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revision 1.1 by helen, Wed Dec 19 14:34:39 2001 UTC revision 1.5 by edhill, Sat Oct 16 03:40:13 2004 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 capability, was designed to explore
33  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
34  period of oceanic deep convection. It is  period of oceanic deep convection. It is
35    
# Line 39  period of oceanic deep convection. It is Line 43  period of oceanic deep convection. It is
43  \end{itemize}  \end{itemize}
44    
45  \subsection{Overview}  \subsection{Overview}
46    \label{www:tutorials}
47    
48  The model domain consists of an approximately 3  The model domain consists of an approximately 3
49  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 55  uniform reference potential temperature
55  used in this experiment is linear  used in this experiment is linear
56    
57  \begin{equation}  \begin{equation}
58  \label{EQ:linear1_eos}  \label{EQ:eg-bconv-linear1_eos}
59  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
60  \end{equation}  \end{equation}
61    
62  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
63    
64  \begin{equation}  \begin{equation}
65  \label{EQ:linear1_eos_pert}  \label{EQ:eg-bconv-linear1_eos_pert}
66  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
67  \end{equation}  \end{equation}
68    
# Line 72  the quantity that is carried in the mode Line 77  the quantity that is carried in the mode
77  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
78  convectively unstable and  convectively unstable and
79  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
80  (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
81  rotation ($f_o = 10^{-4}$ s$^{-1}$) .  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
82    
83    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
84  \begin{figure}  \begin{figure}
85  \begin{center}  \begin{center}
86   \resizebox{15cm}{10cm}{   \resizebox{15cm}{10cm}{
# Line 83  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 89  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
89  \end{center}  \end{center}
90  \caption{  \caption{
91  }  }
92  \label{FIG:vertsection}  \label{FIG:eg-bconv-vertsection}
93    \label{fig:surf-convection-vertsection}
94  \end{figure}  \end{figure}
95    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
96    
97    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-horizsection\end{rawhtml}
98  \begin{figure}  \begin{figure}
99  \begin{center}  \begin{center}
100   \resizebox{10cm}{10cm}{   \resizebox{10cm}{10cm}{
# Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 103  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
103  \end{center}  \end{center}
104  \caption{  \caption{
105  }  }
106  \label{FIG:horizsection}  \label{FIG:eg-bconv-horizsection}
107    \label{fig:surf-convection-horizsection}
108  \end{figure}  \end{figure}
109    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
110    
111  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
112  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
113  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}.
114    
115  \subsection{Equations solved}  \subsection{Equations solved}
116    \label{www:tutorials}
117    
118  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
119  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 123  The implicit free surface form of the
123  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
124  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
125  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,
126  $\theta$, 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
127  solved in this configuration as follows:  solved in this configuration as follows:
128    
129  \begin{eqnarray}  \begin{eqnarray}
130  \label{EQ:model_equations}  \label{EQ:eg-bconv-model_equations}
131  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
132    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
133    \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 183  equations and continuity (see section \r
183  \\  \\
184    
185  \subsection{Discrete numerical configuration}  \subsection{Discrete numerical configuration}
186    \label{www:tutorials}
187    
188  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
189  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
190  comprises a total of just over 80 000 gridpoints.  comprises a total of just over 80 000 gridpoints.
191    
192  \subsection{Numerical stability criteria and other considerations}  \subsection{Numerical stability criteria and other considerations}
193    \label{www:tutorials}
194    
195  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
196  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 204  For an extreme maximum flow speed of $ |
204  50 m, the implied maximum timestep for stability, $\delta t_u$ is  50 m, the implied maximum timestep for stability, $\delta t_u$ is
205    
206  \begin{eqnarray}  \begin{eqnarray}
207  \label{EQ:advectiveCFLcondition}  \label{EQ:eg-bconv-advectiveCFLcondition}
208  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
209  \end{eqnarray}  \end{eqnarray}
210    
# Line 202  diffusion coefficient $\kappa_h (= Line 216  diffusion coefficient $\kappa_h (=
216  correlated over 50 m.    correlated over 50 m.  
217    
218  \subsection{Experiment configuration}  \subsection{Experiment configuration}
219    \label{www:tutorials}
220    
221  The model configuration for this experiment resides under the directory  The model configuration for this experiment resides under the directory
222  {\it verification/convection/}. The experiment files  {\it verification/convection/}. The experiment files
# Line 218  contain the code customisations and para Line 233  contain the code customisations and para
233  experiment. Below we describe these experiment-specific customisations.  experiment. Below we describe these experiment-specific customisations.
234    
235  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
236    \label{www:tutorials}
237    
238  This file uses standard default values and does not contain  This file uses standard default values and does not contain
239  customisations for this experiment.  customisations for this experiment.
240    
241  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
242    \label{www:tutorials}
243    
244  This file uses standard default values and does not contain  This file uses standard default values and does not contain
245  customisations for this experiment.  customisations for this experiment.
246    
247  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
248    \label{www:tutorials}
249    
250  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.
251  \begin{itemize}  \begin{itemize}
# Line 255  the vertical domain extent in grid point Line 273  the vertical domain extent in grid point
273  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
274    
275  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
276    \label{www:tutorials}
277    
278  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
279  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 283  are
283    
284  \item Line 4,  \item Line 4,
285  \begin{verbatim}  \begin{verbatim}
286       4   tRef=20*20.0,       4   tRef=20*20.0,
287  \end{verbatim}  \end{verbatim}
288  this line sets  this line sets
289  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
# Line 274  For each depth level the initial and ref Line 293  For each depth level the initial and ref
293  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
294  variable  variable
295  {\bf  {\bf
296  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
297  tRef  tRef
298  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
299  }  }
300  in the model code, by procedure  in the model code, by procedure
301  {\it  {\it
302  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
303  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
304  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
305  }  }
306  The temperature field is initialised, by procedure  The temperature field is initialised, by procedure
307  {\it  {\it
308  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
309  S/R INI\_THETA ({\it ini\_theta.F})  S/R INI\_THETA ({\it ini\_theta.F})
310  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
311  }  }
# Line 294  S/R INI\_THETA ({\it ini\_theta.F}) Line 313  S/R INI\_THETA ({\it ini\_theta.F})
313    
314  \item Line 5,  \item Line 5,
315  \begin{verbatim}  \begin{verbatim}
316       5   sRef=20*35.0,       5   sRef=20*35.0,
317  \end{verbatim}  \end{verbatim}
318  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
319  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 323  tracer. For each depth level the initial
323  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
324  variable  variable
325  {\bf  {\bf
326  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
327  sRef  sRef
328  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
329  }  }
330  in the model code, by procedure  in the model code, by procedure
331  {\it  {\it
332  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
333  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
334  }  }
335  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
336  The salinity field is initialised, by procedure  The salinity field is initialised, by procedure
337  {\it  {\it
338  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
339  S/R INI\_SALT ({\it ini\_salt.F})  S/R INI\_SALT ({\it ini\_salt.F})
340  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
341  }  }
# Line 324  S/R INI\_SALT ({\it ini\_salt.F}) Line 343  S/R INI\_SALT ({\it ini\_salt.F})
343    
344  \item Line 6,  \item Line 6,
345  \begin{verbatim}  \begin{verbatim}
346       6   viscAh=0.1,       6   viscAh=0.1,
347  \end{verbatim}  \end{verbatim}
348  this line sets the horizontal laplacian dissipation coefficient to  this line sets the horizontal laplacian dissipation coefficient to
349  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
350  for this operator are specified later.  for this operator are specified later.
351  The variable  The variable
352  {\bf  {\bf
353  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
354  viscAh  viscAh
355  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
356  }  }
357  is read in the routine  is read in the routine
358  {\it  {\it
359  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
360  S/R INI\_PARMS ({\it ini\_params.F})  S/R INI\_PARMS ({\it ini\_params.F})
361  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
362  } and applied in routines  } and applied in routines
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 CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
366  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
367  } and  } and
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\_GW ({\it calc\_gw.F})  S/R CALC\_GW ({\it calc\_gw.F})
371  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
372  }.  }.
# Line 355  S/R CALC\_GW ({\it calc\_gw.F}) Line 374  S/R CALC\_GW ({\it calc\_gw.F})
374    
375  \item Line 7,  \item Line 7,
376  \begin{verbatim}  \begin{verbatim}
377       7   viscAz=0.1,       7   viscAz=0.1,
378  \end{verbatim}  \end{verbatim}
379  this line sets the vertical laplacian frictional dissipation coefficient to  this line sets the vertical laplacian frictional dissipation coefficient to
380  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
381  for this operator are specified later.  for this operator are specified later.
382  The variable  The variable
383  {\bf  {\bf
384  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
385  viscAz  viscAz
386  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
387  }  }
388  is read in the routine  is read in the routine
389  {\it  {\it
390  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
391  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
392  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
393  }  }
394  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
395  {\bf  {\bf
396  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
397  viscAr  viscAr
398  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
399  }. At each time step, the viscous term contribution to the momentum equations  }. At each time step, the viscous term contribution to the momentum equations
400  is calculated in routine  is calculated in routine
401  {\it  {\it
402  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
403  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
404  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
405  }.  }.
# Line 396  e.g. $\frac{\partial u}{\partial y}$=0 a Line 415  e.g. $\frac{\partial u}{\partial y}$=0 a
415  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
416  The variable  The variable
417  {\bf  {\bf
418  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
419  no\_slip\_sides  no\_slip\_sides
420  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
421  }  }
422  is read in the routine  is read in the routine
423  {\it  {\it
424  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
425  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
426  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
427  } and the boundary condition is evaluated in routine  } and the boundary condition is evaluated in 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 CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
431  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
432  }.  }.
# Line 422  boundary condition in the vertical lapla Line 441  boundary condition in the vertical lapla
441  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.
442  The variable  The variable
443  {\bf  {\bf
444  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
445  no\_slip\_bottom  no\_slip\_bottom
446  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
447  }  }
448  is read in the routine  is read in the routine
449  {\it  {\it
450  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
451  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
452  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
453  } and is applied in the routine  } and is applied 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 CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
457  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
458  }.  }.
# Line 448  operator is $\frac{\partial}{\partial x} Line 467  operator is $\frac{\partial}{\partial x}
467  all boundaries.  all boundaries.
468  The variable  The variable
469  {\bf  {\bf
470  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
471  diffKhT  diffKhT
472  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
473  }  }
474  is read in the routine  is read in the routine
475  {\it  {\it
476  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
477  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
478  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
479  } and used in routine  } and used in 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 CALC\_GT ({\it calc\_gt.F})  S/R CALC\_GT ({\it calc\_gt.F})
483  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
484  }.  }.
# Line 473  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 492  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
492  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
493  The variable  The variable
494  {\bf  {\bf
495  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
496  diffKzT  diffKzT
497  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
498  }  }
499  is read in the routine  is read in the routine
500  {\it  {\it
501  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
502  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
503  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
504  }.  }.
505  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
506  {\bf  {\bf
507  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
508  diffKrT  diffKrT
509  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
510  } which is used in routine  } which is used in routine
511  {\it  {\it
512  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
513  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
514  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
515  }.  }.
# Line 506  operator is $\frac{\partial}{\partial x} Line 525  operator is $\frac{\partial}{\partial x}
525  all boundaries.  all boundaries.
526  The variable  The variable
527  {\bf  {\bf
528  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
529  diffKsT  diffKsT
530  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
531  }  }
532  is read in the routine  is read in the routine
533  {\it  {\it
534  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
535  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
536  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
537  } and used in routine  } and used in 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 CALC\_GS ({\it calc\_gs.F})  S/R CALC\_GS ({\it calc\_gs.F})
541  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
542  }.  }.
# Line 532  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 551  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
551  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
552  The variable  The variable
553  {\bf  {\bf
554  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
555  diffKzS  diffKzS
556  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
557  }  }
558  is read in the routine  is read in the routine
559  {\it  {\it
560  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
561  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
562  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
563  }.  }.
564  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
565  {\bf  {\bf
566  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
567  diffKrS  diffKrS
568  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
569  } which is used in routine  } which is used in routine
570  {\it  {\it
571  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
572  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
573  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
574  }.  }.
# Line 578  This line sets the thermal expansion coe Line 597  This line sets the thermal expansion coe
597  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.
598  The variable  The variable
599  {\bf  {\bf
600  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
601  tAlpha  tAlpha
602  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
603  }  }
604  is read in the routine  is read in the routine
605  {\it  {\it
606  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
607  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
608  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
609  }.  }.
610  The routine  The routine
611  {\it  {\it
612  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
613  S/R FIND\_RHO ({\it find\_rho.F})  S/R FIND\_RHO ({\it find\_rho.F})
614  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
615  } makes use of {\bf tAlpha}.  } makes use of {\bf tAlpha}.
# Line 656  This line sets the  maximum number of it Line 675  This line sets the  maximum number of it
675  gradient solver will use to 40, {\bf irrespective of the convergence  gradient solver will use to 40, {\bf irrespective of the convergence
676  criteria being met}. Used in routine  criteria being met}. Used in routine
677  {\it  {\it
678  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
679  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
680  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
681  }.  }.
# Line 669  cg3dTargetResidual=1.E-9, Line 688  cg3dTargetResidual=1.E-9,
688  \end{verbatim}  \end{verbatim}
689  Sets the tolerance which the three-dimensional, conjugate  Sets the tolerance which the three-dimensional, conjugate
690  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
691  \ref{EQ:congrad_3d_resid} to $1 \times 10^{-9}$.  \ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.
692  The solver will iterate until the  The solver will iterate until the
693  tolerance falls below this value or until the maximum number of  tolerance falls below this value or until the maximum number of
694  solver iterations is reached. Used in routine  solver iterations is reached. Used in routine
695  {\it  {\it
696  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
697  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
698  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
699  }.  }.
# Line 743  to high coordinate for both axes. The ma Line 762  to high coordinate for both axes. The ma
762  surface heat flux file used in the example.  surface heat flux file used in the example.
763  The variable  The variable
764  {\bf  {\bf
765  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
766  Qsurf  Qsurf
767  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
768  }  }
769  is read in the routine  is read in the routine
770  {\it  {\it
771  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
772  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
773  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
774  }  }
775  and applied in    and applied in  
776  {\it  {\it
777  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
778  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})
779  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
780  } 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 791  S/R EXTERNAL\_FORCING\_SURF ({\it extern
791    
792    
793  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
794    \label{www:tutorials}
795    
796  This file uses standard default values and does not contain  This file uses standard default values and does not contain
797  customisations for this experiment.  customisations for this experiment.
798    
799  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
800    \label{www:tutorials}
801    
802  This file uses standard default values and does not contain  This file uses standard default values and does not contain
803  customisations for this experiment.  customisations for this experiment.
804    
805    
806  \subsubsection{File {\it input/Qsurf.bin}}  \subsubsection{File {\it input/Qsurf.bin}}
807    \label{www:tutorials}
808    
809  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)
810  map of heat flux values where  map of heat flux values where
# Line 801  directed upwards, according to the model Line 823  directed upwards, according to the model
823  \end{center}  \end{center}
824  \caption{  \caption{
825  }  }
826  \label{FIG:Qsurf}  \label{FIG:eg-bconv-Qsurf}
827  \end{figure}  \end{figure}
828    
829  \subsection{Running the example}  \subsection{Running the example}
830    \label{www:tutorials}
831    
832  \subsubsection{Code download}  \subsubsection{Code download}
833    \label{www:tutorials}
834    
835  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.
836  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.
837    
838  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
839    \label{www:tutorials}
840    
841   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
842    
# Line 819  Instructions for downloading the code ca Line 844  Instructions for downloading the code ca
844  {\it verification/convection/ }  {\it verification/convection/ }
845    
846  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
847    \label{www:tutorials}
848    
849   To run the experiment   To run the experiment
850    
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