr> |
| 10514 |
<tr> |
| 10515 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10516 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10517 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10518 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10519 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10520 |
10.0pt;font-family:Helvetica'>metricTerms<o:p></o:p></span></i></p> |
| 10521 |
</td> |
| 10522 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10523 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10524 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10525 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10526 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10527 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10528 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10529 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10530 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10531 |
</td> |
| 10532 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10533 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10534 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10535 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10536 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10537 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10538 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10539 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10540 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10541 |
</td> |
| 10542 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10543 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10544 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10545 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10546 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10547 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10548 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10549 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10550 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10551 |
</td> |
| 10552 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10553 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10554 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10555 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10556 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10557 |
</td> |
| 10558 |
</tr> |
| 10559 |
<tr style='height:23.35pt'> |
| 10560 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10561 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10562 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10563 |
height:23.35pt'> |
| 10564 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10565 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10566 |
10.0pt;font-family:Helvetica'>Coriolis<o:p></o:p></span></i></p> |
| 10567 |
</td> |
| 10568 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10569 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10570 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10571 |
height:23.35pt'> |
| 10572 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10573 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10574 |
</td> |
| 10575 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10576 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10577 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10578 |
height:23.35pt'> |
| 10579 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10580 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10581 |
</td> |
| 10582 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10583 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10584 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10585 |
height:23.35pt'> |
| 10586 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10587 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10588 |
</td> |
| 10589 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10590 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10591 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 10592 |
height:23.35pt'> |
| 10593 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10594 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10595 |
</td> |
| 10596 |
</tr> |
| 10597 |
<tr> |
| 10598 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10599 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10600 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10601 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10602 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10603 |
10.0pt;font-family:Helvetica'>VerticalCoriolis<o:p></o:p></span></i></p> |
| 10604 |
</td> |
| 10605 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10606 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10607 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10608 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10609 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10610 |
</td> |
| 10611 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10612 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10613 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10614 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10615 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10616 |
</td> |
| 10617 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10618 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10619 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10620 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10621 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10622 |
</td> |
| 10623 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10624 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10625 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10626 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10627 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10628 |
</td> |
| 10629 |
</tr> |
| 10630 |
<tr> |
| 10631 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10632 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10633 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10634 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10635 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10636 |
10.0pt;font-family:Helvetica'>raja<o:p></o:p></span></i></p> |
| 10637 |
</td> |
| 10638 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10639 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10640 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10641 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10642 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10643 |
</td> |
| 10644 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10645 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10646 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10647 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10648 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10649 |
</td> |
| 10650 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10651 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10652 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10653 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10654 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10655 |
</td> |
| 10656 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10657 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10658 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10659 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10660 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10661 |
</td> |
| 10662 |
</tr> |
| 10663 |
<tr> |
| 10664 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10665 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10666 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10667 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10668 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10669 |
10.0pt;font-family:Helvetica'>CoriolisPlane<o:p></o:p></span></i></p> |
| 10670 |
</td> |
| 10671 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10672 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10673 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10674 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10675 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'betaplane'<o:p></o:p></span></p> |
| 10676 |
</td> |
| 10677 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10678 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10679 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10680 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10681 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'fPlane'<o:p></o:p></span></p> |
| 10682 |
</td> |
| 10683 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10684 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10685 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10686 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10687 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'fPlane'<o:p></o:p></span></p> |
| 10688 |
</td> |
| 10689 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10690 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10691 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10692 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10693 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10694 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10695 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10696 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10697 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10698 |
</td> |
| 10699 |
</tr> |
| 10700 |
<tr> |
| 10701 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10702 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10703 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10704 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10705 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10706 |
10.0pt;font-family:Helvetica'>fcori </span></i><span style='font-size:12.0pt; |
| 10707 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(s<sup>-1</sup>)<o:p></o:p></span></p> |
| 10708 |
</td> |
| 10709 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10710 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10711 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10712 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10713 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>7.3 </span><span |
| 10714 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10715 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10716 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10717 |
mso-symbol-font-family:Symbol'>´</span></span><span style='font-size:12.0pt; |
| 10718 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> 10<sup>-5</sup><o:p></o:p></span></p> |
| 10719 |
</td> |
| 10720 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10721 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10722 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10723 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10724 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>10<sup>-4</sup><o:p></o:p></span></p> |
| 10725 |
</td> |
| 10726 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10727 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10728 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10729 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10730 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>10<sup>-4</sup><o:p></o:p></span></p> |
| 10731 |
</td> |
| 10732 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10733 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10734 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10735 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10736 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10737 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10738 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10739 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10740 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10741 |
</td> |
| 10742 |
</tr> |
| 10743 |
<tr> |
| 10744 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10745 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10746 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10747 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10748 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10749 |
10.0pt;font-family:Helvetica'>beta </span></i><span style='font-size:12.0pt; |
| 10750 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(m<sup>-1</sup> s<sup>-1</sup>)<o:p></o:p></span></p> |
| 10751 |
</td> |
| 10752 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10753 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10754 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10755 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10756 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>2 </span><span |
| 10757 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10758 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10759 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10760 |
mso-symbol-font-family:Symbol'>´</span></span><span style='font-size:12.0pt; |
| 10761 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> 10<sup>-11</sup><o:p></o:p></span></p> |
| 10762 |
</td> |
| 10763 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10764 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10765 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10766 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10767 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10768 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10769 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10770 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10771 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10772 |
</td> |
| 10773 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10774 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10775 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10776 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10777 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10778 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10779 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10780 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10781 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10782 |
</td> |
| 10783 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10784 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10785 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10786 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10787 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10788 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10789 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10790 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10791 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10792 |
</td> |
| 10793 |
</tr> |
| 10794 |
<tr> |
| 10795 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10796 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10797 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10798 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10799 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10800 |
10.0pt;font-family:Helvetica'>MomentumDiffusion<o:p></o:p></span></i></p> |
| 10801 |
</td> |
| 10802 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10803 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10804 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10805 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10806 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10807 |
</td> |
| 10808 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10809 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10810 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10811 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10812 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10813 |
</td> |
| 10814 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10815 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10816 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10817 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10818 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10819 |
</td> |
| 10820 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10821 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10822 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10823 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10824 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10825 |
</td> |
| 10826 |
</tr> |
| 10827 |
<tr> |
| 10828 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10829 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10830 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10831 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10832 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10833 |
10.0pt;font-family:Helvetica'>CAPUV<o:p></o:p></span></i></p> |
| 10834 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10835 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10836 |
10.0pt;font-family:Helvetica'>RKPUV </span></i><span style='font-size:12.0pt; |
| 10837 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(m<sup>2</sup> s<sup>-1</sup>)<o:p></o:p></span></p> |
| 10838 |
</td> |
| 10839 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10840 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10841 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10842 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10843 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>330<o:p></o:p></span></p> |
| 10844 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10845 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 10846 |
</td> |
| 10847 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10848 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10849 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10850 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10851 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>5<o:p></o:p></span></p> |
| 10852 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10853 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0.2<o:p></o:p></span></p> |
| 10854 |
</td> |
| 10855 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10856 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10857 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10858 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10859 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10860 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10861 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>10<sup>-3</sup><o:p></o:p></span></p> |
| 10862 |
</td> |
| 10863 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10864 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10865 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10866 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10867 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10868 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10869 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10870 |
</td> |
| 10871 |
</tr> |
| 10872 |
<tr> |
| 10873 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10874 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10875 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10876 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10877 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10878 |
10.0pt;font-family:Helvetica'>MomBhDiffusion<o:p></o:p></span></i></p> |
| 10879 |
</td> |
| 10880 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10881 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10882 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10883 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10884 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10885 |
</td> |
| 10886 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10887 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10888 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10889 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10890 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10891 |
</td> |
| 10892 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10893 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10894 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10895 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10896 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10897 |
</td> |
| 10898 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10899 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10900 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10901 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10902 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10903 |
</td> |
| 10904 |
</tr> |
| 10905 |
<tr> |
| 10906 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10907 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10908 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10909 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10910 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10911 |
10.0pt;font-family:Helvetica'>C4PUV </span></i><span style='font-size:12.0pt; |
| 10912 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(m<sup>4</sup> s<sup>-1</sup>)<o:p></o:p></span></p> |
| 10913 |
</td> |
| 10914 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10915 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10916 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10917 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10918 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10919 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10920 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10921 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10922 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10923 |
</td> |
| 10924 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10925 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10926 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10927 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10928 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 10929 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 10930 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 10931 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 10932 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10933 |
</td> |
| 10934 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10935 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10936 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10937 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10938 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10939 |
</td> |
| 10940 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10941 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10942 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10943 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10944 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 10945 |
</td> |
| 10946 |
</tr> |
| 10947 |
<tr> |
| 10948 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 10949 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10950 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10951 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 10952 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 10953 |
10.0pt;font-family:Helvetica'>MomentumForcing<o:p></o:p></span></i></p> |
| 10954 |
</td> |
| 10955 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10956 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10957 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10958 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10959 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10960 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10961 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>cosine |
| 10962 |
wind<o:p></o:p></span></p> |
| 10963 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10964 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0.1 |
| 10965 |
Pa<o:p></o:p></span></p> |
| 10966 |
</td> |
| 10967 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 10968 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10969 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10970 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10971 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 10972 |
</td> |
| 10973 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 10974 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10975 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10976 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10977 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10978 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10979 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>cosine |
| 10980 |
wind<o:p></o:p></span></p> |
| 10981 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10982 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0.2 |
| 10983 |
Pa<o:p></o:p></span></p> |
| 10984 |
</td> |
| 10985 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 10986 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 10987 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 10988 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10989 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 10990 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 10991 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>wind |
| 10992 |
data<o:p></o:p></span></p> |
| 10993 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 10994 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 10995 |
</td> |
| 10996 |
</tr> |
| 10997 |
<tr> |
| 10998 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 10999 |
border-top:none;mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11000 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11001 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11002 |
10.0pt;font-family:Helvetica'>FreeslipSide<o:p></o:p></span></i></p> |
| 11003 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11004 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11005 |
10.0pt;font-family:Helvetica'>FreeslipBottom<o:p></o:p></span></i></p> |
| 11006 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11007 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11008 |
10.0pt;font-family:Helvetica'>FreeslipTop<o:p></o:p></span></i></p> |
| 11009 |
</td> |
| 11010 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11011 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11012 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11013 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11014 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11015 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11016 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11017 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11018 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11019 |
</td> |
| 11020 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11021 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11022 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11023 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11024 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11025 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11026 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11027 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11028 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11029 |
</td> |
| 11030 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11031 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11032 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11033 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11034 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11035 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11036 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11037 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11038 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11039 |
</td> |
| 11040 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11041 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11042 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11043 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11044 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11045 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11046 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11047 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11048 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11049 |
</td> |
| 11050 |
</tr> |
| 11051 |
<tr> |
| 11052 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11053 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11054 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11055 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11056 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11057 |
10.0pt;font-family:Helvetica'>PressureStepping<o:p></o:p></span></i></p> |
| 11058 |
</td> |
| 11059 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11060 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11061 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11062 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11063 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11064 |
</td> |
| 11065 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11066 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11067 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11068 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11069 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11070 |
</td> |
| 11071 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11072 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11073 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11074 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11075 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11076 |
</td> |
| 11077 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11078 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11079 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11080 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11081 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11082 |
</td> |
| 11083 |
</tr> |
| 11084 |
<tr style='height:18.4pt'> |
| 11085 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11086 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11087 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 11088 |
height:18.4pt'> |
| 11089 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11090 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11091 |
10.0pt;font-family:Helvetica'>SeparatePh<o:p></o:p></span></i></p> |
| 11092 |
</td> |
| 11093 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11094 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11095 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 11096 |
height:18.4pt'> |
| 11097 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11098 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11099 |
</td> |
| 11100 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11101 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11102 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 11103 |
height:18.4pt'> |
| 11104 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11105 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11106 |
</td> |
| 11107 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11108 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11109 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 11110 |
height:18.4pt'> |
| 11111 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11112 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11113 |
</td> |
| 11114 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11115 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11116 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt; |
| 11117 |
height:18.4pt'> |
| 11118 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11119 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11120 |
</td> |
| 11121 |
</tr> |
| 11122 |
<tr> |
| 11123 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11124 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11125 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11126 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11127 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11128 |
10.0pt;font-family:Helvetica'>phSurfBC<o:p></o:p></span></i></p> |
| 11129 |
</td> |
| 11130 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11131 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11132 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11133 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11134 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'zero'<o:p></o:p></span></p> |
| 11135 |
</td> |
| 11136 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11137 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11138 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11139 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11140 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'zero'<o:p></o:p></span></p> |
| 11141 |
</td> |
| 11142 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11143 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11144 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11145 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11146 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'zero'<o:p></o:p></span></p> |
| 11147 |
</td> |
| 11148 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11149 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11150 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11151 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11152 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'zero'<o:p></o:p></span></p> |
| 11153 |
</td> |
| 11154 |
</tr> |
| 11155 |
<tr> |
| 11156 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11157 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11158 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11159 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11160 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11161 |
10.0pt;font-family:Helvetica'>SeparatePs<o:p></o:p></span></i></p> |
| 11162 |
</td> |
| 11163 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11164 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11165 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11166 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11167 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11168 |
</td> |
| 11169 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11170 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11171 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11172 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11173 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11174 |
</td> |
| 11175 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11176 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11177 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11178 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11179 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11180 |
</td> |
| 11181 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11182 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11183 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11184 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11185 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11186 |
</td> |
| 11187 |
</tr> |
| 11188 |
<tr> |
| 11189 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11190 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11191 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11192 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11193 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>rigid |
| 11194 |
lid<o:p></o:p></span></p> |
| 11195 |
</td> |
| 11196 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11197 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11198 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11199 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11200 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>yes<o:p></o:p></span></p> |
| 11201 |
</td> |
| 11202 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11203 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11204 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11205 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11206 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>yes<o:p></o:p></span></p> |
| 11207 |
</td> |
| 11208 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11209 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11210 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11211 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11212 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>yes<o:p></o:p></span></p> |
| 11213 |
</td> |
| 11214 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11215 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11216 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11217 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11218 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>no<o:p></o:p></span></p> |
| 11219 |
</td> |
| 11220 |
</tr> |
| 11221 |
<tr> |
| 11222 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11223 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11224 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11225 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11226 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11227 |
10.0pt;font-family:Helvetica'>toler2d<o:p></o:p></span></i></p> |
| 11228 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11229 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11230 |
10.0pt;font-family:Helvetica'>max2dIt<o:p></o:p></span></i></p> |
| 11231 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11232 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11233 |
10.0pt;font-family:Helvetica'>FreqCheckToler2d<o:p></o:p></span></i></p> |
| 11234 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11235 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11236 |
10.0pt;font-family:Helvetica'>divHmax<o:p></o:p></span></i></p> |
| 11237 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11238 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11239 |
10.0pt;font-family:Helvetica'>divHmin<o:p></o:p></span></i></p> |
| 11240 |
</td> |
| 11241 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11242 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11243 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11244 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11245 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11246 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11247 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11248 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11249 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11250 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11251 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11252 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 11253 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11254 |
</td> |
| 11255 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11256 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11257 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11258 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 11259 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11260 |
</td> |
| 11261 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11262 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11263 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11264 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11265 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11266 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11267 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11268 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 11269 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11270 |
</td> |
| 11271 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11272 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11273 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11274 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11275 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11276 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11277 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11278 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 11279 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11280 |
</td> |
| 11281 |
</tr> |
| 11282 |
<tr> |
| 11283 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11284 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11285 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11286 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11287 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11288 |
10.0pt;font-family:Helvetica'>stericEffect<o:p></o:p></span></i></p> |
| 11289 |
</td> |
| 11290 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11291 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11292 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11293 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11294 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11295 |
</td> |
| 11296 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11297 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11298 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11299 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11300 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11301 |
</td> |
| 11302 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11303 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11304 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11305 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11306 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11307 |
</td> |
| 11308 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11309 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11310 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11311 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11312 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11313 |
</td> |
| 11314 |
</tr> |
| 11315 |
<tr> |
| 11316 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11317 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11318 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11319 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11320 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11321 |
10.0pt;font-family:Helvetica'>rhorefsurf<o:p></o:p></span></i></p> |
| 11322 |
</td> |
| 11323 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11324 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11325 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11326 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11327 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11328 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11329 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11330 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11331 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11332 |
</td> |
| 11333 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11334 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11335 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11336 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11337 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11338 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11339 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11340 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11341 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11342 |
</td> |
| 11343 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11344 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11345 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11346 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11347 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11348 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11349 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11350 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11351 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11352 |
</td> |
| 11353 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11354 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11355 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11356 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11357 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11358 |
</td> |
| 11359 |
</tr> |
| 11360 |
<tr> |
| 11361 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11362 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11363 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11364 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11365 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11366 |
10.0pt;font-family:Helvetica'>toler3d<o:p></o:p></span></i></p> |
| 11367 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11368 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11369 |
10.0pt;font-family:Helvetica'>max3dIt<o:p></o:p></span></i></p> |
| 11370 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11371 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11372 |
10.0pt;font-family:Helvetica'>FreqCheckToler3d<o:p></o:p></span></i></p> |
| 11373 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11374 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11375 |
10.0pt;font-family:Helvetica'>divmax<o:p></o:p></span></i></p> |
| 11376 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11377 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11378 |
10.0pt;font-family:Helvetica'>divmin<o:p></o:p></span></i></p> |
| 11379 |
</td> |
| 11380 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11381 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11382 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11383 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11384 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11385 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11386 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11387 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11388 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11389 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11390 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11391 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11392 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11393 |
</td> |
| 11394 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11395 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11396 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11397 |
<p class=MsoNormal align=center style='text-align:center'><![if !supportEmptyParas]> <![endif]><span |
| 11398 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11399 |
</td> |
| 11400 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11401 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11402 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11403 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11404 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11405 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11406 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11407 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11408 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11409 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11410 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11411 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11412 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11413 |
</td> |
| 11414 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11415 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11416 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11417 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11418 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11419 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11420 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11421 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11422 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11423 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11424 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11425 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11426 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11427 |
</td> |
| 11428 |
</tr> |
| 11429 |
<tr> |
| 11430 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 11431 |
border-top:none;mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11432 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11433 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11434 |
10.0pt;font-family:Helvetica'>findD2pnhDZ2<o:p></o:p></span></i></p> |
| 11435 |
</td> |
| 11436 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11437 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11438 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11439 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11440 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11441 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11442 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11443 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11444 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11445 |
</td> |
| 11446 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11447 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11448 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11449 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11450 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11451 |
</td> |
| 11452 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11453 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11454 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11455 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11456 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11457 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11458 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11459 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11460 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11461 |
</td> |
| 11462 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11463 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11464 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11465 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11466 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11467 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11468 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11469 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11470 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11471 |
</td> |
| 11472 |
</tr> |
| 11473 |
<tr> |
| 11474 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11475 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11476 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11477 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11478 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>Initial |
| 11479 |
condition<o:p></o:p></span></p> |
| 11480 |
</td> |
| 11481 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11482 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11483 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11484 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11485 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>see <i |
| 11486 |
style='mso-bidi-font-style:normal'>ths<o:p></o:p></i></span></p> |
| 11487 |
</td> |
| 11488 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11489 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11490 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11491 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11492 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>see <i |
| 11493 |
style='mso-bidi-font-style:normal'>ths</i><o:p></o:p></span></p> |
| 11494 |
</td> |
| 11495 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11496 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11497 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11498 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11499 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>see <i |
| 11500 |
style='mso-bidi-font-style:normal'>ths</i><o:p></o:p></span></p> |
| 11501 |
</td> |
| 11502 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11503 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11504 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11505 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11506 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>Levitus |
| 11507 |
data<o:p></o:p></span></p> |
| 11508 |
</td> |
| 11509 |
</tr> |
| 11510 |
<tr> |
| 11511 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11512 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11513 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11514 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11515 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11516 |
10.0pt;font-family:Helvetica'>TempStepping<o:p></o:p></span></i></p> |
| 11517 |
</td> |
| 11518 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11519 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11520 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11521 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11522 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11523 |
</td> |
| 11524 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11525 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11526 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11527 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11528 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11529 |
</td> |
| 11530 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11531 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11532 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11533 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11534 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11535 |
</td> |
| 11536 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11537 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11538 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11539 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11540 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11541 |
</td> |
| 11542 |
</tr> |
| 11543 |
<tr> |
| 11544 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11545 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11546 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11547 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11548 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11549 |
10.0pt;font-family:Helvetica'>TempAdvection<o:p></o:p></span></i></p> |
| 11550 |
</td> |
| 11551 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11552 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11553 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11554 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11555 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11556 |
</td> |
| 11557 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11558 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11559 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11560 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11561 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11562 |
</td> |
| 11563 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11564 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11565 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11566 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11567 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11568 |
</td> |
| 11569 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11570 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11571 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11572 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11573 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11574 |
</td> |
| 11575 |
</tr> |
| 11576 |
<tr> |
| 11577 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11578 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11579 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11580 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11581 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11582 |
10.0pt;font-family:Helvetica'>TradvecScheme<o:p></o:p></span></i></p> |
| 11583 |
</td> |
| 11584 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11585 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11586 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11587 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11588 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'centered'<o:p></o:p></span></p> |
| 11589 |
</td> |
| 11590 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11591 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11592 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11593 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11594 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'centered'<o:p></o:p></span></p> |
| 11595 |
</td> |
| 11596 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11597 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11598 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11599 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11600 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'centered'<o:p></o:p></span></p> |
| 11601 |
</td> |
| 11602 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11603 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11604 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11605 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11606 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'centered'<o:p></o:p></span></p> |
| 11607 |
</td> |
| 11608 |
</tr> |
| 11609 |
<tr> |
| 11610 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11611 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11612 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11613 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11614 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11615 |
10.0pt;font-family:Helvetica'>TempDiffusion<o:p></o:p></span></i></p> |
| 11616 |
</td> |
| 11617 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11618 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11619 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11620 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11621 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11622 |
</td> |
| 11623 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11624 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11625 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11626 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11627 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11628 |
</td> |
| 11629 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11630 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11631 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11632 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11633 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11634 |
</td> |
| 11635 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11636 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11637 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11638 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11639 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11640 |
</td> |
| 11641 |
</tr> |
| 11642 |
<tr> |
| 11643 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11644 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11645 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11646 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11647 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11648 |
10.0pt;font-family:Helvetica'>TrdifScheme<o:p></o:p></span></i></p> |
| 11649 |
</td> |
| 11650 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11651 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11652 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11653 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11654 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'constant'<o:p></o:p></span></p> |
| 11655 |
</td> |
| 11656 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11657 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11658 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11659 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11660 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'constant'<o:p></o:p></span></p> |
| 11661 |
</td> |
| 11662 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11663 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11664 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11665 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11666 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'constant'<o:p></o:p></span></p> |
| 11667 |
</td> |
| 11668 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11669 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11670 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11671 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11672 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>'GM'<o:p></o:p></span></p> |
| 11673 |
</td> |
| 11674 |
</tr> |
| 11675 |
<tr> |
| 11676 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11677 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11678 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11679 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11680 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11681 |
10.0pt;font-family:Helvetica'>CAPTH<o:p></o:p></span></i></p> |
| 11682 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11683 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11684 |
10.0pt;font-family:Helvetica'>RKPTH </span></i><span style='font-size:12.0pt; |
| 11685 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(m<sup>2 </sup>s<sup>-1</sup>)<o:p></o:p></span></p> |
| 11686 |
</td> |
| 11687 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11688 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11689 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11690 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11691 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11692 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11693 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11694 |
</td> |
| 11695 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11696 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11697 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11698 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11699 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>5<o:p></o:p></span></p> |
| 11700 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11701 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0.2<o:p></o:p></span></p> |
| 11702 |
</td> |
| 11703 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11704 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11705 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11706 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11707 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>0<o:p></o:p></span></p> |
| 11708 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11709 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>10<sup>-5</sup><o:p></o:p></span></p> |
| 11710 |
</td> |
| 11711 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11712 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11713 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11714 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11715 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11716 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11717 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11718 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11719 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11720 |
</td> |
| 11721 |
</tr> |
| 11722 |
<tr> |
| 11723 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11724 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11725 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11726 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11727 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11728 |
10.0pt;font-family:Helvetica'>tempBhdiffusion<o:p></o:p></span></i></p> |
| 11729 |
</td> |
| 11730 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11731 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11732 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11733 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11734 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11735 |
</td> |
| 11736 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11737 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11738 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11739 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11740 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11741 |
</td> |
| 11742 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11743 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11744 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11745 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11746 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11747 |
</td> |
| 11748 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11749 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11750 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11751 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11752 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11753 |
</td> |
| 11754 |
</tr> |
| 11755 |
<tr> |
| 11756 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11757 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11758 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11759 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11760 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11761 |
10.0pt;font-family:Helvetica'>C4PTH </span></i><span style='font-size:12.0pt; |
| 11762 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'>(m<sup>4</sup>s<sup>-1</sup>)<o:p></o:p></span></p> |
| 11763 |
</td> |
| 11764 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11765 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11766 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11767 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11768 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11769 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11770 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11771 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11772 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11773 |
</td> |
| 11774 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11775 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11776 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11777 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11778 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11779 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11780 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11781 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11782 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11783 |
</td> |
| 11784 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11785 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11786 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11787 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11788 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>10<sup>10</sup><o:p></o:p></span></p> |
| 11789 |
</td> |
| 11790 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11791 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11792 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11793 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11794 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol; |
| 11795 |
mso-ascii-font-family:Helvetica;mso-hansi-font-family:Helvetica;mso-char-type: |
| 11796 |
symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol; |
| 11797 |
mso-symbol-font-family:Symbol'>-</span></span><span style='font-size:12.0pt; |
| 11798 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><o:p></o:p></span></p> |
| 11799 |
</td> |
| 11800 |
</tr> |
| 11801 |
<tr> |
| 11802 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11803 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11804 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11805 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11806 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11807 |
10.0pt;font-family:Helvetica'>tempForcing<o:p></o:p></span></i></p> |
| 11808 |
</td> |
| 11809 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11810 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11811 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11812 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11813 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11814 |
</td> |
| 11815 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11816 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11817 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11818 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11819 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11820 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11821 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>constant<o:p></o:p></span></p> |
| 11822 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11823 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>cooling<o:p></o:p></span></p> |
| 11824 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11825 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>800 |
| 11826 |
W m<sup>-2</sup><o:p></o:p></span></p> |
| 11827 |
</td> |
| 11828 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11829 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11830 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11831 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11832 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.FALSE.<o:p></o:p></span></p> |
| 11833 |
</td> |
| 11834 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11835 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11836 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11837 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11838 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11839 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11840 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>heat |
| 11841 |
and<o:p></o:p></span></p> |
| 11842 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11843 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>freshwater<o:p></o:p></span></p> |
| 11844 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11845 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>fluxes |
| 11846 |
data<o:p></o:p></span></p> |
| 11847 |
</td> |
| 11848 |
</tr> |
| 11849 |
<tr> |
| 11850 |
<td width=175 valign=top style='width:131.4pt;border-top:none;border-left: |
| 11851 |
solid windowtext 3.0pt;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11852 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11853 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11854 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11855 |
10.0pt;font-family:Helvetica'>convectiveAdjustment<o:p></o:p></span></i></p> |
| 11856 |
</td> |
| 11857 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11858 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11859 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11860 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11861 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11862 |
</td> |
| 11863 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11864 |
border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11865 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11866 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11867 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11868 |
</td> |
| 11869 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11870 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11871 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11872 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11873 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11874 |
</td> |
| 11875 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11876 |
none;border-bottom:solid windowtext .5pt;border-right:solid windowtext 3.0pt; |
| 11877 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11878 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11879 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>.TRUE.<o:p></o:p></span></p> |
| 11880 |
</td> |
| 11881 |
</tr> |
| 11882 |
<tr> |
| 11883 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 11884 |
border-top:none;mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11885 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11886 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11887 |
10.0pt;font-family:Helvetica'>cadjFreq<o:p></o:p></span></i></p> |
| 11888 |
</td> |
| 11889 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11890 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11891 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11892 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11893 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11894 |
</td> |
| 11895 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11896 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11897 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11898 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11899 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11900 |
</td> |
| 11901 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11902 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11903 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11904 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11905 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11906 |
</td> |
| 11907 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11908 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11909 |
mso-border-top-alt:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11910 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11911 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11912 |
</td> |
| 11913 |
</tr> |
| 11914 |
<tr> |
| 11915 |
<td width=175 valign=top style='width:131.4pt;border:solid windowtext 3.0pt; |
| 11916 |
border-top:none;mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11917 |
<p class=MsoNormal align=center style='text-align:center'><i |
| 11918 |
style='mso-bidi-font-style:normal'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11919 |
10.0pt;font-family:Helvetica'>Idelt</span></i><span style='font-size:12.0pt; |
| 11920 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'> (s)<o:p></o:p></span></p> |
| 11921 |
</td> |
| 11922 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11923 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11924 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11925 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11926 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>1200<o:p></o:p></span></p> |
| 11927 |
</td> |
| 11928 |
<td width=96 valign=top style='width:72.0pt;border-top:none;border-left:none; |
| 11929 |
border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11930 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11931 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11932 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>60<o:p></o:p></span></p> |
| 11933 |
</td> |
| 11934 |
<td width=114 valign=top style='width:85.5pt;border-top:none;border-left: |
| 11935 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11936 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11937 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11938 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'>?<o:p></o:p></span></p> |
| 11939 |
</td> |
| 11940 |
<td width=109 valign=top style='width:81.85pt;border-top:none;border-left: |
| 11941 |
none;border-bottom:solid windowtext 3.0pt;border-right:solid windowtext 3.0pt; |
| 11942 |
mso-border-top-alt:solid windowtext 3.0pt;padding:0pt 5.4pt 0pt 5.4pt'> |
| 11943 |
<p class=MsoNormal align=center style='text-align:center;page-break-after: |
| 11944 |
avoid'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family: |
| 11945 |
Helvetica'>3600<o:p></o:p></span></p> |
| 11946 |
</td> |
| 11947 |
</tr> |
| 11948 |
</table> |
| 11949 |
|
| 11950 |
<p class=MsoNormal align=center style='text-align:center'><span |
| 11951 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11952 |
|
| 11953 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 11954 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11955 |
|
| 11956 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 11957 |
mso-bidi-font-size:10.0pt;font-family:Helvetica'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11958 |
|
| 11959 |
</div> |
| 11960 |
|
| 11961 |
<span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Helvetica; |
| 11962 |
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; |
| 11963 |
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br |
| 11964 |
clear=all style='page-break-before:always;mso-break-type:section-break'> |
| 11965 |
</span> |
| 11966 |
|
| 11967 |
<div class=Section6> |
| 11968 |
|
| 11969 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 11970 |
|
| 11971 |
<h1><a name="_Toc407078272"></a><a name="_Toc407090424"></a><a |
| 11972 |
name="_Toc407090627"></a><a name="_Toc407169657"><span style='mso-bookmark: |
| 11973 |
_Toc407090627'><span style='mso-bookmark:_Toc407090424'><span style='mso-bookmark: |
| 11974 |
_Toc407078272'>APPENDICES</span></span></span></a><span style='mso-bookmark: |
| 11975 |
_Toc407078272'></span></h1> |
| 11976 |
|
| 11977 |
</div> |
| 11978 |
|
| 11979 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078272'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 11980 |
|
| 11981 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078272'><span |
| 11982 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></span></p> |
| 11983 |
|
| 11984 |
<p class=MsoBodyText><span style='mso-bookmark:_Toc407078272'><span |
| 11985 |
style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>Not |
| 11986 |
written yet<o:p></o:p></span></span></p> |
| 11987 |
|
| 11988 |
<span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino; |
| 11989 |
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; |
| 11990 |
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><br |
| 11991 |
clear=all style='mso-special-character:line-break;page-break-before:always'> |
| 11992 |
</span> |
| 11993 |
|
| 11994 |
<p class=MsoBodyText><![if !supportEmptyParas]> <![endif]><span |
| 11995 |
style='mso-bookmark:_Toc407078272'><span style='font-size:12.0pt;mso-bidi-font-size: |
| 11996 |
10.0pt;font-family:Palatino'><o:p></o:p></span></span></p> |
| 11997 |
|
| 11998 |
<div style='border:none;border-bottom:solid windowtext .75pt;padding:0pt 0pt 3.0pt 0pt'> |
| 11999 |
|
| 12000 |
<h1><span style='mso-bookmark:_Toc407078272'><a name="_Toc407090425"></a><a |
| 12001 |
name="_Toc407090628"></a><a name="_Toc407169658"><span style='mso-bookmark: |
| 12002 |
_Toc407090628'><span style='mso-bookmark:_Toc407090425'>References</span></span></a></span></h1> |
| 12003 |
|
| 12004 |
</div> |
| 12005 |
|
| 12006 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12007 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12008 |
|
| 12009 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12010 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12011 |
|
| 12012 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12013 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Adcroft, A. (1995) Numerical |
| 12014 |
algorithms for use in a dynamical model of the ocean. Ph.D. thesis, Imperial College, |
| 12015 |
London.<o:p></o:p></span></p> |
| 12016 |
|
| 12017 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12018 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12019 |
|
| 12020 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12021 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Adcroft, A., Hill, C., and |
| 12022 |
Marshall, J. (1997) Representation of topography by shaved cells in a height |
| 12023 |
coordinate ocean model. <i style='mso-bidi-font-style:normal'>Mon. Weather Rev.</i>, |
| 12024 |
<b style='mso-bidi-font-weight:normal'>125</b>, 2293-2315.<o:p></o:p></span></p> |
| 12025 |
|
| 12026 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12027 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12028 |
|
| 12029 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12030 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Arakawa, A., and Lamb, V. |
| 12031 |
(1977) Computational design of the basic dynamical processes of the UCLA |
| 12032 |
General Circulation Model. <i style='mso-bidi-font-style:normal'>Methods |
| 12033 |
Comput. Phys.</i>, <b style='mso-bidi-font-weight:normal'>17</b>, 174-267.<o:p></o:p></span></p> |
| 12034 |
|
| 12035 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12036 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12037 |
|
| 12038 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12039 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Bryan, K. (1969) A numerical |
| 12040 |
model for the study of the circulation of the world ocean. <i style='mso-bidi-font-style: |
| 12041 |
normal'>J. Comput. Phys.</i>, <b style='mso-bidi-font-weight:normal'>4</b>, |
| 12042 |
347-376.<o:p></o:p></span></p> |
| 12043 |
|
| 12044 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12045 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12046 |
|
| 12047 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12048 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Dukowicz, J. K., Smith, R. D., |
| 12049 |
and Malone, R. C. (1993) A reformulation and implementation of the |
| 12050 |
Bryan-Cox-Semtner ocean model on the connection machine. <i style='mso-bidi-font-style: |
| 12051 |
normal'>J. Atmos. Oceanic Technol.</i>, <b style='mso-bidi-font-weight:normal'>10</b>, |
| 12052 |
195-208.<o:p></o:p></span></p> |
| 12053 |
|
| 12054 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12055 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12056 |
|
| 12057 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12058 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Dukowicz, J. K. (1995) <b |
| 12059 |
style='mso-bidi-font-weight:normal'>I don't have this one!</b><o:p></o:p></span></p> |
| 12060 |
|
| 12061 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12062 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12063 |
|
| 12064 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12065 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Harlow, F. H., and Welch, J. E. |
| 12066 |
(1965) Numerical calculation of time-dependent viscous incompressible flow of |
| 12067 |
fluid with free surface. <i style='mso-bidi-font-style:normal'>Phys. Fluids</i>, |
| 12068 |
<b style='mso-bidi-font-weight:normal'>8</b>, 2182-2189.<o:p></o:p></span></p> |
| 12069 |
|
| 12070 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12071 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12072 |
|
| 12073 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12074 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Holland, W. R., and Lin, L. B. |
| 12075 |
(1975) On the generation of mesoscale eddies and their contribution to the |
| 12076 |
oceanic general circulation I. A preliminary numerical experiment. <i |
| 12077 |
style='mso-bidi-font-style:normal'>J. Phys. Oceanogr.</i>, <b style='mso-bidi-font-weight: |
| 12078 |
normal'>5</b>, 642-657.<o:p></o:p></span></p> |
| 12079 |
|
| 12080 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12081 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12082 |
|
| 12083 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12084 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Jones, H., and Marshall, J. |
| 12085 |
(1993) Convection with rotation in a neutral ocean: a study of open-ocean deep |
| 12086 |
convection. <i style='mso-bidi-font-style:normal'>J. Phys. Oceanogr.</i>, <b |
| 12087 |
style='mso-bidi-font-weight:normal'>23</b>, 1009-1039.<o:p></o:p></span></p> |
| 12088 |
|
| 12089 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12090 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12091 |
|
| 12092 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12093 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Marshall, J., Hill, C., |
| 12094 |
Perelman, L., and Adcroft, A. (1997a) Hydrostatic, quasi-hydrostatic, and |
| 12095 |
nonhydrostatic ocean modeling. <i style='mso-bidi-font-style:normal'>J. |
| 12096 |
Geophys. Res.</i>, <b style='mso-bidi-font-weight:normal'>102</b>, 5733-5752.<o:p></o:p></span></p> |
| 12097 |
|
| 12098 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12099 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12100 |
|
| 12101 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12102 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Marshall, J., Adcroft, A., |
| 12103 |
Hill, C., Perelman, L., and Heisey, C. (1997b) A finite volume, incompressible |
| 12104 |
Navier Stokes model for studies of the ocean on parallel computers. <i |
| 12105 |
style='mso-bidi-font-style:normal'>J. Geophys. Res.</i>, <b style='mso-bidi-font-weight: |
| 12106 |
normal'>102</b>, 5753-5766.<o:p></o:p></span></p> |
| 12107 |
|
| 12108 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12109 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12110 |
|
| 12111 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12112 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Potter, D. (1976) <i |
| 12113 |
style='mso-bidi-font-style:normal'>Computational Physics</i>, John Wiley, New |
| 12114 |
York.<o:p></o:p></span></p> |
| 12115 |
|
| 12116 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12117 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12118 |
|
| 12119 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12120 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Press, W. H., Flannery, B. P., |
| 12121 |
Teukolsky, S. A., and Vettering, W. T. (1986) <i style='mso-bidi-font-style: |
| 12122 |
normal'>Numerical Recipes</i>, Cambridge University Press, New York.<o:p></o:p></span></p> |
| 12123 |
|
| 12124 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12125 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12126 |
|
| 12127 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12128 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Visbeck, M., Marshall, J., |
| 12129 |
Haine, T., and Spall, M. (1997) Specification of eddy transfer coefficients in |
| 12130 |
coarse-resolution ocean circulation models. <i style='mso-bidi-font-style:normal'>J. |
| 12131 |
Phys. Oceanogr.</i>, <b style='mso-bidi-font-weight:normal'>27</b>, 381-402.<o:p></o:p></span></p> |
| 12132 |
|
| 12133 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12134 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12135 |
|
| 12136 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12137 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>White, A. A., and Bromley, R. |
| 12138 |
A. (1995) Dynamically consistent, quasi-hydrostatic equations for global models |
| 12139 |
with a complete representation of the Coriolis force. <i style='mso-bidi-font-style: |
| 12140 |
normal'>Q. J. R. Meteorol. Soc.</i>, <b style='mso-bidi-font-weight:normal'>121</b>, |
| 12141 |
399-418.<o:p></o:p></span></p> |
| 12142 |
|
| 12143 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12144 |
mso-bidi-font-size:10.0pt;font-family:Palatino'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p> |
| 12145 |
|
| 12146 |
<p class=MsoNormal style='text-align:justify'><span style='font-size:12.0pt; |
| 12147 |
mso-bidi-font-size:10.0pt;font-family:Palatino'>Williams, G. P. (1969) |
| 12148 |
Numerical integrations of the three-dimensional Navier-Stokes equations for |
| 12149 |
incompressible flow. <i style='mso-bidi-font-style:normal'>J. Fluid Mech.</i>, <b |
| 12150 |
style='mso-bidi-font-weight:normal'>37</b>, 727-750.</span></p> |
| 12151 |
|
| 12152 |
</div> |
| 12153 |
|
| 12154 |
<span style='font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family: |
| 12155 |
"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US; |
| 12156 |
mso-bidi-language:AR-SA'><br clear=all style='page-break-before:always; |
| 12157 |
mso-break-type:section-break'> |
| 12158 |
</span> |
| 12159 |
|
| 12160 |
<div class=Section7> |
| 12161 |
|
| 12162 |
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p> |
| 12163 |
|
| 12164 |
</div> |
| 12165 |
|
| 12166 |
<div style='mso-element:footnote-list'><![if !supportFootnotes]><br clear=all> |
| 12167 |
|
| 12168 |
<hr align=left size=1 width="33%"> |
| 12169 |
|
| 12170 |
<![endif]> |
| 12171 |
|
| 12172 |
<div style='mso-element:footnote' id=ftn1> |
| 12173 |
|
| 12174 |
<p class=MsoFootnoteText style='text-align:justify'><a style='mso-footnote-id: |
| 12175 |
ftn1' href="#_ftnref1" name="_ftn1" title=""><span class=MsoFootnoteReference><span |
| 12176 |
style='mso-special-character:footnote'><![if !supportFootnotes]>[1]<![endif]></span></span></a> |
| 12177 |
<span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Palatino'>In |
| 12178 |
the hydrostatic primitive equations (<b style='mso-bidi-font-weight:normal'>HPE</b>) |
| 12179 |
all underlined terms in (1.3.2), (1.3.3) and (1.3.4) are omitted; the |
| 12180 |
singly-underlined terms are included the quasi-hydrostatic model (<b |
| 12181 |
style='mso-bidi-font-weight:normal'>QH</b>). The fully non-hydrostatic model (<b |
| 12182 |
style='mso-bidi-font-weight:normal'>NH</b>) includes all terms</span>.</p> |
| 12183 |
|
| 12184 |
</div> |
| 12185 |
|
| 12186 |
<div style='mso-element:footnote' id=ftn2> |
| 12187 |
|
| 12188 |
<p class=MsoFootnoteText style='text-align:justify'><a style='mso-footnote-id: |
| 12189 |
ftn2' href="#_ftnref2" name="_ftn2" title=""><span class=MsoFootnoteReference><span |
| 12190 |
style='mso-special-character:footnote'><![if !supportFootnotes]>[2]<![endif]></span></span></a>Since |
| 12191 |
solid boundaries always coincide with the faces of zones, the imposition of |
| 12192 |
boundary conditions in the formulation of the Elliptic problem presents no |
| 12193 |
problem even in the case of shaved cells; the non-divergence condition (2.2.1) |
| 12194 |
is applied to the zone adjacent to the wall noting that the component of |
| 12195 |
velocity normal to the solid boundary is identically zero.<span |
| 12196 |
style="mso-spacerun: yes"> </span>It is readily seen that the inhomogeneous |
| 12197 |
Neumann boundary condition on pressure at the wall of the continuous problem |
| 12198 |
never explicitly enters in to the discrete problem.<span style="mso-spacerun: |
| 12199 |
yes"> </span>Rather, information about the boundary is contained in the |
| 12200 |
source function in the zone adjacent to the boundary in a manner which is |
| 12201 |
exactly analogous to the continuous problem; there inhomogeneous conditions are |
| 12202 |
replaced with homogeneous conditions together with an interior <span |
| 12203 |
style='font-family:Symbol;mso-ascii-font-family:"Tms Rmn";mso-hansi-font-family: |
| 12204 |
"Tms Rmn";mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 12205 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>d</span></span> |
| 12206 |
function sheet of source adjacent to the boundary - see the discussion in |
| 12207 |
section 3.2 of Marshall et al. 1997a.<span style="mso-spacerun: yes"> |
| 12208 |
</span>Note also that Eqs.(2.3.1) and (2.3.2) above are discrete forms of the |
| 12209 |
continuous equations Eqs.(1.5.9) and (1.5.10) of section 1.5.</p> |
| 12210 |
|
| 12211 |
</div> |
| 12212 |
|
| 12213 |
<div style='mso-element:footnote' id=ftn3> |
| 12214 |
|
| 12215 |
<p class=MsoFootnoteText><a style='mso-footnote-id:ftn3' href="#_ftnref3" |
| 12216 |
name="_ftn3" title=""><span class=MsoFootnoteReference><span style='mso-special-character: |
| 12217 |
footnote'><![if !supportFootnotes]>[3]<![endif]></span></span></a> <sub><!--[if gte vml 1]><v:shapetype |
| 12218 |
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" |
| 12219 |
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> |
| 12220 |
<v:stroke joinstyle="miter"/> |
| 12221 |
<v:formulas> |
| 12222 |
<v:f eqn="if lineDrawn pixelLineWidth 0"/> |
| 12223 |
<v:f eqn="sum @0 1 0"/> |
| 12224 |
<v:f eqn="sum 0 0 @1"/> |
| 12225 |
<v:f eqn="prod @2 1 2"/> |
| 12226 |
<v:f eqn="prod @3 21600 pixelWidth"/> |
| 12227 |
<v:f eqn="prod @3 21600 pixelHeight"/> |
| 12228 |
<v:f eqn="sum @0 0 1"/> |
| 12229 |
<v:f eqn="prod @6 1 2"/> |
| 12230 |
<v:f eqn="prod @7 21600 pixelWidth"/> |
| 12231 |
<v:f eqn="sum @8 21600 0"/> |
| 12232 |
<v:f eqn="prod @7 21600 pixelHeight"/> |
| 12233 |
<v:f eqn="sum @10 21600 0"/> |
| 12234 |
</v:formulas> |
| 12235 |
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> |
| 12236 |
<o:lock v:ext="edit" aspectratio="t"/> |
| 12237 |
</v:shapetype><v:shape id="_x0000_i1838" type="#_x0000_t75" style='width:21pt; |
| 12238 |
height:17.25pt' o:ole=""> |
| 12239 |
<v:imagedata src="./fulldoc_files/image400.wmz" o:title=""/> |
| 12240 |
</v:shape><![endif]--><![if !vml]><img width=28 height=23 |
| 12241 |
src="./fulldoc_files/image530.gif" v:shapes="_x0000_i1838"><![endif]></sub><!--[if gte mso 9]><xml> |
| 12242 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1838" |
| 12243 |
DrawAspect="Content" ObjectID="_1051901479"> |
| 12244 |
</o:OLEObject> |
| 12245 |
</xml><![endif]-->has five diagonals corresponding to the coupling of the |
| 12246 |
central point with surrounding points along the four arms of the horizontal <span |
| 12247 |
style='font-family:Symbol;mso-ascii-font-family:"Tms Rmn";mso-hansi-font-family: |
| 12248 |
"Tms Rmn";mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 12249 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>Ñ</span></span><sup>2</sup> |
| 12250 |
operator.</p> |
| 12251 |
|
| 12252 |
</div> |
| 12253 |
|
| 12254 |
<div style='mso-element:footnote' id=ftn4> |
| 12255 |
|
| 12256 |
<p class=MsoFootnoteText style='text-align:justify'><a style='mso-footnote-id: |
| 12257 |
ftn4' href="#_ftnref4" name="_ftn4" title=""><span class=MsoFootnoteReference><span |
| 12258 |
style='mso-special-character:footnote'><![if !supportFootnotes]>[4]<![endif]></span></span></a> |
| 12259 |
If the ocean column is made up of cells stacked up on top of one-another which |
| 12260 |
do not have equal heights <i style='mso-bidi-font-style:normal'><span |
| 12261 |
style='font-family:Symbol;mso-ascii-font-family:"Tms Rmn";mso-hansi-font-family: |
| 12262 |
"Tms Rmn";mso-char-type:symbol;mso-symbol-font-family:Symbol'><span |
| 12263 |
style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>D</span></span>z</i>, |
| 12264 |
then <b style='mso-bidi-font-weight:normal'>A</b> is not symmetric, but it can |
| 12265 |
easily be symmetrized by pre-multiplying it with a symmetrization matrix <b |
| 12266 |
style='mso-bidi-font-weight:normal'>W</b>, where</p> |
| 12267 |
|
| 12268 |
<p class=MsoFootnoteText align=center style='text-align:center'><sub><!--[if gte vml 1]><v:shape |
| 12269 |
id="_x0000_i1839" type="#_x0000_t75" style='width:134.25pt;height:1in' o:ole=""> |
| 12270 |
<v:imagedata src="./fulldoc_files/image531.wmz" o:title=""/> |
| 12271 |
</v:shape><![endif]--><![if !vml]><img width=179 height=96 |
| 12272 |
src="./fulldoc_files/image532.gif" v:shapes="_x0000_i1839"><![endif]></sub><!--[if gte mso 9]><xml> |
| 12273 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1839" |
| 12274 |
DrawAspect="Content" ObjectID="_1051901481"> |
| 12275 |
</o:OLEObject> |
| 12276 |
</xml><![endif]--></p> |
| 12277 |
|
| 12278 |
</div> |
| 12279 |
|
| 12280 |
<div style='mso-element:footnote' id=ftn5> |
| 12281 |
|
| 12282 |
<p class=MsoFootnoteText><a style='mso-footnote-id:ftn5' href="#_ftnref5" |
| 12283 |
name="_ftn5" title=""><span class=MsoFootnoteReference><span style='mso-special-character: |
| 12284 |
footnote'><![if !supportFootnotes]>[5]<![endif]></span></span></a> The name |
| 12285 |
conjugate gradient stems from the property that <sub><!--[if gte vml 1]><v:shape |
| 12286 |
id="_x0000_i1228" type="#_x0000_t75" style='width:75pt;height:21.75pt' o:ole=""> |
| 12287 |
<v:imagedata src="./fulldoc_files/image533.wmz" o:title=""/> |
| 12288 |
</v:shape><![endif]--><![if !vml]><img width=100 height=29 |
| 12289 |
src="./fulldoc_files/image534.gif" v:shapes="_x0000_i1228"><![endif]></sub><!--[if gte mso 9]><xml> |
| 12290 |
<o:OLEObject Type="Embed" ProgID="Equation.2" ShapeID="_x0000_i1228" |
| 12291 |
DrawAspect="Content" ObjectID="_1051901482"> |
| 12292 |
</o:OLEObject> |
| 12293 |
</xml><![endif]-->; the search directions on consecutive iterations are |
| 12294 |
conjugate to one another.</p> |
| 12295 |
|
| 12296 |
</div> |
| 12297 |
|
| 12298 |
</div> |
| 12299 |
|
| 12300 |
</body> |
| 12301 |
|
| 12302 |
</html> |
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