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revision 1.1 by helen, Wed Dec 19 14:34:39 2001 UTC revision 1.8 by jmc, Tue Jan 15 18:11:50 2008 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    \begin{center}
8    (in directory: {\it verification/tutorial\_deep\_convection/})
9    \end{center}
10    
11  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
12    
# Line 22  Line 29 
29  for the surface driven convection experiment. The domain is doubly periodic  for the surface driven convection experiment. The domain is doubly periodic
30  with an initially uniform temperature of 20 $^oC$.  with an initially uniform temperature of 20 $^oC$.
31  }  }
32  \label{FIG:simulation_config}  \label{FIG:eg-bconv-simulation_config}
33  \end{figure}  \end{figure}
34    
35  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
36    capability, was designed to explore
37  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
38  period of oceanic deep convection. It is  period of oceanic deep convection. The files for this experiment can be found in the verification
39    directory under tutorial\_deep\_convection. It is
40    
41  \begin{itemize}  \begin{itemize}
42  \item non-hydrostatic  \item non-hydrostatic
# Line 39  period of oceanic deep convection. It is Line 48  period of oceanic deep convection. It is
48  \end{itemize}  \end{itemize}
49    
50  \subsection{Overview}  \subsection{Overview}
51    \label{www:tutorials}
52    
53  The model domain consists of an approximately 3  The model domain consists of an approximately 3
54  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 60  uniform reference potential temperature
60  used in this experiment is linear  used in this experiment is linear
61    
62  \begin{equation}  \begin{equation}
63  \label{EQ:linear1_eos}  \label{EQ:eg-bconv-linear1_eos}
64  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
65  \end{equation}  \end{equation}
66    
67  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
68    
69  \begin{equation}  \begin{equation}
70  \label{EQ:linear1_eos_pert}  \label{EQ:eg-bconv-linear1_eos_pert}
71  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
72  \end{equation}  \end{equation}
73    
# Line 72  the quantity that is carried in the mode Line 82  the quantity that is carried in the mode
82  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
83  convectively unstable and  convectively unstable and
84  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
85  (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
86  rotation ($f_o = 10^{-4}$ s$^{-1}$) .  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
87    
88    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
89  \begin{figure}  \begin{figure}
90  \begin{center}  \begin{center}
91   \resizebox{15cm}{10cm}{   \resizebox{15cm}{10cm}{
# Line 83  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
94  \end{center}  \end{center}
95  \caption{  \caption{
96  }  }
97  \label{FIG:vertsection}  \label{FIG:eg-bconv-vertsection}
98    \label{fig:surf-convection-vertsection}
99  \end{figure}  \end{figure}
100    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
101    
102    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-horizsection\end{rawhtml}
103  \begin{figure}  \begin{figure}
104  \begin{center}  \begin{center}
105   \resizebox{10cm}{10cm}{   \resizebox{10cm}{10cm}{
# Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 108  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
108  \end{center}  \end{center}
109  \caption{  \caption{
110  }  }
111  \label{FIG:horizsection}  \label{FIG:eg-bconv-horizsection}
112    \label{fig:surf-convection-horizsection}
113  \end{figure}  \end{figure}
114    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
115    
116  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
117  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
118  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}.
119    
120  \subsection{Equations solved}  \subsection{Equations solved}
121    \label{www:tutorials}
122    
123  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
124  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 128  The implicit free surface form of the
128  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
129  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
130  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,
131  $\theta$, 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
132  solved in this configuration as follows:  solved in this configuration as follows:
133    
134  \begin{eqnarray}  \begin{eqnarray}
135  \label{EQ:model_equations}  \label{EQ:eg-bconv-model_equations}
136  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
137    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
138    \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 188  equations and continuity (see section \r
188  \\  \\
189    
190  \subsection{Discrete numerical configuration}  \subsection{Discrete numerical configuration}
191    \label{www:tutorials}
192    
193  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
194  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
195  comprises a total of just over 80 000 gridpoints.  comprises a total of just over 80 000 gridpoints.
196    
197  \subsection{Numerical stability criteria and other considerations}  \subsection{Numerical stability criteria and other considerations}
198    \label{www:tutorials}
199    
200  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
201  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 209  For an extreme maximum flow speed of $ |
209  50 m, the implied maximum timestep for stability, $\delta t_u$ is  50 m, the implied maximum timestep for stability, $\delta t_u$ is
210    
211  \begin{eqnarray}  \begin{eqnarray}
212  \label{EQ:advectiveCFLcondition}  \label{EQ:eg-bconv-advectiveCFLcondition}
213  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
214  \end{eqnarray}  \end{eqnarray}
215    
# Line 202  diffusion coefficient $\kappa_h (= Line 221  diffusion coefficient $\kappa_h (=
221  correlated over 50 m.    correlated over 50 m.  
222    
223  \subsection{Experiment configuration}  \subsection{Experiment configuration}
224    \label{www:tutorials}
225    
226  The model configuration for this experiment resides under the directory  The model configuration for this experiment resides under the directory
227  {\it verification/convection/}. The experiment files  {\it verification/convection/}. The experiment files
# Line 218  contain the code customisations and para Line 238  contain the code customisations and para
238  experiment. Below we describe these experiment-specific customisations.  experiment. Below we describe these experiment-specific customisations.
239    
240  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
241    \label{www:tutorials}
242    
243  This file uses standard default values and does not contain  This file uses standard default values and does not contain
244  customisations for this experiment.  customisations for this experiment.
245    
246  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
247    \label{www:tutorials}
248    
249  This file uses standard default values and does not contain  This file uses standard default values and does not contain
250  customisations for this experiment.  customisations for this experiment.
251    
252  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
253    \label{www:tutorials}
254    
255  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.
256  \begin{itemize}  \begin{itemize}
# Line 255  the vertical domain extent in grid point Line 278  the vertical domain extent in grid point
278  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
279    
280  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
281    \label{www:tutorials}
282    
283  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
284  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 288  are
288    
289  \item Line 4,  \item Line 4,
290  \begin{verbatim}  \begin{verbatim}
291       4   tRef=20*20.0,       4   tRef=20*20.0,
292  \end{verbatim}  \end{verbatim}
293  this line sets  this line sets
294  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
295  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
296  flow evolves independently of the absolute magnitude of the reference temperature.  flow evolves independently of the absolute magnitude of the reference temperature.
297  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
298  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
299  variable  variable
300  {\bf  {\bf
301  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
302  tRef  tRef
303  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
304  }  }
305  in the model code, by procedure  in the model code, by procedure
306  {\it  {\it
307  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
308  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
309  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
310  }  }
311  The temperature field is initialised, by procedure  The temperature field is initialised, by procedure
312  {\it  {\it
313  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
314  S/R INI\_THETA ({\it ini\_theta.F})  S/R INI\_THETA ({\it ini\_theta.F})
315  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
316  }  }
# Line 294  S/R INI\_THETA ({\it ini\_theta.F}) Line 318  S/R INI\_THETA ({\it ini\_theta.F})
318    
319  \item Line 5,  \item Line 5,
320  \begin{verbatim}  \begin{verbatim}
321       5   sRef=20*35.0,       5   sRef=20*35.0,
322  \end{verbatim}  \end{verbatim}
323  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
324  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 328  tracer. For each depth level the initial
328  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
329  variable  variable
330  {\bf  {\bf
331  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
332  sRef  sRef
333  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
334  }  }
335  in the model code, by procedure  in the model code, by procedure
336  {\it  {\it
337  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
338  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
339  }  }
340  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
341  The salinity field is initialised, by procedure  The salinity field is initialised, by procedure
342  {\it  {\it
343  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
344  S/R INI\_SALT ({\it ini\_salt.F})  S/R INI\_SALT ({\it ini\_salt.F})
345  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
346  }  }
# Line 324  S/R INI\_SALT ({\it ini\_salt.F}) Line 348  S/R INI\_SALT ({\it ini\_salt.F})
348    
349  \item Line 6,  \item Line 6,
350  \begin{verbatim}  \begin{verbatim}
351       6   viscAh=0.1,       6   viscAh=0.1,
352  \end{verbatim}  \end{verbatim}
353  this line sets the horizontal laplacian dissipation coefficient to  this line sets the horizontal laplacian dissipation coefficient to
354  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
355  for this operator are specified later.  for this operator are specified later.
356  The variable  The variable
357  {\bf  {\bf
358  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
359  viscAh  viscAh
360  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
361  }  }
362  is read in the routine  is read in the routine
363  {\it  {\it
364  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
365  S/R INI\_PARMS ({\it ini\_params.F})  S/R INI\_PARMS ({\it ini\_params.F})
366  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
367  } and applied in routines  } and applied in routines
368  {\it  {\it
369  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
370  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
371  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
372  } and  } and
373  {\it  {\it
374  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
375  S/R CALC\_GW ({\it calc\_gw.F})  S/R CALC\_GW ({\it calc\_gw.F})
376  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
377  }.  }.
# Line 355  S/R CALC\_GW ({\it calc\_gw.F}) Line 379  S/R CALC\_GW ({\it calc\_gw.F})
379    
380  \item Line 7,  \item Line 7,
381  \begin{verbatim}  \begin{verbatim}
382       7   viscAz=0.1,       7   viscAz=0.1,
383  \end{verbatim}  \end{verbatim}
384  this line sets the vertical laplacian frictional dissipation coefficient to  this line sets the vertical laplacian frictional dissipation coefficient to
385  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
386  for this operator are specified later.  for this operator are specified later.
387  The variable  The variable
388  {\bf  {\bf
389  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
390  viscAz  viscAz
391  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
392  }  }
393  is read in the routine  is read in the routine
394  {\it  {\it
395  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
396  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
397  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
398  }  }
399  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
400  {\bf  {\bf
401  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
402  viscAr  viscAr
403  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
404  }. At each time step, the viscous term contribution to the momentum equations  }. At each time step, the viscous term contribution to the momentum equations
405  is calculated in routine  is calculated in routine
406  {\it  {\it
407  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
408  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
409  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
410  }.  }.
# Line 396  e.g. $\frac{\partial u}{\partial y}$=0 a Line 420  e.g. $\frac{\partial u}{\partial y}$=0 a
420  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
421  The variable  The variable
422  {\bf  {\bf
423  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
424  no\_slip\_sides  no\_slip\_sides
425  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
426  }  }
427  is read in the routine  is read in the routine
428  {\it  {\it
429  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
430  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
431  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
432  } and the boundary condition is evaluated in routine  } and the boundary condition is evaluated in routine
433  {\it  {\it
434  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
435  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
436  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
437  }.  }.
# Line 422  boundary condition in the vertical lapla Line 446  boundary condition in the vertical lapla
446  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.
447  The variable  The variable
448  {\bf  {\bf
449  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
450  no\_slip\_bottom  no\_slip\_bottom
451  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
452  }  }
453  is read in the routine  is read in the routine
454  {\it  {\it
455  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
456  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
457  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
458  } and is applied in the routine  } and is applied in the routine
459  {\it  {\it
460  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
461  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
462  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
463  }.  }.
# Line 448  operator is $\frac{\partial}{\partial x} Line 472  operator is $\frac{\partial}{\partial x}
472  all boundaries.  all boundaries.
473  The variable  The variable
474  {\bf  {\bf
475  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
476  diffKhT  diffKhT
477  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
478  }  }
479  is read in the routine  is read in the routine
480  {\it  {\it
481  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
482  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
483  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
484  } and used in routine  } and used in routine
485  {\it  {\it
486  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
487  S/R CALC\_GT ({\it calc\_gt.F})  S/R CALC\_GT ({\it calc\_gt.F})
488  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
489  }.  }.
# Line 473  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 497  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
497  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
498  The variable  The variable
499  {\bf  {\bf
500  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
501  diffKzT  diffKzT
502  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
503  }  }
504  is read in the routine  is read in the routine
505  {\it  {\it
506  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
507  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
508  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
509  }.  }.
510  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
511  {\bf  {\bf
512  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
513  diffKrT  diffKrT
514  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
515  } which is used in routine  } which is used in routine
516  {\it  {\it
517  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
518  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
519  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
520  }.  }.
# Line 506  operator is $\frac{\partial}{\partial x} Line 530  operator is $\frac{\partial}{\partial x}
530  all boundaries.  all boundaries.
531  The variable  The variable
532  {\bf  {\bf
533  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
534  diffKsT  diffKsT
535  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
536  }  }
537  is read in the routine  is read in the routine
538  {\it  {\it
539  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
540  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
541  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
542  } and used in routine  } and used in routine
543  {\it  {\it
544  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
545  S/R CALC\_GS ({\it calc\_gs.F})  S/R CALC\_GS ({\it calc\_gs.F})
546  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
547  }.  }.
# Line 532  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 556  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
556  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
557  The variable  The variable
558  {\bf  {\bf
559  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
560  diffKzS  diffKzS
561  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
562  }  }
563  is read in the routine  is read in the routine
564  {\it  {\it
565  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
566  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
567  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
568  }.  }.
569  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
570  {\bf  {\bf
571  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
572  diffKrS  diffKrS
573  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
574  } which is used in routine  } which is used in routine
575  {\it  {\it
576  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
577  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
578  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
579  }.  }.
# Line 578  This line sets the thermal expansion coe Line 602  This line sets the thermal expansion coe
602  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.
603  The variable  The variable
604  {\bf  {\bf
605  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
606  tAlpha  tAlpha
607  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
608  }  }
609  is read in the routine  is read in the routine
610  {\it  {\it
611  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
612  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
613  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
614  }.  }.
615  The routine  The routine
616  {\it  {\it
617  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
618  S/R FIND\_RHO ({\it find\_rho.F})  S/R FIND\_RHO ({\it find\_rho.F})
619  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
620  } makes use of {\bf tAlpha}.  } makes use of {\bf tAlpha}.
# Line 656  This line sets the  maximum number of it Line 680  This line sets the  maximum number of it
680  gradient solver will use to 40, {\bf irrespective of the convergence  gradient solver will use to 40, {\bf irrespective of the convergence
681  criteria being met}. Used in routine  criteria being met}. Used in routine
682  {\it  {\it
683  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
684  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
685  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
686  }.  }.
# Line 669  cg3dTargetResidual=1.E-9, Line 693  cg3dTargetResidual=1.E-9,
693  \end{verbatim}  \end{verbatim}
694  Sets the tolerance which the three-dimensional, conjugate  Sets the tolerance which the three-dimensional, conjugate
695  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
696  \ref{EQ:congrad_3d_resid} to $1 \times 10^{-9}$.  \ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.
697  The solver will iterate until the  The solver will iterate until the
698  tolerance falls below this value or until the maximum number of  tolerance falls below this value or until the maximum number of
699  solver iterations is reached. Used in routine  solver iterations is reached. Used in 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  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
703  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
704  }.  }.
# Line 743  to high coordinate for both axes. The ma Line 767  to high coordinate for both axes. The ma
767  surface heat flux file used in the example.  surface heat flux file used in the example.
768  The variable  The variable
769  {\bf  {\bf
770  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
771  Qsurf  Qsurf
772  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
773  }  }
774  is read in the routine  is read in the routine
775  {\it  {\it
776  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
777  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
778  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
779  }  }
780  and applied in    and applied in  
781  {\it  {\it
782  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
783  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})
784  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
785  } 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 796  S/R EXTERNAL\_FORCING\_SURF ({\it extern
796    
797    
798  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
799    \label{www:tutorials}
800    
801  This file uses standard default values and does not contain  This file uses standard default values and does not contain
802  customisations for this experiment.  customisations for this experiment.
803    
804  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
805    \label{www:tutorials}
806    
807  This file uses standard default values and does not contain  This file uses standard default values and does not contain
808  customisations for this experiment.  customisations for this experiment.
809    
810    
811  \subsubsection{File {\it input/Qsurf.bin}}  \subsubsection{File {\it input/Qsurf.bin}}
812    \label{www:tutorials}
813    
814  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)
815  map of heat flux values where  map of heat flux values where
# Line 801  directed upwards, according to the model Line 828  directed upwards, according to the model
828  \end{center}  \end{center}
829  \caption{  \caption{
830  }  }
831  \label{FIG:Qsurf}  \label{FIG:eg-bconv-Qsurf}
832  \end{figure}  \end{figure}
833    
834  \subsection{Running the example}  \subsection{Running the example}
835    \label{www:tutorials}
836    
837  \subsubsection{Code download}  \subsubsection{Code download}
838    \label{www:tutorials}
839    
840  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.
841  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.
842    
843  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
844    \label{www:tutorials}
845    
846   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
847    
# Line 819  Instructions for downloading the code ca Line 849  Instructions for downloading the code ca
849  {\it verification/convection/ }  {\it verification/convection/ }
850    
851  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
852    \label{www:tutorials}
853    
854   To run the experiment   To run the experiment
855    
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