/[MITgcm]/manual/s_examples/baroclinic_gyre/fourlayer.tex
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revision 1.11 by adcroft, Tue Nov 13 20:13:54 2001 UTC revision 1.15 by edhill, Thu Aug 7 18:27:52 2003 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}  \section{Four Layer Baroclinic Ocean Gyre In Spherical Coordinates}
5    \label{www:tutorials}
6  \label{sect:eg-fourlayer}  \label{sect:eg-fourlayer}
7    
8  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
# Line 26  is simulated, but the code is now config Line 27  is simulated, but the code is now config
27  for four layers and in a spherical polar coordinate system.  for four layers and in a spherical polar coordinate system.
28    
29  \subsection{Overview}  \subsection{Overview}
30    \label{www:tutorials}
31    
32  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
33  a baroclinic, wind-forced, ocean gyre circulation. The experiment  a baroclinic, wind-forced, ocean gyre circulation. The experiment
# Line 43  domain is a sector on a sphere and the c Line 45  domain is a sector on a sphere and the c
45  according to latitude, $\varphi$  according to latitude, $\varphi$
46    
47  \begin{equation}  \begin{equation}
48  \label{EQ:fcori}  \label{EQ:eg-fourlayer-fcori}
49  f(\varphi) = 2 \Omega \sin( \varphi )  f(\varphi) = 2 \Omega \sin( \varphi )
50  \end{equation}  \end{equation}
51    
# Line 61  f(\varphi) = 2 \Omega \sin( \varphi ) Line 63  f(\varphi) = 2 \Omega \sin( \varphi )
63  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
64  \\  \\
65    
66  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-fourlayer-simulation_config}
67  summarizes the configuration simulated.  summarizes the configuration simulated.
68  In contrast to the example in section \ref{sect:eg-baro}, the  In contrast to the example in section \ref{sect:eg-baro}, the
69  current experiment simulates a spherical polar domain. As indicated  current experiment simulates a spherical polar domain. As indicated
# Line 82  $\theta_{1750}=6^{\circ}$~C. The equatio Line 84  $\theta_{1750}=6^{\circ}$~C. The equatio
84  linear  linear
85    
86  \begin{equation}  \begin{equation}
87  \label{EQ:linear1_eos}  \label{EQ:eg-fourlayer-linear1_eos}
88  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
89  \end{equation}  \end{equation}
90    
91  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
92    
93  \begin{equation}  \begin{equation}
94  \label{EQ:linear1_eos_pert}  \label{EQ:eg-fourlayer-linear1_eos_pert}
95  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
96  \end{equation}  \end{equation}
97    
# Line 114  An initial stratification is Line 116  An initial stratification is
116  imposed by setting the potential temperature, $\theta$, in each layer.  imposed by setting the potential temperature, $\theta$, in each layer.
117  The vertical spacing, $\Delta z$, is constant and equal to $500$m.  The vertical spacing, $\Delta z$, is constant and equal to $500$m.
118  }  }
119  \label{FIG:simulation_config}  \label{FIG:eg-fourlayer-simulation_config}
120  \end{figure}  \end{figure}
121    
122  \subsection{Equations solved}  \subsection{Equations solved}
123    \label{www:tutorials}
124  For this problem  For this problem
125  the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the  the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the
126  equations described in Marshall et. al \cite{marshall:97a} are  equations described in Marshall et. al \cite{marshall:97a} are
# Line 133  solved in this configuration, written in Line 136  solved in this configuration, written in
136  follows  follows
137    
138  \begin{eqnarray}  \begin{eqnarray}
139  \label{EQ:model_equations}  \label{EQ:eg-fourlayer-model_equations}
140  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
141    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -
142    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}
# Line 202  e.g. $\frac{\partial \theta}{\partial \v Line 205  e.g. $\frac{\partial \theta}{\partial \v
205    
206    
207  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
208    \label{www:tutorials}
209    
210   The domain is discretised with   The domain is discretised with
211  a uniform grid spacing in latitude and longitude  a uniform grid spacing in latitude and longitude
# Line 261  field solution method is described in se Line 265  field solution method is described in se
265  \ref{sect:finding_the_pressure_field}.  \ref{sect:finding_the_pressure_field}.
266    
267  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
268    \label{www:tutorials}
269    
270  The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
271  This value is chosen to yield a Munk layer width,  This value is chosen to yield a Munk layer width,
272    
273  \begin{eqnarray}  \begin{eqnarray}
274  \label{EQ:munk_layer}  \label{EQ:eg-fourlayer-munk_layer}
275  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
276  \end{eqnarray}  \end{eqnarray}
277    
# Line 282  time step $\delta t=1200$secs. With this Line 287  time step $\delta t=1200$secs. With this
287  parameter to the horizontal Laplacian friction  parameter to the horizontal Laplacian friction
288    
289  \begin{eqnarray}  \begin{eqnarray}
290  \label{EQ:laplacian_stability}  \label{EQ:eg-fourlayer-laplacian_stability}
291  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
292  \end{eqnarray}  \end{eqnarray}
293    
# Line 294  for stability for this term under ABII t Line 299  for stability for this term under ABII t
299  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
300    
301  \begin{eqnarray}  \begin{eqnarray}
302  \label{EQ:laplacian_stability_z}  \label{EQ:eg-fourlayer-laplacian_stability_z}
303  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
304  \end{eqnarray}  \end{eqnarray}
305    
# Line 307  and vertical ($K_{z}$) diffusion coeffic Line 312  and vertical ($K_{z}$) diffusion coeffic
312  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
313    
314  \begin{eqnarray}  \begin{eqnarray}
315  \label{EQ:inertial_stability}  \label{EQ:eg-fourlayer-inertial_stability}
316  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
317  \end{eqnarray}  \end{eqnarray}
318    
# Line 320  horizontal flow Line 325  horizontal flow
325  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
326    
327  \begin{eqnarray}  \begin{eqnarray}
328  \label{EQ:cfl_stability}  \label{EQ:eg-fourlayer-cfl_stability}
329  C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
330  \end{eqnarray}  \end{eqnarray}
331    
# Line 332  limit of 0.5. Line 337  limit of 0.5.
337  propagating at $2~{\rm m}~{\rm s}^{-1}$  propagating at $2~{\rm m}~{\rm s}^{-1}$
338    
339  \begin{eqnarray}  \begin{eqnarray}
340  \label{EQ:igw_stability}  \label{EQ:eg-fourlayer-igw_stability}
341  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
342  \end{eqnarray}  \end{eqnarray}
343    
# Line 340  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 345  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
345  stability limit of 0.25.  stability limit of 0.25.
346        
347  \subsection{Code Configuration}  \subsection{Code Configuration}
348    \label{www:tutorials}
349  \label{SEC:eg_fourl_code_config}  \label{SEC:eg_fourl_code_config}
350    
351  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
# Line 354  directory {\it verification/exp2/}.  The Line 360  directory {\it verification/exp2/}.  The
360  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
361  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
362  \end{itemize}  \end{itemize}
363  contain the code customisations and parameter settings for this  contain the code customisations and parameter settings for this
364  experiments. Below we describe the customisations  experiment. Below we describe the customisations to these files
365  to these files associated with this experiment.  associated with this experiment.
366    
367  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
368    \label{www:tutorials}
369    
370  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
371  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 375  The entries are ordered from surface to Line 382  The entries are ordered from surface to
382  depth level the initial and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
383  $x$ and $y$. The values specified here are read into the  $x$ and $y$. The values specified here are read into the
384  variable  variable
385  {\bf  \varlink{tRef}{tRef}
386  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  %{\bf
387  tRef  %\begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
388  \begin{rawhtml} </A>\end{rawhtml}  %tRef
389  }  %\begin{rawhtml} </A>\end{rawhtml}
390    %}
391  in the model code, by procedure  in the model code, by procedure
392  {\it  \filelink{INI\_PARMS}{model-src-ini_parms.F}
393  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  %{\it
394  INI\_PARMS  %\begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
395  \begin{rawhtml} </A>\end{rawhtml}  %INI\_PARMS
396  }.  %\begin{rawhtml} </A>\end{rawhtml}
397    %}.
398    
399  %% \codelink{var:tref} tRef \endlink  %% \codelink{var:tref} tRef \endlink
400  %% \codelink{file:ini_parms} {\it INI\_PARMS } \endlink  %% \codelink{file:ini_parms} {\it INI\_PARMS } \endlink
# Line 395  INI\_PARMS Line 404  INI\_PARMS
404  %% \file{ini_parms}  %% \file{ini_parms}
405  \newcommand{\VARtref}{  \newcommand{\VARtref}{
406  {\bf  {\bf
407  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
408  tRef  tRef
409  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
410  }  }
# Line 409  tRef Line 418  tRef
418  ({\it ini\_theta.F})  ({\it ini\_theta.F})
419  \end{minipage}  \end{minipage}
420  }  }
421  {\bf  \filelink{ini\_theta.F}{model-src-ini_theta.F}
422  \begin{rawhtml} <A href=../../../code_reference/vdb/code/98.htm> \end{rawhtml}  %{\bf
423  goto code  %\begin{rawhtml} <A href=../code_reference/vdb/code/98.htm> \end{rawhtml}
424  \begin{rawhtml} </A>\end{rawhtml}  %goto code
425  }  %\begin{rawhtml} </A>\end{rawhtml}
426    %}
427    
428    
429  \item Line 6,  \item Line 6,
# Line 422  this line sets the vertical Laplacian di Line 432  this line sets the vertical Laplacian di
432  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
433  for this operator are specified later.  for this operator are specified later.
434  The variable  The variable
435  {\bf  \varlink{viscAz}{viscAz}
436  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  %{\bf
437  viscAz  %\begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
438  \begin{rawhtml} </A>\end{rawhtml}  %viscAz
439  }  %\begin{rawhtml} </A>\end{rawhtml}
440    %}
441  is read in the routine  is read in the routine
442  {\it  \filelink{ini\_parms.F}{model-src-ini_parms.F}
443  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  %{\it
444  INI\_PARMS  %\begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
445  \begin{rawhtml} </A>\end{rawhtml}  %INI\_PARMS
446  }  %\begin{rawhtml} </A>\end{rawhtml}
447    %}
448  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
449  {\bf  \varlink{viscAr}{viscAr}
450  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  %{\bf
451  viscAr  %\begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
452  \begin{rawhtml} </A>\end{rawhtml}  %viscAr
453  }. At each time step, the viscous term contribution to the momentum equations  %\begin{rawhtml} </A>\end{rawhtml}
454    %}.
455    At each time step, the viscous term contribution to the momentum equations
456  is calculated in routine  is calculated in routine
457  {\it S/R CALC\_DIFFUSIVITY}.  %{\it S/R CALC\_DIFFUSIVITY}.
458    \varlink{CALC\_DIFFUSIVITY}{CALC_DIFFUSIVITY}
459    
460  \fbox{  \fbox{
461  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
462  {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})  {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
463  \end{minipage}  \end{minipage}
464  }  }
465  {\bf  %{\bf
466  \begin{rawhtml} <A href=../../../code_reference/vdb/code/53.htm> \end{rawhtml}  %\begin{rawhtml} <A href=../code_reference/vdb/code/53.htm> \end{rawhtml}
467  goto code  %goto code
468  \begin{rawhtml} </A>\end{rawhtml}  %\begin{rawhtml} </A>\end{rawhtml}
469  }  %}
470    
471  \item Line 7,  \item Line 7,
472  \begin{verbatim}  \begin{verbatim}
# Line 461  this line sets the horizontal laplacian Line 476  this line sets the horizontal laplacian
476  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
477  for this operator are specified later.  for this operator are specified later.
478  The variable  The variable
479  {\bf  \varlink{viscAh}{viscAh}
480  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  %{\bf
481  viscAh  %\begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
482  \begin{rawhtml} </A>\end{rawhtml}  %viscAh
483  }  %\begin{rawhtml} </A>\end{rawhtml}
484    %}
485  is read in the routine  is read in the routine
486  {\it  \varlink{INI\_PARMS}{INI_PARMS}
487  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  %{\it
488  INI\_PARMS  %\begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
489  \begin{rawhtml} </A>\end{rawhtml}  %INI\_PARMS
490  } and applied in routines {\it CALC\_MOM\_RHS} and {\it CALC\_GW}.  %\begin{rawhtml} </A>\end{rawhtml}
491    %}
492    and applied in routines
493    %{\it CALC\_MOM\_RHS} and {\it CALC\_GW}.
494    \varlink{CALC\_MOM\_RHS}{CALC_MOM_RHS}
495    and
496    \varlink{CALC\_GW}{CALC_GW}.
497    
498    
499  \fbox{  \fbox{
500  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
501  {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})  {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})
502  \end{minipage}  \end{minipage}
503  }  }
504  {\bf  %{\bf
505  \begin{rawhtml} <A href=../../../code_reference/vdb/code/60.htm> \end{rawhtml}  %\begin{rawhtml} <A href=../code_reference/vdb/code/60.htm> \end{rawhtml}
506  goto code  %goto code
507  \begin{rawhtml} </A>\end{rawhtml}  %\begin{rawhtml} </A>\end{rawhtml}
508  }  %}
509    
510  \fbox{  \fbox{
511  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
512  {\it S/R CALC\_GW}({\it calc\_gw.F})  {\it S/R CALC\_GW}({\it calc\_gw.F})
513  \end{minipage}  \end{minipage}
514  }  }
515  {\bf  %{\bf
516  \begin{rawhtml} <A href=../../../code_reference/vdb/code/58.htm> \end{rawhtml}  %\begin{rawhtml} <A href=../code_reference/vdb/code/58.htm> \end{rawhtml}
517  goto code  %goto code
518  \begin{rawhtml} </A>\end{rawhtml}  %\begin{rawhtml} </A>\end{rawhtml}
519  }  %}
520    
521  \item Lines 8,  \item Lines 8,
522  \begin{verbatim}  \begin{verbatim}
# Line 504  the horizontal laplacian friction operat Line 527  the horizontal laplacian friction operat
527  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
528  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
529  The variable  The variable
530  {\bf  \varlink{no\_slip\_sides}{no_slip_sides}
531  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  %{\bf
532  no\_slip\_sides  %\begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
533  \begin{rawhtml} </A>\end{rawhtml}  %no\_slip\_sides
534  }  %\begin{rawhtml} </A>\end{rawhtml}
535    %}
536  is read in the routine  is read in the routine
537  {\it  \varlink{INI\_PARMS}{INI_PARMS}
538  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  %{\it
539  INI\_PARMS  %\begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
540  \begin{rawhtml} </A>\end{rawhtml}  %INI\_PARMS
541  } and the boundary condition is evaluated in routine  %\begin{rawhtml} </A>\end{rawhtml}
542  {\it S/R CALC\_MOM\_RHS}.  %}
543    and the boundary condition is evaluated in routine
544    %{\it S/R CALC\_MOM\_RHS}.
545    
546    
547  \fbox{  \fbox{
# Line 524  INI\_PARMS Line 550  INI\_PARMS
550  \end{minipage}  \end{minipage}
551  }  }
552  {\bf  {\bf
553  \begin{rawhtml} <A href=../../../code_reference/vdb/code/60.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/60.htm> \end{rawhtml}
554  goto code  goto code
555  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
556  }  }
# Line 538  boundary condition in the vertical lapla Line 564  boundary condition in the vertical lapla
564  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
565  The variable  The variable
566  {\bf  {\bf
567  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
568  no\_slip\_bottom  no\_slip\_bottom
569  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
570  }  }
571  is read in the routine  is read in the routine
572  {\it  {\it
573  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
574  INI\_PARMS  INI\_PARMS
575  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
576  } and is applied in the routine {\it S/R CALC\_MOM\_RHS}.  } and is applied in the routine {\it S/R CALC\_MOM\_RHS}.
# Line 555  INI\_PARMS Line 581  INI\_PARMS
581  \end{minipage}  \end{minipage}
582  }  }
583  {\bf  {\bf
584  \begin{rawhtml} <A href=../../../code_reference/vdb/code/60.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/60.htm> \end{rawhtml}
585  goto code  goto code
586  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
587  }  }
# Line 570  operator is $\frac{\partial}{\partial x} Line 596  operator is $\frac{\partial}{\partial x}
596  all boundaries.  all boundaries.
597  The variable  The variable
598  {\bf  {\bf
599  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
600  diffKhT  diffKhT
601  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
602  }  }
603  is read in the routine  is read in the routine
604  {\it  {\it
605  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
606  INI\_PARMS  INI\_PARMS
607  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
608  } and used in routine {\it S/R CALC\_GT}.  } and used in routine {\it S/R CALC\_GT}.
# Line 586  INI\_PARMS Line 612  INI\_PARMS
612  \end{minipage}  \end{minipage}
613  }  }
614  {\bf  {\bf
615  \begin{rawhtml} <A href=../../../code_reference/vdb/code/57.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/57.htm> \end{rawhtml}
616  goto code  goto code
617  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
618  }  }
# Line 600  to $10^{-2}\,{\rm m^{2}s^{-1}}$. The bou Line 626  to $10^{-2}\,{\rm m^{2}s^{-1}}$. The bou
626  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
627  The variable  The variable
628  {\bf  {\bf
629  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
630  diffKzT  diffKzT
631  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
632  }  }
633  is read in the routine  is read in the routine
634  {\it  {\it
635  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
636  INI\_PARMS  INI\_PARMS
637  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
638  }.  }.
639  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
640  {\bf  {\bf
641  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
642  diffKrT  diffKrT
643  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
644  } which is used in routine {\it S/R CALC\_DIFFUSIVITY}.  } which is used in routine {\it S/R CALC\_DIFFUSIVITY}.
# Line 622  diffKrT Line 648  diffKrT
648  \end{minipage}  \end{minipage}
649  }  }
650  {\bf  {\bf
651  \begin{rawhtml} <A href=../../../code_reference/vdb/code/53.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/53.htm> \end{rawhtml}
652  goto code  goto code
653  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
654  }  }
# Line 637  This line sets the thermal expansion coe Line 663  This line sets the thermal expansion coe
663  to $2 \times 10^{-4}\,{\rm degrees}^{-1}$  to $2 \times 10^{-4}\,{\rm degrees}^{-1}$
664  The variable  The variable
665  {\bf  {\bf
666  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
667  tAlpha  tAlpha
668  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
669  }  }
670  is read in the routine  is read in the routine
671  {\it  {\it
672  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
673  INI\_PARMS  INI\_PARMS
674  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
675  }. The routine {\it S/R FIND\_RHO} makes use of {\bf tAlpha}.  }. The routine {\it S/R FIND\_RHO} makes use of {\bf tAlpha}.
# Line 654  INI\_PARMS Line 680  INI\_PARMS
680  \end{minipage}  \end{minipage}
681  }  }
682  {\bf  {\bf
683  \begin{rawhtml} <A href=../../../code_reference/vdb/code/79.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/79.htm> \end{rawhtml}
684  goto code  goto code
685  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
686  }  }
# Line 666  eosType='LINEAR' Line 692  eosType='LINEAR'
692  This line selects the linear form of the equation of state.  This line selects the linear form of the equation of state.
693  The variable  The variable
694  {\bf  {\bf
695  \begin{rawhtml} <A href=../../../code_reference/vdb/names/WV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/WV.htm> \end{rawhtml}
696  eosType  eosType
697  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
698  }  }
699  is read in the routine  is read in the routine
700  {\it  {\it
701  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
702  INI\_PARMS  INI\_PARMS
703  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
704  }. The values of {\bf eosType} sets which formula in routine  }. The values of {\bf eosType} sets which formula in routine
# Line 684  INI\_PARMS Line 710  INI\_PARMS
710  \end{minipage}  \end{minipage}
711  }  }
712  {\bf  {\bf
713  \begin{rawhtml} <A href=../../../code_reference/vdb/code/79.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/79.htm> \end{rawhtml}
714  goto code  goto code
715  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
716  }  }
# Line 702  causes the grid generation routines to i Line 728  causes the grid generation routines to i
728  on spherical polar geometry.  on spherical polar geometry.
729  The variable  The variable
730  {\bf  {\bf
731  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10T.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10T.htm> \end{rawhtml}
732  usingSphericalPolarGrid  usingSphericalPolarGrid
733  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
734  }  }
735  is read in the routine  is read in the routine
736  {\it  {\it
737  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
738  INI\_PARMS  INI\_PARMS
739  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
740  }. When set to {\bf .TRUE.} the settings of {\bf delX} and {\bf delY} are  }. When set to {\bf .TRUE.} the settings of {\bf delX} and {\bf delY} are
# Line 721  routine {\it INI\_SPEHRICAL\_POLAR\_GRID Line 747  routine {\it INI\_SPEHRICAL\_POLAR\_GRID
747  \end{minipage}  \end{minipage}
748  }  }
749  {\bf  {\bf
750  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
751  goto code  goto code
752  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
753  }  }
# Line 739  a longitude boundary, since the absolute Line 765  a longitude boundary, since the absolute
765  not alter the kernel equation discretisation.  not alter the kernel equation discretisation.
766  The variable  The variable
767  {\bf  {\bf
768  \begin{rawhtml} <A href=../../../code_reference/vdb/names/110.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/110.htm> \end{rawhtml}
769  phiMin  phiMin
770  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
771  }  }
772  is read in the routine  is read in the routine
773  {\it  {\it
774  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
775  INI\_PARMS  INI\_PARMS
776  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
777  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
# Line 756  INI\_PARMS Line 782  INI\_PARMS
782  \end{minipage}  \end{minipage}
783  }  }
784  {\bf  {\bf
785  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
786  goto code  goto code
787  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
788  }  }
# Line 769  This line sets the horizontal grid spaci Line 795  This line sets the horizontal grid spaci
795  in the discrete grid to $1^{\circ}$ in longitude.  in the discrete grid to $1^{\circ}$ in longitude.
796  The variable  The variable
797  {\bf  {\bf
798  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10Z.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10Z.htm> \end{rawhtml}
799  delX  delX
800  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
801  }  }
802  is read in the routine  is read in the routine
803  {\it  {\it
804  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
805  INI\_PARMS  INI\_PARMS
806  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
807  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
# Line 786  INI\_PARMS Line 812  INI\_PARMS
812  \end{minipage}  \end{minipage}
813  }  }
814  {\bf  {\bf
815  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
816  goto code  goto code
817  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
818  }  }
# Line 799  This line sets the horizontal grid spaci Line 825  This line sets the horizontal grid spaci
825  in the discrete grid to $1^{\circ}$ in latitude.  in the discrete grid to $1^{\circ}$ in latitude.
826  The variable  The variable
827  {\bf  {\bf
828  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UB.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UB.htm> \end{rawhtml}
829  delY    delY  
830  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
831  }  }
832  is read in the routine  is read in the routine
833  {\it  {\it
834  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
835  INI\_PARMS  INI\_PARMS
836  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
837  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
# Line 816  INI\_PARMS Line 842  INI\_PARMS
842  \end{minipage}  \end{minipage}
843  }  }
844  {\bf  {\bf
845  \begin{rawhtml} <A href=../../../code_reference/vdb/code/97.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/97.htm> \end{rawhtml}
846  goto code  goto code
847  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
848  }  }
# Line 830  in the discrete grid to $500\,{\rm m}$, Line 856  in the discrete grid to $500\,{\rm m}$,
856  is $2\,{\rm km}$.  is $2\,{\rm km}$.
857  The variable  The variable
858  {\bf  {\bf
859  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10W.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10W.htm> \end{rawhtml}
860  delZ  delZ
861  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
862  }  }
863  is read in the routine  is read in the routine
864  {\it  {\it
865  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
866  INI\_PARMS  INI\_PARMS
867  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
868  }.  }.
869  It is copied into the internal  It is copied into the internal
870  model coordinate variable  model coordinate variable
871  {\bf  {\bf
872  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10Y.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/10Y.htm> \end{rawhtml}
873  delR  delR
874  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
875  } which is used in routine {\it INI\_VERTICAL\_GRID}.  } which is used in routine {\it INI\_VERTICAL\_GRID}.
# Line 854  delR Line 880  delR
880  \end{minipage}  \end{minipage}
881  }  }
882  {\bf  {\bf
883  \begin{rawhtml} <A href=../../../code_reference/vdb/code/100.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/100.htm> \end{rawhtml}
884  goto code  goto code
885  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
886  }  }
# Line 876  of $-2000m$ indicates open ocean. The ma Line 902  of $-2000m$ indicates open ocean. The ma
902  bathymetry file.  bathymetry file.
903  The variable  The variable
904  {\bf  {\bf
905  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
906  bathyFile  bathyFile
907  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
908  }  }
909  is read in the routine  is read in the routine
910  {\it  {\it
911  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
912  INI\_PARMS  INI\_PARMS
913  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
914  }. The bathymetry file is read in the routine {\it INI\_DEPTHS}.  }. The bathymetry file is read in the routine {\it INI\_DEPTHS}.
# Line 893  INI\_PARMS Line 919  INI\_PARMS
919  \end{minipage}  \end{minipage}
920  }  }
921  {\bf  {\bf
922  \begin{rawhtml} <A href=../../../code_reference/vdb/code/88.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/88.htm> \end{rawhtml}
923  goto code  goto code
924  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
925  }  }
# Line 912  code to generate a valid Line 938  code to generate a valid
938  file.    file.  
939  The variable  The variable
940  {\bf  {\bf
941  \begin{rawhtml} <A href=../../../code_reference/vdb/names/13W.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/13W.htm> \end{rawhtml}
942  zonalWindFile  zonalWindFile
943  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
944  }  }
945  is read in the routine  is read in the routine
946  {\it  {\it
947  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
948  INI\_PARMS  INI\_PARMS
949  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
950  }.  The wind-stress file is read in the routine  }.  The wind-stress file is read in the routine
# Line 930  INI\_PARMS Line 956  INI\_PARMS
956  \end{minipage}  \end{minipage}
957  }  }
958  {\bf  {\bf
959  \begin{rawhtml} <A href=../../../code_reference/vdb/code/75.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/75.htm> \end{rawhtml}
960  goto code  goto code
961  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
962  }  }
# Line 946  goto code Line 972  goto code
972  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
973    
974  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
975    \label{www:tutorials}
976    
977  This file uses standard default values and does not contain  This file uses standard default values and does not contain
978  customisations for this experiment.  customisations for this experiment.
979    
980  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
981    \label{www:tutorials}
982    
983  This file uses standard default values and does not contain  This file uses standard default values and does not contain
984  customisations for this experiment.  customisations for this experiment.
985    
986  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
987    \label{www:tutorials}
988    
989  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
990  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the
# Line 969  The included matlab program {\it input/g Line 998  The included matlab program {\it input/g
998  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
999    
1000  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
1001    \label{www:tutorials}
1002    
1003    
1004  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
# Line 980  The included matlab program {\it input/g Line 1010  The included matlab program {\it input/g
1010  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
1011    
1012  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
1013    \label{www:tutorials}
1014    
1015  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
1016    
# Line 1006  the vertical domain extent in grid point Line 1037  the vertical domain extent in grid point
1037  \end{small}  \end{small}
1038    
1039  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
1040    \label{www:tutorials}
1041    
1042  This file uses standard default values and does not contain  This file uses standard default values and does not contain
1043  customisations for this experiment.  customisations for this experiment.
1044    
1045    
1046  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
1047    \label{www:tutorials}
1048    
1049  This file uses standard default values and does not contain  This file uses standard default values and does not contain
1050  customisations for this experiment.  customisations for this experiment.
1051    
1052  \subsubsection{Other Files }  \subsubsection{Other Files }
1053    \label{www:tutorials}
1054    
1055  Other files relevant to this experiment are  Other files relevant to this experiment are
1056  \begin{itemize}  \begin{itemize}
# Line 1029  dxF, dyF, dxG, dyG, dxC, dyC}. Line 1063  dxF, dyF, dxG, dyG, dxC, dyC}.
1063  \end{itemize}  \end{itemize}
1064    
1065  \subsection{Running The Example}  \subsection{Running The Example}
1066    \label{www:tutorials}
1067  \label{SEC:running_the_example}  \label{SEC:running_the_example}
1068    
1069  \subsubsection{Code Download}  \subsubsection{Code Download}
1070    \label{www:tutorials}
1071    
1072   In order to run the examples you must first download the code distribution.   In order to run the examples you must first download the code distribution.
1073  Instructions for downloading the code can be found in section  Instructions for downloading the code can be found in section
1074  \ref{sect:obtainingCode}.  \ref{sect:obtainingCode}.
1075    
1076  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
1077    \label{www:tutorials}
1078    
1079   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
1080    
# Line 1045  Instructions for downloading the code ca Line 1082  Instructions for downloading the code ca
1082  {\it verification/exp2/ }  {\it verification/exp2/ }
1083    
1084  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
1085    \label{www:tutorials}
1086    
1087   To run the experiment   To run the experiment
1088    
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