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revision 1.1 by helen, Wed Dec 19 14:34:39 2001 UTC revision 1.7 by molod, Tue Jun 27 19:08:22 2006 UTC
# Line 1  Line 1 
1  \section{Example: Surface driven convection}  \section{Surface Driven Convection}
2    \label{www:tutorials}
3  \label{sect:eg-bconv}  \label{sect:eg-bconv}
4    \begin{rawhtml}
5    <!-- CMIREDIR:eg-bconv: -->
6    \end{rawhtml}
7    
8  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
9    
# Line 22  Line 26 
26  for the surface driven convection experiment. The domain is doubly periodic  for the surface driven convection experiment. The domain is doubly periodic
27  with an initially uniform temperature of 20 $^oC$.  with an initially uniform temperature of 20 $^oC$.
28  }  }
29  \label{FIG:simulation_config}  \label{FIG:eg-bconv-simulation_config}
30  \end{figure}  \end{figure}
31    
32  This experiment, figure \ref{FIG:simulation_config}, showcasing MITgcm's non-hydrostatic capability, was designed to explore  This experiment, figure \ref{FIG:eg-bconv-simulation_config}, showcasing MITgcm's non-hydrostatic
33    capability, was designed to explore
34  the temporal and spatial characteristics of convection plumes as they might exist during a  the temporal and spatial characteristics of convection plumes as they might exist during a
35  period of oceanic deep convection. It is  period of oceanic deep convection. The files for this experiment can be found in the verification
36    directory under tutorial\_deep\_convection. It is
37    
38  \begin{itemize}  \begin{itemize}
39  \item non-hydrostatic  \item non-hydrostatic
# Line 39  period of oceanic deep convection. It is Line 45  period of oceanic deep convection. It is
45  \end{itemize}  \end{itemize}
46    
47  \subsection{Overview}  \subsection{Overview}
48    \label{www:tutorials}
49    
50  The model domain consists of an approximately 3  The model domain consists of an approximately 3
51  km square by 1 km deep box of initially  km square by 1 km deep box of initially
# Line 50  uniform reference potential temperature Line 57  uniform reference potential temperature
57  used in this experiment is linear  used in this experiment is linear
58    
59  \begin{equation}  \begin{equation}
60  \label{EQ:linear1_eos}  \label{EQ:eg-bconv-linear1_eos}
61  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
62  \end{equation}  \end{equation}
63    
64  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
65    
66  \begin{equation}  \begin{equation}
67  \label{EQ:linear1_eos_pert}  \label{EQ:eg-bconv-linear1_eos_pert}
68  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
69  \end{equation}  \end{equation}
70    
# Line 72  the quantity that is carried in the mode Line 79  the quantity that is carried in the mode
79  As the fluid in the surface layer is cooled (at a mean rate of 800 Wm$^2$), it becomes  As the fluid in the surface layer is cooled (at a mean rate of 800 Wm$^2$), it becomes
80  convectively unstable and  convectively unstable and
81  overturns, at first close to the grid-scale, but, as the flow matures, on larger scales  overturns, at first close to the grid-scale, but, as the flow matures, on larger scales
82  (figures \ref{FIG:vertsection} and \ref{FIG:horizsection}), under the influence of  (figures \ref{FIG:eg-bconv-vertsection} and \ref{FIG:eg-bconv-horizsection}), under the influence of
83  rotation ($f_o = 10^{-4}$ s$^{-1}$) .  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
84    
85    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
86  \begin{figure}  \begin{figure}
87  \begin{center}  \begin{center}
88   \resizebox{15cm}{10cm}{   \resizebox{15cm}{10cm}{
# Line 83  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 91  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
91  \end{center}  \end{center}
92  \caption{  \caption{
93  }  }
94  \label{FIG:vertsection}  \label{FIG:eg-bconv-vertsection}
95    \label{fig:surf-convection-vertsection}
96  \end{figure}  \end{figure}
97    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
98    
99    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-horizsection\end{rawhtml}
100  \begin{figure}  \begin{figure}
101  \begin{center}  \begin{center}
102   \resizebox{10cm}{10cm}{   \resizebox{10cm}{10cm}{
# Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 105  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
105  \end{center}  \end{center}
106  \caption{  \caption{
107  }  }
108  \label{FIG:horizsection}  \label{FIG:eg-bconv-horizsection}
109    \label{fig:surf-convection-horizsection}
110  \end{figure}  \end{figure}
111    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
112    
113  Model parameters are specified in file {\it input/data}. The grid dimensions are  Model parameters are specified in file {\it input/data}. The grid dimensions are
114  prescribed in {\it code/SIZE.h}. The forcing (file {\it input/Qsurf.bin}) is specified  prescribed in {\it code/SIZE.h}. The forcing (file {\it input/Qsurf.bin}) is specified
115  in a binary data file generated using the Matlab script {\it input/gendata.m}.  in a binary data file generated using the Matlab script {\it input/gendata.m}.
116    
117  \subsection{Equations solved}  \subsection{Equations solved}
118    \label{www:tutorials}
119    
120  The model is configured in nonhydrostatic form, that is, all terms in the Navier  The model is configured in nonhydrostatic form, that is, all terms in the Navier
121  Stokes equations are retained and the pressure field is found, subject to appropriate  Stokes equations are retained and the pressure field is found, subject to appropriate
# Line 111  The implicit free surface form of the Line 125  The implicit free surface form of the
125  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
126  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
127  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,
128  $\theta$, equation (\ref{EQ:global_forcing_ft}). This produces a set of equations  $\theta$, equation (\ref{EQ:eg-bconv-global_forcing_ft}). This produces a set of equations
129  solved in this configuration as follows:  solved in this configuration as follows:
130    
131  \begin{eqnarray}  \begin{eqnarray}
132  \label{EQ:model_equations}  \label{EQ:eg-bconv-model_equations}
133  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
134    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
135    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
# Line 171  equations and continuity (see section \r Line 185  equations and continuity (see section \r
185  \\  \\
186    
187  \subsection{Discrete numerical configuration}  \subsection{Discrete numerical configuration}
188    \label{www:tutorials}
189    
190  The domain is discretised with a uniform grid spacing in each direction. There are 64  The domain is discretised with a uniform grid spacing in each direction. There are 64
191  grid cells in directions $x$ and $y$ and 20 vertical levels thus the domain  grid cells in directions $x$ and $y$ and 20 vertical levels thus the domain
192  comprises a total of just over 80 000 gridpoints.  comprises a total of just over 80 000 gridpoints.
193    
194  \subsection{Numerical stability criteria and other considerations}  \subsection{Numerical stability criteria and other considerations}
195    \label{www:tutorials}
196    
197  For a heat flux of 800 Wm$^2$ and a rotation rate of $10^{-4}$ s$^{-1}$ the  For a heat flux of 800 Wm$^2$ and a rotation rate of $10^{-4}$ s$^{-1}$ the
198  plume-scale can be expected to be a few hundred meters guiding our choice of grid  plume-scale can be expected to be a few hundred meters guiding our choice of grid
# Line 190  For an extreme maximum flow speed of $ | Line 206  For an extreme maximum flow speed of $ |
206  50 m, the implied maximum timestep for stability, $\delta t_u$ is  50 m, the implied maximum timestep for stability, $\delta t_u$ is
207    
208  \begin{eqnarray}  \begin{eqnarray}
209  \label{EQ:advectiveCFLcondition}  \label{EQ:eg-bconv-advectiveCFLcondition}
210  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
211  \end{eqnarray}  \end{eqnarray}
212    
# Line 202  diffusion coefficient $\kappa_h (= Line 218  diffusion coefficient $\kappa_h (=
218  correlated over 50 m.    correlated over 50 m.  
219    
220  \subsection{Experiment configuration}  \subsection{Experiment configuration}
221    \label{www:tutorials}
222    
223  The model configuration for this experiment resides under the directory  The model configuration for this experiment resides under the directory
224  {\it verification/convection/}. The experiment files  {\it verification/convection/}. The experiment files
# Line 218  contain the code customisations and para Line 235  contain the code customisations and para
235  experiment. Below we describe these experiment-specific customisations.  experiment. Below we describe these experiment-specific customisations.
236    
237  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
238    \label{www:tutorials}
239    
240  This file uses standard default values and does not contain  This file uses standard default values and does not contain
241  customisations for this experiment.  customisations for this experiment.
242    
243  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
244    \label{www:tutorials}
245    
246  This file uses standard default values and does not contain  This file uses standard default values and does not contain
247  customisations for this experiment.  customisations for this experiment.
248    
249  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
250    \label{www:tutorials}
251    
252  Three lines are customized in this file. These prescribe the domain grid dimensions.  Three lines are customized in this file. These prescribe the domain grid dimensions.
253  \begin{itemize}  \begin{itemize}
# Line 255  the vertical domain extent in grid point Line 275  the vertical domain extent in grid point
275  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
276    
277  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
278    \label{www:tutorials}
279    
280  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
281  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 264  are Line 285  are
285    
286  \item Line 4,  \item Line 4,
287  \begin{verbatim}  \begin{verbatim}
288       4   tRef=20*20.0,       4   tRef=20*20.0,
289  \end{verbatim}  \end{verbatim}
290  this line sets  this line sets
291  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
292  level in units of $^{\circ}$C. Here the value is arbitrary since, in this case, the  level in units of $^{\circ}\mathrm{C}$. Here the value is arbitrary since, in this case, the
293  flow evolves independently of the absolute magnitude of the reference temperature.  flow evolves independently of the absolute magnitude of the reference temperature.
294  For each depth level the initial and reference profiles will be uniform in  For each depth level the initial and reference profiles will be uniform in
295  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
296  variable  variable
297  {\bf  {\bf
298  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
299  tRef  tRef
300  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
301  }  }
302  in the model code, by procedure  in the model code, by procedure
303  {\it  {\it
304  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
305  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
306  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
307  }  }
308  The temperature field is initialised, by procedure  The temperature field is initialised, by procedure
309  {\it  {\it
310  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
311  S/R INI\_THETA ({\it ini\_theta.F})  S/R INI\_THETA ({\it ini\_theta.F})
312  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
313  }  }
# Line 294  S/R INI\_THETA ({\it ini\_theta.F}) Line 315  S/R INI\_THETA ({\it ini\_theta.F})
315    
316  \item Line 5,  \item Line 5,
317  \begin{verbatim}  \begin{verbatim}
318       5   sRef=20*35.0,       5   sRef=20*35.0,
319  \end{verbatim}  \end{verbatim}
320  this line sets the initial and reference values of salinity at each model  this line sets the initial and reference values of salinity at each model
321  level in units of ppt. In this case salinity is set to an (arbitrary) uniform value of  level in units of ppt. In this case salinity is set to an (arbitrary) uniform value of
# Line 304  tracer. For each depth level the initial Line 325  tracer. For each depth level the initial
325  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
326  variable  variable
327  {\bf  {\bf
328  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
329  sRef  sRef
330  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
331  }  }
332  in the model code, by procedure  in the model code, by procedure
333  {\it  {\it
334  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
335  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
336  }  }
337  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
338  The salinity field is initialised, by procedure  The salinity field is initialised, by procedure
339  {\it  {\it
340  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
341  S/R INI\_SALT ({\it ini\_salt.F})  S/R INI\_SALT ({\it ini\_salt.F})
342  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
343  }  }
# Line 324  S/R INI\_SALT ({\it ini\_salt.F}) Line 345  S/R INI\_SALT ({\it ini\_salt.F})
345    
346  \item Line 6,  \item Line 6,
347  \begin{verbatim}  \begin{verbatim}
348       6   viscAh=0.1,       6   viscAh=0.1,
349  \end{verbatim}  \end{verbatim}
350  this line sets the horizontal laplacian dissipation coefficient to  this line sets the horizontal laplacian dissipation coefficient to
351  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
352  for this operator are specified later.  for this operator are specified later.
353  The variable  The variable
354  {\bf  {\bf
355  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
356  viscAh  viscAh
357  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
358  }  }
359  is read in the routine  is read in the routine
360  {\it  {\it
361  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
362  S/R INI\_PARMS ({\it ini\_params.F})  S/R INI\_PARMS ({\it ini\_params.F})
363  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
364  } and applied in routines  } and applied in routines
365  {\it  {\it
366  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
367  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
368  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
369  } and  } and
370  {\it  {\it
371  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
372  S/R CALC\_GW ({\it calc\_gw.F})  S/R CALC\_GW ({\it calc\_gw.F})
373  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
374  }.  }.
# Line 355  S/R CALC\_GW ({\it calc\_gw.F}) Line 376  S/R CALC\_GW ({\it calc\_gw.F})
376    
377  \item Line 7,  \item Line 7,
378  \begin{verbatim}  \begin{verbatim}
379       7   viscAz=0.1,       7   viscAz=0.1,
380  \end{verbatim}  \end{verbatim}
381  this line sets the vertical laplacian frictional dissipation coefficient to  this line sets the vertical laplacian frictional dissipation coefficient to
382  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
383  for this operator are specified later.  for this operator are specified later.
384  The variable  The variable
385  {\bf  {\bf
386  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
387  viscAz  viscAz
388  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
389  }  }
390  is read in the routine  is read in the routine
391  {\it  {\it
392  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
393  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
394  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
395  }  }
396  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
397  {\bf  {\bf
398  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
399  viscAr  viscAr
400  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
401  }. At each time step, the viscous term contribution to the momentum equations  }. At each time step, the viscous term contribution to the momentum equations
402  is calculated in routine  is calculated in routine
403  {\it  {\it
404  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
405  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
406  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
407  }.  }.
# Line 396  e.g. $\frac{\partial u}{\partial y}$=0 a Line 417  e.g. $\frac{\partial u}{\partial y}$=0 a
417  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
418  The variable  The variable
419  {\bf  {\bf
420  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
421  no\_slip\_sides  no\_slip\_sides
422  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
423  }  }
424  is read in the routine  is read in the routine
425  {\it  {\it
426  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
427  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
428  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
429  } and the boundary condition is evaluated in routine  } and the boundary condition is evaluated in routine
430  {\it  {\it
431  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
432  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
433  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
434  }.  }.
# Line 422  boundary condition in the vertical lapla Line 443  boundary condition in the vertical lapla
443  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.
444  The variable  The variable
445  {\bf  {\bf
446  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
447  no\_slip\_bottom  no\_slip\_bottom
448  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
449  }  }
450  is read in the routine  is read in the routine
451  {\it  {\it
452  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
453  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
454  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
455  } and is applied in the routine  } and is applied in the routine
456  {\it  {\it
457  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
458  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
459  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
460  }.  }.
# Line 448  operator is $\frac{\partial}{\partial x} Line 469  operator is $\frac{\partial}{\partial x}
469  all boundaries.  all boundaries.
470  The variable  The variable
471  {\bf  {\bf
472  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
473  diffKhT  diffKhT
474  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
475  }  }
476  is read in the routine  is read in the routine
477  {\it  {\it
478  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
479  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
480  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
481  } and used in routine  } and used in routine
482  {\it  {\it
483  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
484  S/R CALC\_GT ({\it calc\_gt.F})  S/R CALC\_GT ({\it calc\_gt.F})
485  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
486  }.  }.
# Line 473  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 494  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
494  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
495  The variable  The variable
496  {\bf  {\bf
497  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
498  diffKzT  diffKzT
499  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
500  }  }
501  is read in the routine  is read in the routine
502  {\it  {\it
503  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
504  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
505  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
506  }.  }.
507  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
508  {\bf  {\bf
509  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
510  diffKrT  diffKrT
511  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
512  } which is used in routine  } which is used in routine
513  {\it  {\it
514  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
515  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
516  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
517  }.  }.
# Line 506  operator is $\frac{\partial}{\partial x} Line 527  operator is $\frac{\partial}{\partial x}
527  all boundaries.  all boundaries.
528  The variable  The variable
529  {\bf  {\bf
530  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
531  diffKsT  diffKsT
532  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
533  }  }
534  is read in the routine  is read in the routine
535  {\it  {\it
536  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
537  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
538  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
539  } and used in routine  } and used in routine
540  {\it  {\it
541  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
542  S/R CALC\_GS ({\it calc\_gs.F})  S/R CALC\_GS ({\it calc\_gs.F})
543  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
544  }.  }.
# Line 532  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 553  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
553  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
554  The variable  The variable
555  {\bf  {\bf
556  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
557  diffKzS  diffKzS
558  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
559  }  }
560  is read in the routine  is read in the routine
561  {\it  {\it
562  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
563  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
564  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
565  }.  }.
566  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
567  {\bf  {\bf
568  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
569  diffKrS  diffKrS
570  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
571  } which is used in routine  } which is used in 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  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
575  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
576  }.  }.
# Line 578  This line sets the thermal expansion coe Line 599  This line sets the thermal expansion coe
599  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.
600  The variable  The variable
601  {\bf  {\bf
602  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
603  tAlpha  tAlpha
604  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
605  }  }
606  is read in the routine  is read in the routine
607  {\it  {\it
608  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
609  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
610  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
611  }.  }.
612  The routine  The routine
613  {\it  {\it
614  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
615  S/R FIND\_RHO ({\it find\_rho.F})  S/R FIND\_RHO ({\it find\_rho.F})
616  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
617  } makes use of {\bf tAlpha}.  } makes use of {\bf tAlpha}.
# Line 656  This line sets the  maximum number of it Line 677  This line sets the  maximum number of it
677  gradient solver will use to 40, {\bf irrespective of the convergence  gradient solver will use to 40, {\bf irrespective of the convergence
678  criteria being met}. Used in routine  criteria being met}. Used in routine
679  {\it  {\it
680  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
681  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
682  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
683  }.  }.
# Line 669  cg3dTargetResidual=1.E-9, Line 690  cg3dTargetResidual=1.E-9,
690  \end{verbatim}  \end{verbatim}
691  Sets the tolerance which the three-dimensional, conjugate  Sets the tolerance which the three-dimensional, conjugate
692  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
693  \ref{EQ:congrad_3d_resid} to $1 \times 10^{-9}$.  \ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.
694  The solver will iterate until the  The solver will iterate until the
695  tolerance falls below this value or until the maximum number of  tolerance falls below this value or until the maximum number of
696  solver iterations is reached. Used in routine  solver iterations is reached. Used in routine
697  {\it  {\it
698  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
699  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
700  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
701  }.  }.
# Line 743  to high coordinate for both axes. The ma Line 764  to high coordinate for both axes. The ma
764  surface heat flux file used in the example.  surface heat flux file used in the example.
765  The variable  The variable
766  {\bf  {\bf
767  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
768  Qsurf  Qsurf
769  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
770  }  }
771  is read in the routine  is read in the routine
772  {\it  {\it
773  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
774  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
775  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
776  }  }
777  and applied in    and applied in  
778  {\it  {\it
779  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
780  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})
781  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
782  } where the flux is converted to a temperature tendency.  } where the flux is converted to a temperature tendency.
# Line 772  S/R EXTERNAL\_FORCING\_SURF ({\it extern Line 793  S/R EXTERNAL\_FORCING\_SURF ({\it extern
793    
794    
795  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
796    \label{www:tutorials}
797    
798  This file uses standard default values and does not contain  This file uses standard default values and does not contain
799  customisations for this experiment.  customisations for this experiment.
800    
801  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
802    \label{www:tutorials}
803    
804  This file uses standard default values and does not contain  This file uses standard default values and does not contain
805  customisations for this experiment.  customisations for this experiment.
806    
807    
808  \subsubsection{File {\it input/Qsurf.bin}}  \subsubsection{File {\it input/Qsurf.bin}}
809    \label{www:tutorials}
810    
811  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)
812  map of heat flux values where  map of heat flux values where
# Line 801  directed upwards, according to the model Line 825  directed upwards, according to the model
825  \end{center}  \end{center}
826  \caption{  \caption{
827  }  }
828  \label{FIG:Qsurf}  \label{FIG:eg-bconv-Qsurf}
829  \end{figure}  \end{figure}
830    
831  \subsection{Running the example}  \subsection{Running the example}
832    \label{www:tutorials}
833    
834  \subsubsection{Code download}  \subsubsection{Code download}
835    \label{www:tutorials}
836    
837  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.
838  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.
839    
840  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
841    \label{www:tutorials}
842    
843   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
844    
# Line 819  Instructions for downloading the code ca Line 846  Instructions for downloading the code ca
846  {\it verification/convection/ }  {\it verification/convection/ }
847    
848  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
849    \label{www:tutorials}
850    
851   To run the experiment   To run the experiment
852    
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