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revision 1.3 by adcroft, Thu May 16 15:54:37 2002 UTC revision 1.10 by jmc, Mon Aug 30 23:09:19 2010 UTC
# Line 1  Line 1 
1  \section{Surface Driven Convection}  \section{Surface Driven Convection}
2  \label{www:tutorials}  %\label{www:tutorials}
3  \label{sect:eg-bconv}  \label{sec: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 17  Line 23 
23  \begin{center}  \begin{center}
24   \resizebox{7.5cm}{5.5cm}{   \resizebox{7.5cm}{5.5cm}{
25     \includegraphics*[0.2in,0.7in][10.5in,10.5in]     \includegraphics*[0.2in,0.7in][10.5in,10.5in]
26     {part3/case_studies/doubly_periodic_convection/simulation_config.eps} }     {s_examples/deep_convection/simulation_config.eps} }
27  \end{center}  \end{center}
28  \caption{Schematic of simulation domain  \caption{Schematic of simulation domain
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:eg-bconv-simulation_config}  \label{fig:eg-bconv-simulation_config}
33  \end{figure}  \end{figure}
34    
35  This experiment, figure \ref{FIG:eg-bconv-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 40  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}  %\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 52  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:eg-bconv-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:eg-bconv-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 74  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:eg-bconv-vertsection} and \ref{FIG:eg-bconv-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}  \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
# Line 82  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 90  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
90  \begin{center}  \begin{center}
91   \resizebox{15cm}{10cm}{   \resizebox{15cm}{10cm}{
92     \includegraphics*[0.2in,0.7in][10.5in,10.5in]     \includegraphics*[0.2in,0.7in][10.5in,10.5in]
93     {part3/case_studies/doubly_periodic_convection/verticalsection.ps} }     {s_examples/deep_convection/verticalsection.ps} }
94  \end{center}  \end{center}
95  \caption{  \caption{
96  }  }
97  \label{FIG:eg-bconv-vertsection}  \label{fig:eg-bconv-vertsection}
98  \label{fig:surf-convection-vertsection}  \label{fig:surf-convection-vertsection}
99  \end{figure}  \end{figure}
100  \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}  \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
# Line 96  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 104  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
104  \begin{center}  \begin{center}
105   \resizebox{10cm}{10cm}{   \resizebox{10cm}{10cm}{
106     \includegraphics*[0.2in,0.7in][10.5in,10.5in]     \includegraphics*[0.2in,0.7in][10.5in,10.5in]
107     {part3/case_studies/doubly_periodic_convection/surfacesection.ps} }     {s_examples/deep_convection/surfacesection.ps} }
108  \end{center}  \end{center}
109  \caption{  \caption{
110  }  }
111  \label{FIG:eg-bconv-horizsection}  \label{fig:eg-bconv-horizsection}
112  \label{fig:surf-convection-horizsection}  \label{fig:surf-convection-horizsection}
113  \end{figure}  \end{figure}
114  \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}  \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
# Line 110  prescribed in {\it code/SIZE.h}. The for Line 118  prescribed in {\it code/SIZE.h}. The for
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}  %\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 120  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:eg-bconv-global_forcing_ft}). This produces a set of equations  $\theta$, equation (\ref{eq:eg-bconv-theta_equations}).
132  solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
133    
134  \begin{eqnarray}  \begin{eqnarray}
135  \label{EQ:eg-bconv-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 169  solved in this configuration as follows: Line 177  solved in this configuration as follows:
177  {\cal F}_\theta & \text{(surface)} \\  {\cal F}_\theta & \text{(surface)} \\
178  0 & \text{(interior)}  0 & \text{(interior)}
179  \end{cases}  \end{cases}
180    \label{eq:eg-bconv-theta_equations}
181  \end{eqnarray}  \end{eqnarray}
182    
183  \noindent where $u=\frac{Dx}{Dt}$, $v=\frac{Dy}{Dt}$  and  \noindent where $u=\frac{Dx}{Dt}$, $v=\frac{Dy}{Dt}$  and
# Line 180  equations and continuity (see section \r Line 189  equations and continuity (see section \r
189  \\  \\
190    
191  \subsection{Discrete numerical configuration}  \subsection{Discrete numerical configuration}
192  \label{www:tutorials}  %\label{www:tutorials}
193    
194  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
195  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
196  comprises a total of just over 80 000 gridpoints.  comprises a total of just over 80 000 gridpoints.
197    
198  \subsection{Numerical stability criteria and other considerations}  \subsection{Numerical stability criteria and other considerations}
199  \label{www:tutorials}  %\label{www:tutorials}
200    
201  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
202  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 201  For an extreme maximum flow speed of $ | Line 210  For an extreme maximum flow speed of $ |
210  50 m, the implied maximum timestep for stability, $\delta t_u$ is  50 m, the implied maximum timestep for stability, $\delta t_u$ is
211    
212  \begin{eqnarray}  \begin{eqnarray}
213  \label{EQ:eg-bconv-advectiveCFLcondition}  \label{eq:eg-bconv-advectiveCFLcondition}
214  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
215  \end{eqnarray}  \end{eqnarray}
216    
# Line 213  diffusion coefficient $\kappa_h (= Line 222  diffusion coefficient $\kappa_h (=
222  correlated over 50 m.    correlated over 50 m.  
223    
224  \subsection{Experiment configuration}  \subsection{Experiment configuration}
225  \label{www:tutorials}  %\label{www:tutorials}
226    
227  The model configuration for this experiment resides under the directory  The model configuration for this experiment resides under the directory
228  {\it verification/convection/}. The experiment files  {\it verification/convection/}. The experiment files
# Line 230  contain the code customisations and para Line 239  contain the code customisations and para
239  experiment. Below we describe these experiment-specific customisations.  experiment. Below we describe these experiment-specific customisations.
240    
241  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
242  \label{www:tutorials}  %\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/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
248  \label{www:tutorials}  %\label{www:tutorials}
249    
250  This file uses standard default values and does not contain  This file uses standard default values and does not contain
251  customisations for this experiment.  customisations for this experiment.
252    
253  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
254  \label{www:tutorials}  %\label{www:tutorials}
255    
256  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.
257  \begin{itemize}  \begin{itemize}
# Line 265  the vertical domain extent in grid point Line 274  the vertical domain extent in grid point
274    
275  \begin{rawhtml}<PRE>\end{rawhtml}  \begin{rawhtml}<PRE>\end{rawhtml}
276  \begin{small}  \begin{small}
277  \input{part3/case_studies/doubly_periodic_convection/code/SIZE.h}  \input{s_examples/deep_convection/code/SIZE.h}
278  \end{small}  \end{small}
279  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
280    
281  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
282  \label{www:tutorials}  %\label{www:tutorials}
283    
284  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
285  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 280  are Line 289  are
289    
290  \item Line 4,  \item Line 4,
291  \begin{verbatim}  \begin{verbatim}
292       4   tRef=20*20.0,       4   tRef=20*20.0,
293  \end{verbatim}  \end{verbatim}
294  this line sets  this line sets
295  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
296  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
297  flow evolves independently of the absolute magnitude of the reference temperature.  flow evolves independently of the absolute magnitude of the reference temperature.
298  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
299  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
300  variable  variable
301  {\bf  {\bf
302  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
303  tRef  tRef
304  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
305  }  }
306  in the model code, by procedure  in the model code, by procedure
307  {\it  {\it
308  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
309  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
310  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
311  }  }
312  The temperature field is initialised, by procedure  The temperature field is initialised, by procedure
313  {\it  {\it
314  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
315  S/R INI\_THETA ({\it ini\_theta.F})  S/R INI\_THETA ({\it ini\_theta.F})
316  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
317  }  }
# Line 310  S/R INI\_THETA ({\it ini\_theta.F}) Line 319  S/R INI\_THETA ({\it ini\_theta.F})
319    
320  \item Line 5,  \item Line 5,
321  \begin{verbatim}  \begin{verbatim}
322       5   sRef=20*35.0,       5   sRef=20*35.0,
323  \end{verbatim}  \end{verbatim}
324  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
325  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 320  tracer. For each depth level the initial Line 329  tracer. For each depth level the initial
329  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
330  variable  variable
331  {\bf  {\bf
332  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
333  sRef  sRef
334  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
335  }  }
336  in the model code, by procedure  in the model code, by procedure
337  {\it  {\it
338  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
339  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
340  }  }
341  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
342  The salinity field is initialised, by procedure  The salinity field is initialised, by procedure
343  {\it  {\it
344  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
345  S/R INI\_SALT ({\it ini\_salt.F})  S/R INI\_SALT ({\it ini\_salt.F})
346  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
347  }  }
# Line 340  S/R INI\_SALT ({\it ini\_salt.F}) Line 349  S/R INI\_SALT ({\it ini\_salt.F})
349    
350  \item Line 6,  \item Line 6,
351  \begin{verbatim}  \begin{verbatim}
352       6   viscAh=0.1,       6   viscAh=0.1,
353  \end{verbatim}  \end{verbatim}
354  this line sets the horizontal laplacian dissipation coefficient to  this line sets the horizontal laplacian dissipation coefficient to
355  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
356  for this operator are specified later.  for this operator are specified later.
357  The variable  The variable
358  {\bf  {\bf
359  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
360  viscAh  viscAh
361  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
362  }  }
363  is read in the routine  is read in the routine
364  {\it  {\it
365  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
366  S/R INI\_PARMS ({\it ini\_params.F})  S/R INI\_PARMS ({\it ini\_params.F})
367  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
368  } and applied in routines  } and applied in routines
369  {\it  {\it
370  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
371  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
372  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
373  } and  } and
374  {\it  {\it
375  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
376  S/R CALC\_GW ({\it calc\_gw.F})  S/R CALC\_GW ({\it calc\_gw.F})
377  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
378  }.  }.
# Line 371  S/R CALC\_GW ({\it calc\_gw.F}) Line 380  S/R CALC\_GW ({\it calc\_gw.F})
380    
381  \item Line 7,  \item Line 7,
382  \begin{verbatim}  \begin{verbatim}
383       7   viscAz=0.1,       7   viscAz=0.1,
384  \end{verbatim}  \end{verbatim}
385  this line sets the vertical laplacian frictional dissipation coefficient to  this line sets the vertical laplacian frictional dissipation coefficient to
386  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions  0.1 ${\rm m^{2}s^{-1}}$. Boundary conditions
387  for this operator are specified later.  for this operator are specified later.
388  The variable  The variable
389  {\bf  {\bf
390  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
391  viscAz  viscAz
392  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
393  }  }
394  is read in the routine  is read in the routine
395  {\it  {\it
396  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
397  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
398  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
399  }  }
400  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
401  {\bf  {\bf
402  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
403  viscAr  viscAr
404  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
405  }. At each time step, the viscous term contribution to the momentum equations  }. At each time step, the viscous term contribution to the momentum equations
406  is calculated in routine  is calculated in routine
407  {\it  {\it
408  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
409  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
410  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
411  }.  }.
# Line 412  e.g. $\frac{\partial u}{\partial y}$=0 a Line 421  e.g. $\frac{\partial u}{\partial y}$=0 a
421  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
422  The variable  The variable
423  {\bf  {\bf
424  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
425  no\_slip\_sides  no\_slip\_sides
426  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
427  }  }
428  is read in the routine  is read in the routine
429  {\it  {\it
430  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
431  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
432  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
433  } and the boundary condition is evaluated in routine  } and the boundary condition is evaluated in routine
434  {\it  {\it
435  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
436  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
437  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
438  }.  }.
# Line 438  boundary condition in the vertical lapla Line 447  boundary condition in the vertical lapla
447  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.
448  The variable  The variable
449  {\bf  {\bf
450  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
451  no\_slip\_bottom  no\_slip\_bottom
452  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
453  }  }
454  is read in the routine  is read in the routine
455  {\it  {\it
456  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
457  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
458  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
459  } and is applied in the routine  } and is applied in the routine
460  {\it  {\it
461  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
462  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
463  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
464  }.  }.
# Line 464  operator is $\frac{\partial}{\partial x} Line 473  operator is $\frac{\partial}{\partial x}
473  all boundaries.  all boundaries.
474  The variable  The variable
475  {\bf  {\bf
476  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
477  diffKhT  diffKhT
478  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
479  }  }
480  is read in the routine  is read in the routine
481  {\it  {\it
482  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
483  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
484  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
485  } and used in routine  } and used in routine
486  {\it  {\it
487  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
488  S/R CALC\_GT ({\it calc\_gt.F})  S/R CALC\_GT ({\it calc\_gt.F})
489  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
490  }.  }.
# Line 489  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 498  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
498  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
499  The variable  The variable
500  {\bf  {\bf
501  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
502  diffKzT  diffKzT
503  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
504  }  }
505  is read in the routine  is read in the routine
506  {\it  {\it
507  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
508  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
509  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
510  }.  }.
511  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
512  {\bf  {\bf
513  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
514  diffKrT  diffKrT
515  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
516  } which is used in routine  } which is used in routine
517  {\it  {\it
518  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
519  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
520  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
521  }.  }.
# Line 522  operator is $\frac{\partial}{\partial x} Line 531  operator is $\frac{\partial}{\partial x}
531  all boundaries.  all boundaries.
532  The variable  The variable
533  {\bf  {\bf
534  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
535  diffKsT  diffKsT
536  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
537  }  }
538  is read in the routine  is read in the routine
539  {\it  {\it
540  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
541  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
542  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
543  } and used in routine  } and used in routine
544  {\it  {\it
545  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
546  S/R CALC\_GS ({\it calc\_gs.F})  S/R CALC\_GS ({\it calc\_gs.F})
547  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
548  }.  }.
# Line 548  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 557  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
557  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
558  The variable  The variable
559  {\bf  {\bf
560  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
561  diffKzS  diffKzS
562  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
563  }  }
564  is read in the routine  is read in the routine
565  {\it  {\it
566  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
567  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
568  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
569  }.  }.
570  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
571  {\bf  {\bf
572  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
573  diffKrS  diffKrS
574  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
575  } which is used in routine  } which is used in routine
576  {\it  {\it
577  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
578  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
579  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
580  }.  }.
# Line 594  This line sets the thermal expansion coe Line 603  This line sets the thermal expansion coe
603  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.
604  The variable  The variable
605  {\bf  {\bf
606  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
607  tAlpha  tAlpha
608  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
609  }  }
610  is read in the routine  is read in 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 INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
614  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
615  }.  }.
616  The routine  The routine
617  {\it  {\it
618  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
619  S/R FIND\_RHO ({\it find\_rho.F})  S/R FIND\_RHO ({\it find\_rho.F})
620  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
621  } makes use of {\bf tAlpha}.  } makes use of {\bf tAlpha}.
# Line 672  This line sets the  maximum number of it Line 681  This line sets the  maximum number of it
681  gradient solver will use to 40, {\bf irrespective of the convergence  gradient solver will use to 40, {\bf irrespective of the convergence
682  criteria being met}. Used in routine  criteria being met}. Used in routine
683  {\it  {\it
684  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
685  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
686  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
687  }.  }.
# Line 685  cg3dTargetResidual=1.E-9, Line 694  cg3dTargetResidual=1.E-9,
694  \end{verbatim}  \end{verbatim}
695  Sets the tolerance which the three-dimensional, conjugate  Sets the tolerance which the three-dimensional, conjugate
696  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
697  \ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.  %- note: Description of Conjugate gradient method (& related params) is missing
698  The solver will iterate until the  %  in the mean time, substitute this eq ref:
699  tolerance falls below this value or until the maximum number of  \ref{eq:phi-nh} %\ref{eq:eg-bconv-congrad_3d_resid}
700  solver iterations is reached. Used in routine  to $1 \times 10^{-9}$.
701    The solver will iterate until the tolerance falls below this value
702    or until the maximum number of solver iterations is reached.
703    Used in routine
704  {\it  {\it
705  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
706  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
707  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
708  }.  }.
# Line 759  to high coordinate for both axes. The ma Line 771  to high coordinate for both axes. The ma
771  surface heat flux file used in the example.  surface heat flux file used in the example.
772  The variable  The variable
773  {\bf  {\bf
774  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
775  Qsurf  Qsurf
776  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
777  }  }
778  is read in the routine  is read in the routine
779  {\it  {\it
780  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
781  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
782  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
783  }  }
784  and applied in    and applied in  
785  {\it  {\it
786  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
787  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})
788  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
789  } where the flux is converted to a temperature tendency.  } where the flux is converted to a temperature tendency.
# Line 782  S/R EXTERNAL\_FORCING\_SURF ({\it extern Line 794  S/R EXTERNAL\_FORCING\_SURF ({\it extern
794    
795  \begin{rawhtml}<PRE>\end{rawhtml}  \begin{rawhtml}<PRE>\end{rawhtml}
796  \begin{small}  \begin{small}
797  \input{part3/case_studies/doubly_periodic_convection/input/data}  \input{s_examples/deep_convection/input/data}
798  \end{small}  \end{small}
799  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
800    
801    
802  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
803  \label{www:tutorials}  %\label{www:tutorials}
804    
805  This file uses standard default values and does not contain  This file uses standard default values and does not contain
806  customisations for this experiment.  customisations for this experiment.
807    
808  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
809  \label{www:tutorials}  %\label{www:tutorials}
810    
811  This file uses standard default values and does not contain  This file uses standard default values and does not contain
812  customisations for this experiment.  customisations for this experiment.
813    
814    
815  \subsubsection{File {\it input/Qsurf.bin}}  \subsubsection{File {\it input/Qsurf.bin}}
816  \label{www:tutorials}  %\label{www:tutorials}
817    
818  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)
819  map of heat flux values where  map of heat flux values where
# Line 816  directed upwards, according to the model Line 828  directed upwards, according to the model
828  \begin{center}  \begin{center}
829  % \resizebox{15cm}{10cm}{  % \resizebox{15cm}{10cm}{
830  %   \includegraphics*[0.2in,0.7in][10.5in,10.5in]  %   \includegraphics*[0.2in,0.7in][10.5in,10.5in]
831  %   {part3/case_studies/doubly_periodic_convection/Qsurf.ps} }  %   {s_examples/deep_convection/Qsurf.ps} }
832  \end{center}  \end{center}
833  \caption{  \caption{
834  }  }
835  \label{FIG:eg-bconv-Qsurf}  \label{fig:eg-bconv-Qsurf}
836  \end{figure}  \end{figure}
837    
838  \subsection{Running the example}  \subsection{Running the example}
839  \label{www:tutorials}  %\label{www:tutorials}
840    
841  \subsubsection{Code download}  \subsubsection{Code download}
842  \label{www:tutorials}  %\label{www:tutorials}
843    
844  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.
845  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.  Instructions for downloading the code can be found in \ref{sec:obtainingCode}.
846    
847  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
848  \label{www:tutorials}  %\label{www:tutorials}
849    
850   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
851    
# Line 841  Instructions for downloading the code ca Line 853  Instructions for downloading the code ca
853  {\it verification/convection/ }  {\it verification/convection/ }
854    
855  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
856  \label{www:tutorials}  %\label{www:tutorials}
857    
858   To run the experiment   To run the experiment
859    
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