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C $Header: /u/gcmpack/models/MITgcmUV/model/src/calc_mom_rhs.F,v 1.50 2001/05/29 14:01:36 adcroft Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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|
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#define COSINEMETH_III |
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#undef ISOTROPIC_COS_SCALING |
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|
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C /==========================================================\ |
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C | S/R CALC_MOM_RHS | |
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C | o Form the right hand-side of the momentum equation. | |
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C |==========================================================| |
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C | Terms are evaluated one layer at a time working from | |
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C | the bottom to the top. The vertically integrated | |
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C | barotropic flow tendency term is evluated by summing the | |
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C | tendencies. | |
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C | Notes: | |
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C | We have not sorted out an entirely satisfactory formula | |
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C | for the diffusion equation bc with lopping. The present | |
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C | form produces a diffusive flux that does not scale with | |
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C | open-area. Need to do something to solidfy this and to | |
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C | deal "properly" with thin walls. | |
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C \==========================================================/ |
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SUBROUTINE CALC_MOM_RHS( |
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I bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown, |
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I phiHyd,KappaRU,KappaRV, |
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U fVerU, fVerV, |
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I myCurrentTime, myThid) |
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|
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IMPLICIT NONE |
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|
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C == Global variables == |
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#include "SIZE.h" |
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#include "DYNVARS.h" |
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#include "FFIELDS.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "SURFACE.h" |
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|
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C == Routine arguments == |
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C fZon - Work array for flux of momentum in the east-west |
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C direction at the west face of a cell. |
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C fMer - Work array for flux of momentum in the north-south |
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C direction at the south face of a cell. |
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C fVerU - Flux of momentum in the vertical |
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C fVerV direction out of the upper face of a cell K |
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C ( flux into the cell above ). |
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C phiHyd - Hydrostatic Potential (pressure/rho) |
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C bi, bj, iMin, iMax, jMin, jMax - Range of points for which calculation |
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C results will be set. |
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C kUp, kDown - Index for upper and lower layers. |
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C myThid - Instance number for this innvocation of CALC_MOM_RHS |
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_RL phiHyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fVerV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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INTEGER kUp,kDown |
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INTEGER myThid |
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_RL myCurrentTime |
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INTEGER bi,bj,iMin,iMax,jMin,jMax,jG |
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|
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C == Local variables == |
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C ab15, ab05 - Weights for Adams-Bashforth time stepping scheme. |
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C i,j,k - Loop counters |
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C wMaskOverride - Land sea flag override for top layer. |
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C afFacMom - Tracer parameters for turning terms |
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C vfFacMom on and off. |
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C pfFacMom afFacMom - Advective terms |
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C cfFacMom vfFacMom - Eddy viscosity terms |
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C mTFacMom pfFacMom - Pressure terms |
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C cfFacMom - Coriolis terms |
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C foFacMom - Forcing |
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C mTFacMom - Metric term |
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C vF - Temporary holding viscous term (Laplacian) |
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C v4F - Temporary holding viscous term (Biharmonic) |
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C cF - Temporary holding coriolis term. |
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C mT - Temporary holding metric terms(s). |
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C pF - Temporary holding pressure|potential gradient terms. |
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C uDudxFac, AhDudxFac, etc ... individual term tracer parameters |
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_RL aF (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vF (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL v4F(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL cF (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL mT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL pF (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fMer (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS xA(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS yA(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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C I,J,K - Loop counters |
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INTEGER i,j,k |
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C rVelMaskOverride - Factor for imposing special surface boundary conditions |
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C ( set according to free-surface condition ). |
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C hFacROpen - Lopped cell factos used tohold fraction of open |
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C hFacRClosed and closed cell wall. |
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_RL rVelMaskOverride |
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_RS hFacZOpen |
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_RS hFacZClosedN |
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_RS hFacZClosedS |
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_RS hFacZClosedE |
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_RS hFacZClosedW |
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C xxxFac - On-off tracer parameters used for switching terms off. |
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_RL uDudxFac |
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_RL AhDudxFac |
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_RL A4DuxxdxFac |
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_RL vDudyFac |
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_RL AhDudyFac |
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_RL A4DuyydyFac |
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_RL rVelDudrFac |
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_RL ArDudrFac |
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_RL fuFac |
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_RL phxFac |
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_RL mtFacU |
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_RL uDvdxFac |
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_RL AhDvdxFac |
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_RL A4DvxxdxFac |
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_RL vDvdyFac |
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_RL AhDvdyFac |
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_RL A4DvyydyFac |
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_RL rVelDvdrFac |
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_RL ArDvdrFac |
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_RL fvFac |
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_RL phyFac |
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_RL vForcFac |
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_RL mtFacV |
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C ab05, ab15 - Adams-Bashforth time-stepping weights. |
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_RL ab05, ab15 |
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INTEGER km1,kp1 |
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_RL maskDown,wVelBottomOverride,rdrckp1 |
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LOGICAL bottomDragTerms |
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_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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|
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km1=MAX(1,k-1) |
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kp1=MIN(Nr,k+1) |
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rVelMaskOverride=afFacMom |
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IF ( k .EQ. 1 ) rVelMaskOverride=freeSurfFac*afFacMom |
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wVelBottomOverride=1. |
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IF (k.EQ.Nr) wVelBottomOverride=0. |
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|
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C Initialise intermediate terms |
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DO J=1-OLy,sNy+OLy |
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DO I=1-OLx,sNx+OLx |
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aF(i,j) = 0. |
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vF(i,j) = 0. |
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v4F(i,j) = 0. |
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cF(i,j) = 0. |
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mT(i,j) = 0. |
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pF(i,j) = 0. |
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fZon(i,j) = 0. |
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fMer(i,j) = 0. |
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ENDDO |
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ENDDO |
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DO J=1-OLy,sNy+OLy-1 |
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DO I=1-OLx,sNx+OLx-1 |
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KE(i,j) = 0.25*( |
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& uVel( i , j ,k,bi,bj)*uVel( i , j ,k,bi,bj) |
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& +uVel(i+1, j ,k,bi,bj)*uVel(i+1, j ,k,bi,bj) |
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& +vVel( i , j ,k,bi,bj)*vVel( i , j ,k,bi,bj) |
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& +vVel( i ,j+1,k,bi,bj)*vVel( i ,j+1,k,bi,bj) ) |
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ENDDO |
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ENDDO |
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C-- Term by term tracer parmeters |
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C o U momentum equation |
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uDudxFac = afFacMom*1. |
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AhDudxFac = vfFacMom*1. |
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A4DuxxdxFac = vfFacMom*1. |
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vDudyFac = afFacMom*1. |
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AhDudyFac = vfFacMom*1. |
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A4DuyydyFac = vfFacMom*1. |
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rVelDudrFac = afFacMom*1. |
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ArDudrFac = vfFacMom*1. |
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mTFacU = mtFacMom*1. |
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fuFac = cfFacMom*1. |
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phxFac = pfFacMom*1. |
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C o V momentum equation |
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uDvdxFac = afFacMom*1. |
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AhDvdxFac = vfFacMom*1. |
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A4DvxxdxFac = vfFacMom*1. |
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vDvdyFac = afFacMom*1. |
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AhDvdyFac = vfFacMom*1. |
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A4DvyydyFac = vfFacMom*1. |
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rVelDvdrFac = afFacMom*1. |
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ArDvdrFac = vfFacMom*1. |
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mTFacV = mtFacMom*1. |
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fvFac = cfFacMom*1. |
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phyFac = pfFacMom*1. |
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vForcFac = foFacMom*1. |
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|
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IF (no_slip_bottom) THEN |
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bottomDragTerms=.TRUE. |
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ELSE |
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bottomDragTerms=.FALSE. |
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ENDIF |
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|
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C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP |
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IF (staggerTimeStep) THEN |
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phxFac = 0. |
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phyFac = 0. |
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ENDIF |
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|
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C-- Adams-Bashforth weighting factors |
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ab15 = 1.5 _d 0 + abEps |
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ab05 = -0.5 _d 0 - abEps |
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|
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C-- Calculate open water fraction at vorticity points |
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DO i=1-Olx,sNx+Olx |
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hFacZ(i,1-Oly)=0. |
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ENDDO |
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DO j=2-Oly,sNy+Oly |
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hFacZ(1-Olx,j)=0. |
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DO i=2-Olx,sNx+Olx |
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hFacZOpen=min(_hFacW(i,j,k,bi,bj), |
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& _hFacW(i,j-1,k,bi,bj)) |
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hFacZOpen=min(_hFacS(i,j,k,bi,bj),hFacZOpen) |
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hFacZOpen=min(_hFacS(i-1,j,k,bi,bj),hFacZOpen) |
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hFacZ(i,j)=hFacZOpen |
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ENDDO |
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ENDDO |
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|
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C---- Calculate common quantities used in both U and V equations |
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C Calculate tracer cell face open areas |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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xA(i,j) = _dyG(i,j,bi,bj) |
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& *drF(k)*_hFacW(i,j,k,bi,bj) |
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yA(i,j) = _dxG(i,j,bi,bj) |
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& *drF(k)*_hFacS(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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C Calculate velocity field "volume transports" through tracer cell faces. |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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uTrans(i,j) = uVel(i,j,k,bi,bj)*xA(i,j) |
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vTrans(i,j) = vVel(i,j,k,bi,bj)*yA(i,j) |
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ENDDO |
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ENDDO |
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|
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C---- Zonal momentum equation starts here |
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|
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#ifdef INCLUDE_BH_MOMENTUM_DIFFUSION_CODE |
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C-- del^2 U (for use in del^4 U) |
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C Zonal flux d/dx U |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx-1 |
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fZon(i,j) = drF(k)*_hFacC(i,j,k,bi,bj) |
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& *_dyF(i,j,bi,bj) |
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& *_recip_dxF(i,j,bi,bj) |
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& *(uVel(i+1,j,k,bi,bj)-uVel(i,j,k,bi,bj)) |
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ENDDO |
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ENDDO |
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C Meridional flux d/dy U |
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DO j=1-Oly+1,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fMer(i,j) = drF(k)*hFacZ(i,j) |
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& *_dxV(i,j,bi,bj) |
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& *_recip_dyU(i,j,bi,bj) |
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& *(uVel(i,j,k,bi,bj)-uVel(i,j-1,k,bi,bj)) |
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ENDDO |
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ENDDO |
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C del^2 U |
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DO j=0,sNy+1 |
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DO i=0,sNx+2 |
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v4F(i,j) = recip_drF(k)*_recip_hFacW(i,j,k,bi,bj) |
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& *recip_rAw(i,j,bi,bj) |
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& *( (fZon(i,j ) - fZon(i-1,j)) |
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#ifdef COSINEMETH_III |
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& *sqcosFacU(J,bi,bj) |
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#endif |
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& +fMer(i,j+1) - fMer(i ,j) |
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& )*_maskW(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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IF (no_slip_sides) THEN |
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C-- No-slip BCs impose a drag at walls... |
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DO j=0,sNy+1 |
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DO i=0,sNx+2 |
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hFacZClosedS = _hFacW(i,j,k,bi,bj) - hFacZ(i,j) |
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hFacZClosedN = _hFacW(i,j,k,bi,bj) - hFacZ(i,j+1) |
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v4F(i,j) = v4F(i,j) |
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& - _recip_hFacW(i,j,k,bi,bj)*recip_drF(k) |
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& *recip_rAw(i,j,bi,bj) |
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& *( hFacZClosedS*dxV(i, j ,bi,bj) |
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& *_recip_dyU(i, j ,bi,bj) |
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& +hFacZClosedN*dxV(i,j+1,bi,bj) |
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& *_recip_dyU(i,j+1,bi,bj) |
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& )*drF(k)*2.*uVel(i,j,k,bi,bj) |
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& *_maskW(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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#endif /* INCLUDE_BH_MOMENTUM_DIFFUSION_CODE */ |
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|
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C--- Calculate mean and eddy fluxes between cells for zonal flow. |
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C-- Zonal flux (fZon is at east face of "u" cell) |
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#define _XAatP( i,j,k,bi,bj) ( XA(i,j)+XA(i+1,j) )* 0.5 _d 0 |
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#define _YAatUBY( i,j,k,bi,bj) ( YA(i,j)+YA(i-1,j) )* 0.5 _d 0 |
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#define _RAatU1( i,j,k,bi,bj) ( rA(i,j,bi,bj)*maskC(i,j) |
| 303 |
#define _RAatU2( i,j,k,bi,bj) + rA(i-1,j,bi,bj) |
| 304 |
#define _RAatU3( i,j,k,bi,bj) *maskC(i-1,j) ) * 0.5 _d 0 |
| 305 |
#define _RAatU_Bot(i,j,k,bi,bj) ( rA(i,j,bi,bj) + rA(i-1,j,bi,bj) ) * 0.5 _d 0 |
| 306 |
C o Mean flow component of zonal flux |
| 307 |
#ifdef INCLUDE_MOMENTUM_ADVECTION_CODE |
| 308 |
DO j=jMin,jMax |
| 309 |
DO i=iMin,iMax |
| 310 |
af(i,j) = |
| 311 |
& (uTrans(i,j)+uTrans(i+1,j) ) |
| 312 |
& *(uVel(i,j,k,bi,bj)+uVel(i+1,j,k,bi,bj))*0.25 _d 0 |
| 313 |
ENDDO |
| 314 |
ENDDO |
| 315 |
#endif /* INCLUDE_MOMENTUM_ADVECTION_CODE */ |
| 316 |
C o Eddy component of zonal flux |
| 317 |
C - Laplacian and bi-harmonic terms |
| 318 |
DO j=jMin,jMax |
| 319 |
DO i=iMin,iMax |
| 320 |
vF(i,j) = |
| 321 |
#ifdef OLD_UV_GEOMETRY |
| 322 |
& ( XA(i,j)+XA(i+1,j) )* 0.5 _d 0 |
| 323 |
#else |
| 324 |
& _dyF(i,j,bi,bj)*drF(k)*_hFacC(i,j,k,bi,bj) |
| 325 |
#endif /* OLD_UV_GEOMETRY */ |
| 326 |
& *( |
| 327 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 328 |
& -viscAh*(uVel(i+1,j,k,bi,bj)-uVel(i,j,k,bi,bj)) |
| 329 |
& *cosFacU(J,bi,bj) |
| 330 |
#else |
| 331 |
& 0. |
| 332 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 333 |
#ifdef INCLUDE_BH_MOMENTUM_DIFFUSION_CODE |
| 334 |
& +viscA4*( v4F(i+1,j) -v4F(i,j) ) |
| 335 |
#ifdef COSINEMETH_III |
| 336 |
& *sqcosFacU(J,bi,bj) |
| 337 |
#else |
| 338 |
& *cosFacU(J,bi,bj) |
| 339 |
#endif |
| 340 |
#endif /* INCLUDE_BH_MOMENTUM_DIFFUSION_CODE */ |
| 341 |
& )*_recip_dxF(i,j,bi,bj) |
| 342 |
|
| 343 |
ENDDO |
| 344 |
ENDDO |
| 345 |
DO j=jMin,jMax |
| 346 |
DO i=iMin,iMax |
| 347 |
fZon(i,j) = 0. |
| 348 |
& _ADM( + uDudxFac * aF (i,j) ) |
| 349 |
& + AhDudxFac * vF (i,j) |
| 350 |
ENDDO |
| 351 |
ENDDO |
| 352 |
|
| 353 |
C-- Meridional flux (fMer is at south face of "u" cell) |
| 354 |
#ifdef INCLUDE_MOMENTUM_ADVECTION_CODE |
| 355 |
C o Mean flow component of meridional flux |
| 356 |
DO j=jMin,jMax |
| 357 |
DO i=iMin,iMax |
| 358 |
af(i,j) = |
| 359 |
& (vTrans(i,j)+vTrans(i-1,j)) |
| 360 |
& *(uVel(i,j,k,bi,bj)+uVel(i,j-1,k,bi,bj))*0.25 _d 0 |
| 361 |
#ifdef OLD_ADV_BCS |
| 362 |
& *_maskW(i,j,k,bi,bj) |
| 363 |
& *_maskW(i,j-1,k,bi,bj) |
| 364 |
#endif /* OLD_ADV_BCS */ |
| 365 |
C Note!!!! The line "*maskW(i,j,k,bi,bj)*maskW(i,j-1,k,bi,bj)" is |
| 366 |
C Note!!!! boundary condition in the standard v010 CM5 code. The |
| 367 |
C Note!!!! FV paper used a different bc in which this line is |
| 368 |
C Note!!!! omitted. |
| 369 |
ENDDO |
| 370 |
ENDDO |
| 371 |
#endif /* INCLUDE_MOMENTUM_ADVECTION_CODE */ |
| 372 |
C Eddy component of meridional flux |
| 373 |
C o Laplacian and bi-harmonic term |
| 374 |
DO j=jMin,jMax |
| 375 |
DO i=iMin,iMax |
| 376 |
vF(i,j) = _dxV(i,j,bi,bj)*drF(k)*hFacZ(i,j) |
| 377 |
& *( |
| 378 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 379 |
#ifdef ISOTROPIC_COS_SCALING |
| 380 |
& -viscAh*(uVel(i,j,k,bi,bj)-uVel(i,j-1,k,bi,bj)) |
| 381 |
& *cosFacV(J,bi,bj) |
| 382 |
#else |
| 383 |
& -viscAh*(uVel(i,j,k,bi,bj)-uVel(i,j-1,k,bi,bj)) |
| 384 |
#endif |
| 385 |
#else |
| 386 |
& 0. |
| 387 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 388 |
#ifdef INCLUDE_BH_MOMENTUM_DIFFUSION_CODE |
| 389 |
#ifdef ISOTROPIC_COS_SCALING |
| 390 |
& +viscA4*( v4F(i,j) -v4F(i,j-1) ) |
| 391 |
& *cosFacV(J,bi,bj) |
| 392 |
#else |
| 393 |
& +viscA4*( v4F(i,j) -v4F(i,j-1) ) |
| 394 |
#endif |
| 395 |
#endif /* INCLUDE_BH_MOMENTUM_DIFFUSION_CODE */ |
| 396 |
& ) |
| 397 |
& *_recip_dyU(i,j,bi,bj) |
| 398 |
ENDDO |
| 399 |
ENDDO |
| 400 |
DO j=jMin,jMax |
| 401 |
DO i=iMin,iMax |
| 402 |
fMer(i,j) = 0. |
| 403 |
& _ADM( + vDudyFac * aF (i,j) ) |
| 404 |
& + AhDudyFac * vF (i,j) |
| 405 |
ENDDO |
| 406 |
ENDDO |
| 407 |
C-- Vertical flux (fVer is at upper face of "u" cell) |
| 408 |
#ifdef INCLUDE_MOMENTUM_ADVECTION_CODE |
| 409 |
C-- Free surface correction temr |
| 410 |
IF (k.EQ.1) THEN |
| 411 |
DO j=jMin,jMax |
| 412 |
DO i=iMin,iMax |
| 413 |
fVerU(i,j,kUp)=rVelMaskOverride*( |
| 414 |
& wVel( i ,j,k,bi,bj)*rA( i ,j,bi,bj) |
| 415 |
& +wVel(i-1,j,k,bi,bj)*rA(i-1,j,bi,bj) |
| 416 |
& )*0.5 |
| 417 |
& *uVel(i,j,k,bi,bj) |
| 418 |
ENDDO |
| 419 |
ENDDO |
| 420 |
ENDIF |
| 421 |
C Mean flow component of vertical flux |
| 422 |
DO j=jMin,jMax |
| 423 |
DO i=iMin,iMax |
| 424 |
af(i,j) = |
| 425 |
& wVelBottomOverride*( |
| 426 |
& wVel( i ,j,kp1,bi,bj)*rA( i ,j,bi,bj) |
| 427 |
& +wVel(i-1,j,kp1,bi,bj)*rA(i-1,j,bi,bj) |
| 428 |
& ) |
| 429 |
& *( uVel(i,j,kp1,bi,bj)+uVel(i,j,k,bi,bj) ) |
| 430 |
& *0.25 _d 0 |
| 431 |
#ifdef OLD_ADV_BCS |
| 432 |
& *_maskW(i,j,kp1,bi,bj) |
| 433 |
& *_maskW(i,j,k,bi,bj) |
| 434 |
#endif /* OLD_ADV_BCS */ |
| 435 |
C Note!!!! The line "*(maskW(i,j,k,bi,bj)*maskW(i,j,kM1,bi,bj))" is |
| 436 |
C Note!!!! boundary condition in the standard v010 CM5 code. The |
| 437 |
C Note!!!! FV paper used a different bc in which this line is |
| 438 |
C Note!!!! omitted. |
| 439 |
ENDDO |
| 440 |
ENDDO |
| 441 |
#endif /* INCLUDE_MOMENTUM_ADVECTION_CODE */ |
| 442 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 443 |
#ifdef OLD_UV_GEOMETRY |
| 444 |
#define _RA_AT_W (RA(i,j,bi,bj)*maskC(i,j)+RA(i-1,j,bi,bj)*maskC(i-1,j))*.5 |
| 445 |
#else |
| 446 |
#define _RA_AT_W rAw(i,j,bi,bj) |
| 447 |
#endif /* OLD_UV_GEOMETRY */ |
| 448 |
C Eddy component of vertical flux (interior component only) |
| 449 |
IF (.NOT.implicitViscosity) THEN |
| 450 |
DO j=jMin,jMax |
| 451 |
DO i=iMin,iMax |
| 452 |
vf(i,j) = |
| 453 |
& -KappaRU(i,j,kp1) |
| 454 |
& *_RA_AT_W |
| 455 |
& *( uVel(i,j,k,bi,bj)-uVel(i,j,kp1,bi,bj) |
| 456 |
& )*rkFac*recip_drC(kp1) |
| 457 |
& *_maskW(i,j,kp1,bi,bj) |
| 458 |
ENDDO |
| 459 |
ENDDO |
| 460 |
ENDIF |
| 461 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 462 |
IF (implicitViscosity) THEN |
| 463 |
DO j=jMin,jMax |
| 464 |
DO i=iMin,iMax |
| 465 |
fVerU(i,j,kDown) = 0. |
| 466 |
& _ADM( + rVelDudrFac * af(i,j) ) |
| 467 |
ENDDO |
| 468 |
ENDDO |
| 469 |
ELSE |
| 470 |
DO j=jMin,jMax |
| 471 |
DO i=iMin,iMax |
| 472 |
fVerU(i,j,kDown) = 0. |
| 473 |
& _ADM( + rVelDudrFac * af(i,j) ) |
| 474 |
& _LPM( + ArDudrFac * vf(i,j) ) |
| 475 |
ENDDO |
| 476 |
ENDDO |
| 477 |
ENDIF |
| 478 |
|
| 479 |
#ifdef INCLUDE_GRADPH_CODE |
| 480 |
C--- Hydrostatic term ( -1/rhoConst . dphi/dx ) |
| 481 |
DO j=jMin,jMax |
| 482 |
DO i=iMin,iMax |
| 483 |
pf(i,j) = - _recip_dxC(i,j,bi,bj) |
| 484 |
& *(phiHyd(i,j,k)-phiHyd(i-1,j,k)) |
| 485 |
ENDDO |
| 486 |
ENDDO |
| 487 |
#endif /* INCLUDE_GRADPH_CODE */ |
| 488 |
|
| 489 |
C-- Tendency is minus divergence of the fluxes + coriolis + pressure |
| 490 |
C-- term |
| 491 |
DO j=jMin,jMax |
| 492 |
DO i=iMin,iMax |
| 493 |
gU(i,j,k,bi,bj) = |
| 494 |
#ifdef OLD_UV_GEOM |
| 495 |
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)/ |
| 496 |
& ( 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj)) ) |
| 497 |
#else |
| 498 |
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k) |
| 499 |
& *recip_rAw(i,j,bi,bj) |
| 500 |
#endif |
| 501 |
& *(fZon(i,j ) - fZon(i-1,j) |
| 502 |
& +fMer(i,j+1) - fMer(i ,j) |
| 503 |
& +fVerU(i,j,kUp)*rkFac - fVerU(i,j,kDown)*rkFac |
| 504 |
& ) |
| 505 |
& _PHM( +phxFac * pf(i,j) ) |
| 506 |
ENDDO |
| 507 |
ENDDO |
| 508 |
|
| 509 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 510 |
C-- No-slip and drag BCs appear as body forces in cell abutting topography |
| 511 |
IF (no_slip_sides) THEN |
| 512 |
C- No-slip BCs impose a drag at walls... |
| 513 |
DO j=jMin,jMax |
| 514 |
DO i=iMin,iMax |
| 515 |
hFacZClosedS = _hFacW(i,j,k,bi,bj) - hFacZ(i,j) |
| 516 |
hFacZClosedN = _hFacW(i,j,k,bi,bj) - hFacZ(i,j+1) |
| 517 |
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) |
| 518 |
& -_recip_hFacW(i,j,k,bi,bj) |
| 519 |
& *recip_drF(k)*recip_rAw(i,j,bi,bj) |
| 520 |
& *( hFacZClosedS*_dxV(i, j ,bi,bj) |
| 521 |
& *_recip_dyU(i, j ,bi,bj) |
| 522 |
& +hFacZClosedN*_dxV(i,j+1,bi,bj) |
| 523 |
& *_recip_dyU(i,j+1,bi,bj) ) |
| 524 |
& *drF(k)*2.*( viscAh*uVel(i,j,k,bi,bj) |
| 525 |
#ifdef ISOTROPIC_COS_SCALING |
| 526 |
& -viscA4*v4F(i,j) ) *cosFacU(J,bi,bj) |
| 527 |
#else |
| 528 |
& -viscA4*v4F(i,j) ) |
| 529 |
#endif |
| 530 |
ENDDO |
| 531 |
ENDDO |
| 532 |
ENDIF |
| 533 |
C- No-slip BCs impose a drag at bottom |
| 534 |
IF (bottomDragTerms) THEN |
| 535 |
rdrckp1=recip_drC(kp1) |
| 536 |
IF (k.EQ.Nr) rdrckp1=recip_drF(k) |
| 537 |
DO j=jMin,jMax |
| 538 |
DO i=iMin,iMax |
| 539 |
maskDown=_maskW(i,j,kp1,bi,bj) |
| 540 |
IF (k.EQ.Nr) maskDown=0. _d 0 |
| 541 |
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) |
| 542 |
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k) |
| 543 |
& *( |
| 544 |
& 2.*KappaRU(i,j,kp1)*rkFac*rdrckp1 |
| 545 |
& + bottomDragLinear |
| 546 |
& )*(1.-maskDown)*uVel(i,j,k,bi,bj) |
| 547 |
IF (KE(i,j)+KE(i-1,j) .NE. 0.) |
| 548 |
& gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) |
| 549 |
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k) |
| 550 |
& *bottomDragQuadratic*sqrt(KE(i,j)+KE(i-1,j)) |
| 551 |
& *(1.-maskDown)*uVel(i,j,k,bi,bj) |
| 552 |
ENDDO |
| 553 |
ENDDO |
| 554 |
ENDIF |
| 555 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 556 |
|
| 557 |
#ifdef INCLUDE_MOMENTUM_FORCING_CODE |
| 558 |
C-- Forcing term |
| 559 |
CALL EXTERNAL_FORCING_U( |
| 560 |
I iMin,iMax,jMin,jMax,bi,bj,k, |
| 561 |
I myCurrentTime,myThid) |
| 562 |
#endif /* INCLUDE_MOMENTUM_FORCING_CODE */ |
| 563 |
|
| 564 |
#ifdef INCLUDE_MOMENTUM_METRIC_TERM_CODE |
| 565 |
C-- Metric terms for curvilinear grid systems |
| 566 |
IF ( usingSphericalPolarMTerms ) THEN |
| 567 |
C o Spherical polar grid metric terms |
| 568 |
DO j=jMin,jMax |
| 569 |
DO i=iMin,iMax |
| 570 |
mT(i,j) = -1.* uVel(i,j,k,bi,bj)*recip_RSphere |
| 571 |
& *0.25 _d 0*(wVelBottomOverride* |
| 572 |
& (wVel(i-1,j,kp1,bi,bj)+wVel(i,j,kp1,bi,bj)) |
| 573 |
& +wVel(i-1,j, k ,bi,bj)+wVel(i,j, k ,bi,bj) |
| 574 |
& )*rkFac*recip_horiVertRatio |
| 575 |
ENDDO |
| 576 |
ENDDO |
| 577 |
DO j=jMin,jMax |
| 578 |
DO i=iMin,iMax |
| 579 |
mT(i,j) = mT(i,j)+uVel(i,j,k,bi,bj)*recip_RSphere |
| 580 |
& *0.25 _d 0*( vVel(i,j ,k,bi,bj)+vVel(i-1,j ,k,bi,bj) |
| 581 |
& +vVel(i,j+1,k,bi,bj)+vVel(i-1,j+1,k,bi,bj) |
| 582 |
& )*_tanPhiAtU(i,j,bi,bj) |
| 583 |
ENDDO |
| 584 |
ENDDO |
| 585 |
DO j=jMin,jMax |
| 586 |
DO i=iMin,iMax |
| 587 |
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+ |
| 588 |
& mTFacU*mT(i,j) |
| 589 |
ENDDO |
| 590 |
ENDDO |
| 591 |
ENDIF |
| 592 |
#endif /* INCLUDE_MOMENTUM_METRIC_TERM_CODE */ |
| 593 |
|
| 594 |
C-- Set du/dt on boundaries to zero |
| 595 |
DO j=jMin,jMax |
| 596 |
DO i=iMin,iMax |
| 597 |
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj) |
| 598 |
ENDDO |
| 599 |
ENDDO |
| 600 |
|
| 601 |
C---- Meridional momentum equation starts here |
| 602 |
|
| 603 |
#ifdef INCLUDE_BH_MOMENTUM_DIFFUSION_CODE |
| 604 |
C-- del^2 V (for use in del^4 V) |
| 605 |
C Zonal flux d/dx V |
| 606 |
DO j=1-Oly,sNy+Oly |
| 607 |
DO i=1-Olx+1,sNx+Olx |
| 608 |
fZon(i,j) = drF(k)*hFacZ(i,j) |
| 609 |
& *_dyU(i,j,bi,bj) |
| 610 |
& *_recip_dxV(i,j,bi,bj) |
| 611 |
& *(vVel(i,j,k,bi,bj)-vVel(i-1,j,k,bi,bj)) |
| 612 |
ENDDO |
| 613 |
ENDDO |
| 614 |
C Meridional flux d/dy V |
| 615 |
DO j=1-Oly,sNy+Oly-1 |
| 616 |
DO i=1-Olx,sNx+Olx |
| 617 |
fMer(i,j) = drF(k)*_hFacC(i,j,k,bi,bj) |
| 618 |
& *_dxF(i,j,bi,bj) |
| 619 |
& *_recip_dyF(i,j,bi,bj) |
| 620 |
& *(vVel(i,j+1,k,bi,bj)-vVel(i,j,k,bi,bj)) |
| 621 |
ENDDO |
| 622 |
ENDDO |
| 623 |
C del^2 U |
| 624 |
DO j=0,sNy+2 |
| 625 |
DO i=0,sNx+1 |
| 626 |
v4F(i,j) = recip_drF(k)*_recip_hFacS(i,j,k,bi,bj) |
| 627 |
& *recip_rAs(i,j,bi,bj) |
| 628 |
& *( (fZon(i+1,j) - fZon(i, j )) |
| 629 |
#ifdef COSINEMETH_III |
| 630 |
& *sqcosFacV(J,bi,bj) |
| 631 |
#endif |
| 632 |
& +fMer( i ,j) - fMer(i,j-1) |
| 633 |
& )*_maskS(i,j,k,bi,bj) |
| 634 |
ENDDO |
| 635 |
ENDDO |
| 636 |
IF (no_slip_sides) THEN |
| 637 |
C-- No-slip BCs impose a drag at walls... |
| 638 |
DO j=0,sNy+2 |
| 639 |
DO i=0,sNx+1 |
| 640 |
hFacZClosedW = _hFacS(i,j,k,bi,bj) - hFacZ(i,j) |
| 641 |
hFacZClosedE = _hFacS(i,j,k,bi,bj) - hFacZ(i+1,j) |
| 642 |
v4F(i,j) = v4F(i,j) |
| 643 |
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
| 644 |
& *recip_rAs(i,j,bi,bj) |
| 645 |
& *( hFacZClosedW*dyU( i ,j,bi,bj) |
| 646 |
& *_recip_dxV( i ,j,bi,bj) |
| 647 |
& +hFacZClosedE*dyU(i+1,j,bi,bj) |
| 648 |
& *_recip_dxV(i+1,j,bi,bj) |
| 649 |
& )*drF(k)*2.*vVel(i,j,k,bi,bj) |
| 650 |
& *_maskS(i,j,k,bi,bj) |
| 651 |
#ifdef COSINEMETH_III |
| 652 |
& *sqcosFacV(J,bi,bj) |
| 653 |
#endif |
| 654 |
ENDDO |
| 655 |
ENDDO |
| 656 |
ENDIF |
| 657 |
#endif /* INCLUDE_BH_MOMENTUM_DIFFUSION_CODE */ |
| 658 |
|
| 659 |
C--- Calculate mean and eddy fluxes between cells for meridional |
| 660 |
C--- velocity. Zonal flux (fZon is at west face of "v" cell) |
| 661 |
#define _XAatVBX( i,j,k,bi,bj) ( XA(i,j)+XA(i,j-1) )* 0.5 _d 0 |
| 662 |
#define _YAatP( i,j,k,bi,bj) ( YA(i,j) + YA(i,j+1) ) *0.5 _d 0 |
| 663 |
#define _RAatV1( i,j,k,bi,bj) ( _rA(i,j,bi,bj)*maskC(i,j) |
| 664 |
#define _RAatV2( i,j,k,bi,bj) + _rA(i,j-1,bi,bj) |
| 665 |
#define _RAatV3( i,j,k,bi,bj) *maskC(i,j-1) ) * 0.5 _d 0 |
| 666 |
#define _RAatV_Bot1(i,j,k,bi,bj) ( _rA(i,j,bi,bj) |
| 667 |
#define _RAatV_Bot2(i,j,k,bi,bj) +_rA(i,j-1,bi,bj))*0.5 _d 0 |
| 668 |
#ifdef INCLUDE_MOMENTUM_ADVECTION_CODE |
| 669 |
C o Mean flow component of zonal flux |
| 670 |
DO j=jMin,jMax |
| 671 |
DO i=iMin,iMax |
| 672 |
af(i,j) = |
| 673 |
& (uTrans(i,j)+uTrans(i,j-1) ) |
| 674 |
& *(vVel(i,j,k,bi,bj)+vVel(i-1,j,k,bi,bj))*0.25 _d 0 |
| 675 |
#ifdef OLD_ADV_BCS |
| 676 |
& *_maskS(i,j,k,bi,bj)*_maskS(i-1,j,k,bi,bj) |
| 677 |
#endif /* OLD_ADV_BCS */ |
| 678 |
C Note!!!! The line "*maskS(i,j,k,bi,bj)*maskS(i-1,j,k,bi,bj)" is |
| 679 |
C Note!!!! boundary condition in the standard v010 CM5 code. The |
| 680 |
C Note!!!! FV paper used a different bc in which this line is |
| 681 |
C Note!!!! omitted. |
| 682 |
ENDDO |
| 683 |
ENDDO |
| 684 |
#endif /* INCLUDE_MOMENTUM_ADVECTION_CODE */ |
| 685 |
C Eddy component of zonal flux |
| 686 |
C o Laplacian term |
| 687 |
DO j=jMin,jMax |
| 688 |
DO i=iMin,iMax |
| 689 |
vf(i,j) = _dyU(i,j,bi,bj)*drF(K)*hFacZ(i,j) |
| 690 |
& *( |
| 691 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 692 |
& -viscAh*(vVel(i,j,k,bi,bj)-vVel(i-1,j,k,bi,bj)) |
| 693 |
& *cosFacV(J,bi,bj) |
| 694 |
#else |
| 695 |
& 0. |
| 696 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 697 |
#ifdef INCLUDE_BH_MOMENTUM_DIFFUSION_CODE |
| 698 |
& +viscA4*(v4F(i,j) -v4F(i-1,j) ) |
| 699 |
#ifdef COSINEMETH_III |
| 700 |
& *sqcosFacV(J,bi,bj) |
| 701 |
#else |
| 702 |
& *cosFacV(J,bi,bj) |
| 703 |
#endif |
| 704 |
#endif /* INCLUDE_BH_MOMENTUM_DIFFUSION_CODE */ |
| 705 |
& )*_recip_dxV(i,j,bi,bj) |
| 706 |
ENDDO |
| 707 |
ENDDO |
| 708 |
DO j=jMin,jMax |
| 709 |
DO i=iMin,iMax |
| 710 |
fZon(i,j) = 0. |
| 711 |
& _ADM( + uDvdxFac * aF (i,j) ) |
| 712 |
& + AhDvdxFac * vF (i,j) |
| 713 |
ENDDO |
| 714 |
ENDDO |
| 715 |
C-- Meridional flux (fMer is at north face of "v" cell) |
| 716 |
#ifdef INCLUDE_MOMENTUM_ADVECTION_CODE |
| 717 |
C o Mean flow component of meridional flux |
| 718 |
DO j=jMin,jMax |
| 719 |
DO i=iMin,iMax |
| 720 |
af(i,j) = |
| 721 |
& (vTrans(i,j)+vTrans(i,j+1)) |
| 722 |
& *(vVel(i,j,k,bi,bj)+vVel(i,j+1,k,bi,bj))*0.25 _d 0 |
| 723 |
ENDDO |
| 724 |
ENDDO |
| 725 |
#endif /* INCLUDE_MOMENTUM_ADVECTION_CODE */ |
| 726 |
C Eddy component of meridional flux |
| 727 |
C o Laplacian term |
| 728 |
DO j=jMin,jMax |
| 729 |
DO i=iMin,iMax |
| 730 |
vF(i,j) = |
| 731 |
#ifdef OLD_UV_GEOMETRY |
| 732 |
& ( YA(i,j) + YA(i,j+1) ) *0.5 _d 0 |
| 733 |
#else |
| 734 |
& _dxF(i,j,bi,bj)*drF(k)*_hFacC(i,j,k,bi,bj) |
| 735 |
#endif /* OLD_UV_GEOMETRY */ |
| 736 |
& *( 0. |
| 737 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 738 |
#ifdef ISOTROPIC_COS_SCALING |
| 739 |
& -viscAh*(vVel(i,j+1,k,bi,bj)-vVel(i,j,k,bi,bj)) |
| 740 |
& *cosFacU(J,bi,bj) |
| 741 |
#else |
| 742 |
& -viscAh*(vVel(i,j+1,k,bi,bj)-vVel(i,j,k,bi,bj)) |
| 743 |
#endif |
| 744 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 745 |
#ifdef INCLUDE_BH_MOMENTUM_DIFFUSION_CODE |
| 746 |
#ifdef ISOTROPIC_COS_SCALING |
| 747 |
& +viscA4*(v4F(i,j+1) -v4F(i,j) ) |
| 748 |
& *cosFacU(J,bi,bj) |
| 749 |
#else |
| 750 |
& +viscA4*(v4F(i,j+1) -v4F(i,j) ) |
| 751 |
#endif |
| 752 |
#endif /* INCLUDE_BH_MOMENTUM_DIFFUSION_CODE */ |
| 753 |
& )*_recip_dyF(i,j,bi,bj) |
| 754 |
|
| 755 |
ENDDO |
| 756 |
ENDDO |
| 757 |
DO j=jMin,jMax |
| 758 |
DO i=iMin,iMax |
| 759 |
fMer(i,j) = 0. |
| 760 |
& _ADM( + vDvdyFac * af(i,j) ) |
| 761 |
& + AhDvdyFac * vf(i,j) |
| 762 |
ENDDO |
| 763 |
ENDDO |
| 764 |
C-- Vertical flux (fVer is at upper face of "v" cell) |
| 765 |
#ifdef INCLUDE_MOMENTUM_ADVECTION_CODE |
| 766 |
C-- Free surface correction temr |
| 767 |
IF (k.EQ.1) THEN |
| 768 |
DO j=jMin,jMax |
| 769 |
DO i=iMin,iMax |
| 770 |
fVerV(i,j,kUp)=rVelMaskOverride*( |
| 771 |
& wVel(i, j ,k,bi,bj)*rA(i, j ,bi,bj) |
| 772 |
& +wVel(i,j-1,k,bi,bj)*rA(i,j-1,bi,bj) |
| 773 |
& )*0.5 |
| 774 |
& *vVel(i,j,k,bi,bj) |
| 775 |
ENDDO |
| 776 |
ENDDO |
| 777 |
ENDIF |
| 778 |
C o Mean flow component of vertical flux |
| 779 |
DO j=jMin,jMax |
| 780 |
DO i=iMin,iMax |
| 781 |
af(i,j) = |
| 782 |
& wVelBottomOverride*( |
| 783 |
& wVel(i, j ,kp1,bi,bj)*rA(i, j ,bi,bj) |
| 784 |
& +wVel(i,j-1,kp1,bi,bj)*rA(i,j-1,bi,bj) |
| 785 |
& ) |
| 786 |
& *( vVel(i,j,kp1,bi,bj)+vVel(i,j,k,bi,bj) ) |
| 787 |
& *0.25 _d 0 |
| 788 |
#ifdef OLD_ADV_BCS |
| 789 |
& *_maskS(i,j,kp1,bi,bj)*_maskS(i,j,k,bi,bj) |
| 790 |
#endif /* OLD_ADV_BCS */ |
| 791 |
C Note!!!! The line "*(maskS(i,j,k,bi,bj)*maskS(i,j,kM1,bi,bj))" is |
| 792 |
C Note!!!! boundary condition in the standard v010 CM5 code. The |
| 793 |
C Note!!!! FV paper used a different bc in which this line is |
| 794 |
C Note!!!! omitted. |
| 795 |
C Note!!!! Is rVelMaskOverridde right for implicit free-surface? |
| 796 |
ENDDO |
| 797 |
ENDDO |
| 798 |
#endif /* INCLUDE_MOMENTUM_ADVECTION_CODE */ |
| 799 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 800 |
#ifdef OLD_UV_GEOMETRY |
| 801 |
#define _RA_AT_S (RA(i,j,bi,bj)*maskC(i,j)+RA(i,j-1,bi,bj)*maskC(i,j-1))*.5 |
| 802 |
#else |
| 803 |
#define _RA_AT_S rAs(i,j,bi,bj) |
| 804 |
#endif /* OLD_UV_GEOMETRY */ |
| 805 |
C Eddy component of vertical flux |
| 806 |
IF (.NOT.implicitViscosity) THEN |
| 807 |
DO j=jMin,jMax |
| 808 |
DO i=iMin,iMax |
| 809 |
vf(i,j) = |
| 810 |
& -KappaRV(i,j,kp1) |
| 811 |
& *_RA_AT_S |
| 812 |
& *(vVel(i,j,k,bi,bj)-vVel(i,j,kp1,bi,bj)) |
| 813 |
& *rkFac*recip_drC(kp1) |
| 814 |
& *_maskS(i,j,kp1,bi,bj) |
| 815 |
ENDDO |
| 816 |
ENDDO |
| 817 |
ENDIF |
| 818 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 819 |
IF (implicitViscosity) THEN |
| 820 |
DO j=jMin,jMax |
| 821 |
DO i=iMin,iMax |
| 822 |
fVerV(i,j,kDown) = rVelDvdrFac * af(i,j) |
| 823 |
ENDDO |
| 824 |
ENDDO |
| 825 |
ELSE |
| 826 |
DO j=jMin,jMax |
| 827 |
DO i=iMin,iMax |
| 828 |
fVerV(i,j,kDown) = rVelDvdrFac * af(i,j) |
| 829 |
& + ArDvdrFac * vf(i,j) |
| 830 |
ENDDO |
| 831 |
ENDDO |
| 832 |
ENDIF |
| 833 |
|
| 834 |
#ifdef INCLUDE_GRADPH_CODE |
| 835 |
C--- Hydorstatic term (-1/rho . dp/dy ) |
| 836 |
DO j=jMin,jMax |
| 837 |
DO i=iMin,iMax |
| 838 |
pF(i,j) = -_recip_dyC(i,j,bi,bj) |
| 839 |
& *(phiHyd(i,j,k)-phiHyd(i,j-1,k)) |
| 840 |
ENDDO |
| 841 |
ENDDO |
| 842 |
#endif /* INCLUDE_GRADPH_CODE */ |
| 843 |
|
| 844 |
C-- Tendency is minus divergence of the fluxes + coriolis + pressure |
| 845 |
C-- term |
| 846 |
DO j=jMin,jMax |
| 847 |
DO i=iMin,iMax |
| 848 |
gV(i,j,k,bi,bj) = |
| 849 |
#ifdef OLD_UV_GEOM |
| 850 |
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)/ |
| 851 |
& ( 0.5 _d 0*(_rA(i,j,bi,bj)+_rA(i,j-1,bi,bj)) ) |
| 852 |
#else |
| 853 |
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
| 854 |
& *recip_rAs(i,j,bi,bj) |
| 855 |
#endif |
| 856 |
& *(fZon(i+1,j) - fZon(i,j ) |
| 857 |
& +fMer(i,j ) - fMer(i,j-1) |
| 858 |
& +fVerV(i,j,kUp)*rkFac - fVerV(i,j,kDown)*rkFac |
| 859 |
& ) |
| 860 |
& _PHM( +phyFac*pf(i,j) ) |
| 861 |
ENDDO |
| 862 |
ENDDO |
| 863 |
|
| 864 |
#ifdef INCLUDE_LP_MOMENTUM_DIFFUSION_CODE |
| 865 |
C-- No-slip and drag BCs appear as body forces in cell abutting topography |
| 866 |
IF (no_slip_sides) THEN |
| 867 |
C- No-slip BCs impose a drag at walls... |
| 868 |
DO j=jMin,jMax |
| 869 |
DO i=iMin,iMax |
| 870 |
hFacZClosedW = _hFacS(i,j,k,bi,bj) - hFacZ(i,j) |
| 871 |
hFacZClosedE = _hFacS(i,j,k,bi,bj) - hFacZ(i+1,j) |
| 872 |
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) |
| 873 |
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
| 874 |
& /rAs(i,j,bi,bj) |
| 875 |
& *( hFacZClosedW*_dyU( i ,j,bi,bj) |
| 876 |
& *_recip_dxV( i ,j,bi,bj) |
| 877 |
& +hFacZClosedE*_dyU(i+1,j,bi,bj) |
| 878 |
& *_recip_dxV(i+1,j,bi,bj) ) |
| 879 |
& *rkFac*drF(k)*2.*( viscAh*vVel(i,j,k,bi,bj)*cosFacV(J,bi,bj) |
| 880 |
& -viscA4*v4F(i,j) |
| 881 |
#ifdef COSINEMETH_III |
| 882 |
& *sqcosFacV(J,bi,bj) |
| 883 |
#else |
| 884 |
& *cosFacV(J,bi,bj) |
| 885 |
#endif |
| 886 |
& ) |
| 887 |
ENDDO |
| 888 |
ENDDO |
| 889 |
ENDIF |
| 890 |
C- No-slip BCs impose a drag at bottom |
| 891 |
IF (bottomDragTerms) THEN |
| 892 |
rdrckp1=recip_drC(kp1) |
| 893 |
IF (k.EQ.Nr) rdrckp1=recip_drF(k) |
| 894 |
DO j=jMin,jMax |
| 895 |
DO i=iMin,iMax |
| 896 |
maskDown=_maskS(i,j,kp1,bi,bj) |
| 897 |
IF (k.EQ.Nr) maskDown=0. |
| 898 |
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) |
| 899 |
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
| 900 |
& *( |
| 901 |
& 2.*KappaRV(i,j,kp1)*rkFac*rdrckp1 |
| 902 |
& + bottomDragLinear |
| 903 |
& )*(1.-maskDown)*vVel(i,j,k,bi,bj) |
| 904 |
IF (KE(i,j)+KE(i,j-1) .NE. 0.) |
| 905 |
& gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) |
| 906 |
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
| 907 |
& *bottomDragQuadratic*sqrt(KE(i,j)+KE(i,j-1)) |
| 908 |
& *(1.-maskDown)*vVel(i,j,k,bi,bj) |
| 909 |
ENDDO |
| 910 |
ENDDO |
| 911 |
ENDIF |
| 912 |
#endif /* INCLUDE_LP_MOMENTUM_DIFFUSION_CODE */ |
| 913 |
|
| 914 |
#ifdef INCLUDE_MOMENTUM_FORCING_CODE |
| 915 |
C-- Forcing term |
| 916 |
CALL EXTERNAL_FORCING_V( |
| 917 |
I iMin,iMax,jMin,jMax,bi,bj,k, |
| 918 |
I myCurrentTime,myThid) |
| 919 |
#endif |
| 920 |
|
| 921 |
#ifdef INCLUDE_MOMENTUM_METRIC_TERM_CODE |
| 922 |
C-- Metric terms for curvilinear grid systems |
| 923 |
IF ( usingSphericalPolarMTerms ) THEN |
| 924 |
C o Spherical polar grid metric terms |
| 925 |
DO j=jMin,jMax |
| 926 |
DO i=iMin,iMax |
| 927 |
mT(i,j) = -vVel(i,j,k,bi,bj)*recip_RSphere |
| 928 |
& *0.25 _d 0*(wVelBottomOverride* |
| 929 |
& (wVel(i,j,kp1,bi,bj)+wVel(i,j-1,kp1,bi,bj)) |
| 930 |
& + wVel(i,j, k ,bi,bj)+wVel(i,j-1, k ,bi,bj) |
| 931 |
& )*rkFac*recip_horiVertRatio |
| 932 |
ENDDO |
| 933 |
ENDDO |
| 934 |
DO j=jMin,jMax |
| 935 |
DO i=iMin,iMax |
| 936 |
mT(i,j) = mT(i,j)-recip_RSphere |
| 937 |
& *0.25 _d 0*( uVel(i,j ,k,bi,bj)+uVel(i+1,j ,k,bi,bj) |
| 938 |
& +uVel(i,j-1,k,bi,bj)+uVel(i+1,j-1,k,bi,bj) |
| 939 |
& ) |
| 940 |
& *0.25 _d 0*( uVel(i,j ,k,bi,bj)+uVel(i+1,j ,k,bi,bj) |
| 941 |
& +uVel(i,j-1,k,bi,bj)+uVel(i+1,j-1,k,bi,bj) |
| 942 |
& ) |
| 943 |
& *_tanPhiAtV(i,j,bi,bj) |
| 944 |
ENDDO |
| 945 |
ENDDO |
| 946 |
DO j=jMin,jMax |
| 947 |
DO i=iMin,iMax |
| 948 |
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+ |
| 949 |
& mTFacV*mT(i,j) |
| 950 |
ENDDO |
| 951 |
ENDDO |
| 952 |
ENDIF |
| 953 |
#endif |
| 954 |
|
| 955 |
C-- Set dv/dt on boundaries to zero |
| 956 |
DO j=jMin,jMax |
| 957 |
DO i=iMin,iMax |
| 958 |
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj) |
| 959 |
ENDDO |
| 960 |
ENDDO |
| 961 |
|
| 962 |
C-- Coriolis term |
| 963 |
C Note. As coded here, coriolis will not work with "thin walls" |
| 964 |
#ifdef INCLUDE_CD_CODE |
| 965 |
C Pressure extrapolated forward in time |
| 966 |
DO j=jMin,jMax |
| 967 |
DO i=iMin,iMax |
| 968 |
pf(i,j) = |
| 969 |
& ab15*( etaN(i,j,bi,bj)*Bo_surf(i,j,bi,bj) ) |
| 970 |
& +ab05*(etaNm1(i,j,bi,bj)*Bo_surf(i,j,bi,bj) ) |
| 971 |
ENDDO |
| 972 |
ENDDO |
| 973 |
IF (staggerTimeStep) THEN |
| 974 |
DO j=jMin,jMax |
| 975 |
DO i=iMin,iMax |
| 976 |
pf(i,j) = pf(i,j)+phiHyd(i,j,k) |
| 977 |
ENDDO |
| 978 |
ENDDO |
| 979 |
ENDIF |
| 980 |
#endif /* INCLUDE_CD_CODE */ |
| 981 |
C-- Zonal velocity coriolis term |
| 982 |
C Note. As coded here, coriolis will not work with "thin walls" |
| 983 |
#ifdef INCLUDE_CD_CODE |
| 984 |
C-- Coriolis with CD scheme allowed |
| 985 |
C grady(p) + gV |
| 986 |
DO j=jMin,jMax |
| 987 |
DO i=iMin,iMax |
| 988 |
af(i,j) = -_maskS(i,j,k,bi,bj) |
| 989 |
& *_recip_dyC(i,j,bi,bj) |
| 990 |
& *(pf(i,j)-pf(i,j-1)) |
| 991 |
& +gV(i,j,k,bi,bj) |
| 992 |
ENDDO |
| 993 |
ENDDO |
| 994 |
C Average to Vd point and add coriolis |
| 995 |
DO j=jMin,jMax |
| 996 |
DO i=iMin,iMax |
| 997 |
vf(i,j) = |
| 998 |
& 0.25 _d 0*( af(i ,j)+af(i ,j+1) |
| 999 |
& +af(i-1,j)+af(i-1,j+1) |
| 1000 |
& )*_maskW(i,j,k,bi,bj) |
| 1001 |
& -0.5 _d 0*(_fCori(i,j,bi,bj)+ |
| 1002 |
& _fCori(i-1,j,bi,bj)) |
| 1003 |
& *uVel(i,j,k,bi,bj) |
| 1004 |
ENDDO |
| 1005 |
ENDDO |
| 1006 |
C Step forward Vd |
| 1007 |
DO j=jMin,jMax |
| 1008 |
DO i=iMin,iMax |
| 1009 |
vVelD(i,j,k,bi,bj) = vVelD(i,j,k,bi,bj) + |
| 1010 |
& deltaTmom*vf(i,j) |
| 1011 |
ENDDO |
| 1012 |
ENDDO |
| 1013 |
C Relax D grid V to C grid V |
| 1014 |
DO j=jMin,jMax |
| 1015 |
DO i=iMin,iMax |
| 1016 |
vVelD(i,j,k,bi,bj) = rCD*vVelD(i,j,k,bi,bj) |
| 1017 |
& +(1. _d 0 - rCD)*( |
| 1018 |
& ab15*0.25 _d 0*( |
| 1019 |
& vVel(i ,j ,k,bi,bj)+vVel(i ,j+1,k,bi,bj) |
| 1020 |
& +vVel(i-1,j ,k,bi,bj)+vVel(i-1,j+1,k,bi,bj) |
| 1021 |
& )*_maskW(i,j,k,bi,bj) |
| 1022 |
& + |
| 1023 |
& ab05*0.25 _d 0*( |
| 1024 |
& vNM1(i ,j ,k,bi,bj)+vNM1(i ,j+1,k,bi,bj) |
| 1025 |
& +vNM1(i-1,j ,k,bi,bj)+vNM1(i-1,j+1,k,bi,bj) |
| 1026 |
& )*_maskW(i,j,k,bi,bj) |
| 1027 |
& ) |
| 1028 |
ENDDO |
| 1029 |
ENDDO |
| 1030 |
C Calculate coriolis force on U |
| 1031 |
DO j=jMin,jMax |
| 1032 |
DO i=iMin,iMax |
| 1033 |
guCD(i,j,k,bi,bj) = |
| 1034 |
& 0.5 _d 0 *( _fCori(i ,j,bi,bj) + |
| 1035 |
& _fCori(i-1,j,bi,bj) ) |
| 1036 |
& *vVelD(i,j,k,bi,bj)*fuFac |
| 1037 |
ENDDO |
| 1038 |
ENDDO |
| 1039 |
#endif /* INCLUDE_CD_CODE */ |
| 1040 |
#ifndef INCLUDE_CD_CODE |
| 1041 |
C-- No CD scheme support |
| 1042 |
DO j=jMin,jMax |
| 1043 |
DO i=iMin,iMax |
| 1044 |
cf(i,j) = |
| 1045 |
& 0.5 _d 0 *( _fCori(i ,j,bi,bj) + |
| 1046 |
& _fCori(i-1,j,bi,bj) ) |
| 1047 |
& *0.25 _d 0 *( |
| 1048 |
& vVel(i ,j,k,bi,bj)+vVel(i ,j+1,k,bi,bj) |
| 1049 |
& +vVel(i-1,j,k,bi,bj)+vVel(i-1,j+1,k,bi,bj) |
| 1050 |
& ) |
| 1051 |
ENDDO |
| 1052 |
ENDDO |
| 1053 |
DO j=jMin,jMax |
| 1054 |
DO i=iMin,iMax |
| 1055 |
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) |
| 1056 |
& +fuFac*cf(i,j) |
| 1057 |
ENDDO |
| 1058 |
ENDDO |
| 1059 |
#endif /* !INCLUDE_CD_CODE */ |
| 1060 |
|
| 1061 |
|
| 1062 |
C-- Meridional velocity coriolis term |
| 1063 |
#ifdef INCLUDE_CD_CODE |
| 1064 |
C gradx(p)+gU |
| 1065 |
DO j=jMin,jMax |
| 1066 |
DO i=iMin,iMax |
| 1067 |
af(i,j) = -_maskW(i,j,k,bi,bj) |
| 1068 |
& *_recip_dxC(i,j,bi,bj)* |
| 1069 |
& (pf(i,j)-pf(i-1,j)) |
| 1070 |
& +gU(i,j,k,bi,bj) |
| 1071 |
ENDDO |
| 1072 |
ENDDO |
| 1073 |
C Average to Ud point and add coriolis |
| 1074 |
DO j=jMin,jMax |
| 1075 |
DO i=iMin,iMax |
| 1076 |
vf(i,j) = |
| 1077 |
& 0.25 _d 0*( af(i ,j)+af(i ,j-1) |
| 1078 |
& +af(i+1,j)+af(i+1,j-1) |
| 1079 |
& )*_maskS(i,j,k,bi,bj) |
| 1080 |
& +0.5 _d 0*( _fCori(i,j,bi,bj) |
| 1081 |
& +_fCori(i,j-1,bi,bj)) |
| 1082 |
& *vVel(i,j,k,bi,bj) |
| 1083 |
ENDDO |
| 1084 |
ENDDO |
| 1085 |
C Step forward Ud |
| 1086 |
DO j=jMin,jMax |
| 1087 |
DO i=iMin,iMax |
| 1088 |
uVelD(i,j,k,bi,bj) = uVelD(i,j,k,bi,bj) + |
| 1089 |
& deltaTmom*vf(i,j)*_maskS(i,j,k,bi,bj) |
| 1090 |
ENDDO |
| 1091 |
ENDDO |
| 1092 |
C Relax D grid U to C grid U |
| 1093 |
DO j=jMin,jMax |
| 1094 |
DO i=iMin,iMax |
| 1095 |
uVelD(i,j,k,bi,bj) = rCD*uVelD(i,j,k,bi,bj) |
| 1096 |
& +(1. _d 0 - rCD)*( |
| 1097 |
& ab15*0.25 _d 0*( |
| 1098 |
& uVel(i,j ,k,bi,bj)+uVel(i+1,j ,k,bi,bj) |
| 1099 |
& +uVel(i,j-1,k,bi,bj)+uVel(i+1,j-1,k,bi,bj) |
| 1100 |
& )*_maskS(i,j,k,bi,bj) |
| 1101 |
& + |
| 1102 |
& ab05*0.25 _d 0*( |
| 1103 |
& uNM1(i,j ,k,bi,bj)+uNM1(i+1,j ,k,bi,bj) |
| 1104 |
& +uNM1(i,j-1,k,bi,bj)+uNM1(i+1,j-1,k,bi,bj) |
| 1105 |
& )*_maskS(i,j,k,bi,bj) |
| 1106 |
& ) |
| 1107 |
ENDDO |
| 1108 |
ENDDO |
| 1109 |
C Calculate coriolis force on V |
| 1110 |
DO j=jMin,jMax |
| 1111 |
DO i=iMin,iMax |
| 1112 |
gvCD(i,j,k,bi,bj) = |
| 1113 |
& -0.5 _d 0 *( _fCori(i ,j,bi,bj) |
| 1114 |
& +_fCori(i,j-1,bi,bj) ) |
| 1115 |
& *uVelD(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)*fvFac |
| 1116 |
ENDDO |
| 1117 |
ENDDO |
| 1118 |
#endif /* INCLUDE_CD_CODE */ |
| 1119 |
#ifndef INCLUDE_CD_CODE |
| 1120 |
C-- No CD scheme support |
| 1121 |
DO j=jMin,jMax |
| 1122 |
DO i=iMin,iMax |
| 1123 |
cf(i,j) = |
| 1124 |
& -0.5 _d 0 *(_fCori(i,j ,bi,bj)+_fCori(i,j-1,bi,bj)) |
| 1125 |
& *0.25 _d 0 |
| 1126 |
& *( uVel(i,j ,k,bi,bj)+uVel(i+1,j ,k,bi,bj) |
| 1127 |
& +uVel(i,j-1,k,bi,bj)+uVel(i+1,j-1,k,bi,bj) |
| 1128 |
& ) |
| 1129 |
ENDDO |
| 1130 |
ENDDO |
| 1131 |
DO j=jMin,jMax |
| 1132 |
DO i=iMin,iMax |
| 1133 |
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) |
| 1134 |
& +fvFac*cf(i,j) |
| 1135 |
ENDDO |
| 1136 |
ENDDO |
| 1137 |
#endif /* !INCLUDE_CD_CODE */ |
| 1138 |
|
| 1139 |
C-- Set du/dt on boundaries to zero |
| 1140 |
DO j=jMin,jMax |
| 1141 |
DO i=iMin,iMax |
| 1142 |
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj) |
| 1143 |
ENDDO |
| 1144 |
ENDDO |
| 1145 |
C-- Set dv/dt on boundaries to zero |
| 1146 |
DO j=jMin,jMax |
| 1147 |
DO i=iMin,iMax |
| 1148 |
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj) |
| 1149 |
ENDDO |
| 1150 |
ENDDO |
| 1151 |
|
| 1152 |
#ifdef INCLUDE_CD_CODE |
| 1153 |
C-- Save "previous time level" variables |
| 1154 |
DO j=1-OLy,sNy+OLy |
| 1155 |
DO i=1-OLx,sNx+OLx |
| 1156 |
uNM1(i,j,k,bi,bj) = uVel(i,j,k,bi,bj) |
| 1157 |
vNM1(i,j,k,bi,bj) = vVel(i,j,k,bi,bj) |
| 1158 |
ENDDO |
| 1159 |
ENDDO |
| 1160 |
#endif /* INCLUDE_CD_CODE */ |
| 1161 |
|
| 1162 |
RETURN |
| 1163 |
END |
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