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revision 1.1 by helen, Wed Dec 19 14:34:39 2001 UTC revision 1.4 by edhill, Wed Jul 30 13:42:52 2003 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    
5  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
# Line 22  Line 23 
23  for the surface driven convection experiment. The domain is doubly periodic  for the surface driven convection experiment. The domain is doubly periodic
24  with an initially uniform temperature of 20 $^oC$.  with an initially uniform temperature of 20 $^oC$.
25  }  }
26  \label{FIG:simulation_config}  \label{FIG:eg-bconv-simulation_config}
27  \end{figure}  \end{figure}
28    
29  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
30  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
31  period of oceanic deep convection. It is  period of oceanic deep convection. It is
32    
# Line 39  period of oceanic deep convection. It is Line 40  period of oceanic deep convection. It is
40  \end{itemize}  \end{itemize}
41    
42  \subsection{Overview}  \subsection{Overview}
43    \label{www:tutorials}
44    
45  The model domain consists of an approximately 3  The model domain consists of an approximately 3
46  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 52  uniform reference potential temperature
52  used in this experiment is linear  used in this experiment is linear
53    
54  \begin{equation}  \begin{equation}
55  \label{EQ:linear1_eos}  \label{EQ:eg-bconv-linear1_eos}
56  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
57  \end{equation}  \end{equation}
58    
59  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
60    
61  \begin{equation}  \begin{equation}
62  \label{EQ:linear1_eos_pert}  \label{EQ:eg-bconv-linear1_eos_pert}
63  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
64  \end{equation}  \end{equation}
65    
# Line 72  the quantity that is carried in the mode Line 74  the quantity that is carried in the mode
74  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
75  convectively unstable and  convectively unstable and
76  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
77  (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
78  rotation ($f_o = 10^{-4}$ s$^{-1}$) .  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
79    
80    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
81  \begin{figure}  \begin{figure}
82  \begin{center}  \begin{center}
83   \resizebox{15cm}{10cm}{   \resizebox{15cm}{10cm}{
# Line 83  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 86  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
86  \end{center}  \end{center}
87  \caption{  \caption{
88  }  }
89  \label{FIG:vertsection}  \label{FIG:eg-bconv-vertsection}
90    \label{fig:surf-convection-vertsection}
91  \end{figure}  \end{figure}
92    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
93    
94    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-horizsection\end{rawhtml}
95  \begin{figure}  \begin{figure}
96  \begin{center}  \begin{center}
97   \resizebox{10cm}{10cm}{   \resizebox{10cm}{10cm}{
# Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 100  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
100  \end{center}  \end{center}
101  \caption{  \caption{
102  }  }
103  \label{FIG:horizsection}  \label{FIG:eg-bconv-horizsection}
104    \label{fig:surf-convection-horizsection}
105  \end{figure}  \end{figure}
106    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
107    
108  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
109  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
110  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}.
111    
112  \subsection{Equations solved}  \subsection{Equations solved}
113    \label{www:tutorials}
114    
115  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
116  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 120  The implicit free surface form of the
120  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
121  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
122  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,
123  $\theta$, 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
124  solved in this configuration as follows:  solved in this configuration as follows:
125    
126  \begin{eqnarray}  \begin{eqnarray}
127  \label{EQ:model_equations}  \label{EQ:eg-bconv-model_equations}
128  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
129    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
130    \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 180  equations and continuity (see section \r
180  \\  \\
181    
182  \subsection{Discrete numerical configuration}  \subsection{Discrete numerical configuration}
183    \label{www:tutorials}
184    
185  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
186  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
187  comprises a total of just over 80 000 gridpoints.  comprises a total of just over 80 000 gridpoints.
188    
189  \subsection{Numerical stability criteria and other considerations}  \subsection{Numerical stability criteria and other considerations}
190    \label{www:tutorials}
191    
192  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
193  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 201  For an extreme maximum flow speed of $ |
201  50 m, the implied maximum timestep for stability, $\delta t_u$ is  50 m, the implied maximum timestep for stability, $\delta t_u$ is
202    
203  \begin{eqnarray}  \begin{eqnarray}
204  \label{EQ:advectiveCFLcondition}  \label{EQ:eg-bconv-advectiveCFLcondition}
205  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
206  \end{eqnarray}  \end{eqnarray}
207    
# Line 202  diffusion coefficient $\kappa_h (= Line 213  diffusion coefficient $\kappa_h (=
213  correlated over 50 m.    correlated over 50 m.  
214    
215  \subsection{Experiment configuration}  \subsection{Experiment configuration}
216    \label{www:tutorials}
217    
218  The model configuration for this experiment resides under the directory  The model configuration for this experiment resides under the directory
219  {\it verification/convection/}. The experiment files  {\it verification/convection/}. The experiment files
# Line 218  contain the code customisations and para Line 230  contain the code customisations and para
230  experiment. Below we describe these experiment-specific customisations.  experiment. Below we describe these experiment-specific customisations.
231    
232  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
233    \label{www:tutorials}
234    
235  This file uses standard default values and does not contain  This file uses standard default values and does not contain
236  customisations for this experiment.  customisations for this experiment.
237    
238  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
239    \label{www:tutorials}
240    
241  This file uses standard default values and does not contain  This file uses standard default values and does not contain
242  customisations for this experiment.  customisations for this experiment.
243    
244  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
245    \label{www:tutorials}
246    
247  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.
248  \begin{itemize}  \begin{itemize}
# Line 255  the vertical domain extent in grid point Line 270  the vertical domain extent in grid point
270  \begin{rawhtml}</PRE>\end{rawhtml}  \begin{rawhtml}</PRE>\end{rawhtml}
271    
272  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
273    \label{www:tutorials}
274    
275  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
276  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 274  For each depth level the initial and ref Line 290  For each depth level the initial and ref
290  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
291  variable  variable
292  {\bf  {\bf
293  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
294  tRef  tRef
295  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
296  }  }
297  in the model code, by procedure  in the model code, by procedure
298  {\it  {\it
299  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
300  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
301  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
302  }  }
303  The temperature field is initialised, by procedure  The temperature field is initialised, by procedure
304  {\it  {\it
305  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
306  S/R INI\_THETA ({\it ini\_theta.F})  S/R INI\_THETA ({\it ini\_theta.F})
307  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
308  }  }
# Line 304  tracer. For each depth level the initial Line 320  tracer. For each depth level the initial
320  $x$ and $y$. The values specified are read into the  $x$ and $y$. The values specified are read into the
321  variable  variable
322  {\bf  {\bf
323  \begin{rawhtml} <A href=../../../code_reference/vdb/names/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/OK.htm> \end{rawhtml}
324  sRef  sRef
325  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
326  }  }
327  in the model code, by procedure  in the model code, by procedure
328  {\it  {\it
329  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
330  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
331  }  }
332  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
333  The salinity field is initialised, by procedure  The salinity field is initialised, by procedure
334  {\it  {\it
335  \begin{rawhtml} <A href=../../../code_reference/vdb/code/OK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/OK.htm> \end{rawhtml}
336  S/R INI\_SALT ({\it ini\_salt.F})  S/R INI\_SALT ({\it ini\_salt.F})
337  \begin{rawhtml} </A>\end{rawhtml}.  \begin{rawhtml} </A>\end{rawhtml}.
338  }  }
# Line 331  this line sets the horizontal laplacian Line 347  this line sets the horizontal laplacian
347  for this operator are specified later.  for this operator are specified later.
348  The variable  The variable
349  {\bf  {\bf
350  \begin{rawhtml} <A href=../../../code_reference/vdb/names/SI.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/SI.htm> \end{rawhtml}
351  viscAh  viscAh
352  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
353  }  }
354  is read in the routine  is read in the routine
355  {\it  {\it
356  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
357  S/R INI\_PARMS ({\it ini\_params.F})  S/R INI\_PARMS ({\it ini\_params.F})
358  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
359  } and applied in routines  } and applied in routines
360  {\it  {\it
361  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
362  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
363  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
364  } and  } and
365  {\it  {\it
366  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
367  S/R CALC\_GW ({\it calc\_gw.F})  S/R CALC\_GW ({\it calc\_gw.F})
368  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
369  }.  }.
# Line 362  this line sets the vertical laplacian fr Line 378  this line sets the vertical laplacian fr
378  for this operator are specified later.  for this operator are specified later.
379  The variable  The variable
380  {\bf  {\bf
381  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZQ.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZQ.htm> \end{rawhtml}
382  viscAz  viscAz
383  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
384  }  }
385  is read in the routine  is read in the routine
386  {\it  {\it
387  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
388  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
389  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
390  }  }
391  and is copied into model general vertical coordinate variable  and is copied into model general vertical coordinate variable
392  {\bf  {\bf
393  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PF.htm> \end{rawhtml}
394  viscAr  viscAr
395  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
396  }. At each time step, the viscous term contribution to the momentum equations  }. At each time step, the viscous term contribution to the momentum equations
397  is calculated in routine  is calculated in routine
398  {\it  {\it
399  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
400  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
401  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
402  }.  }.
# Line 396  e.g. $\frac{\partial u}{\partial y}$=0 a Line 412  e.g. $\frac{\partial u}{\partial y}$=0 a
412  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
413  The variable  The variable
414  {\bf  {\bf
415  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UT.htm> \end{rawhtml}
416  no\_slip\_sides  no\_slip\_sides
417  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
418  }  }
419  is read in the routine  is read in the routine
420  {\it  {\it
421  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
422  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
423  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
424  } and the boundary condition is evaluated in routine  } and the boundary condition is evaluated in routine
425  {\it  {\it
426  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
427  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
428  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
429  }.  }.
# Line 422  boundary condition in the vertical lapla Line 438  boundary condition in the vertical lapla
438  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.
439  The variable  The variable
440  {\bf  {\bf
441  \begin{rawhtml} <A href=../../../code_reference/vdb/names/UK.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/UK.htm> \end{rawhtml}
442  no\_slip\_bottom  no\_slip\_bottom
443  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
444  }  }
445  is read in the routine  is read in the routine
446  {\it  {\it
447  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
448  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
449  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
450  } and is applied in the routine  } and is applied in the routine
451  {\it  {\it
452  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
453  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})  S/R CALC\_MOM\_RHS ({\it calc\_mom\_rhs.F})
454  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
455  }.  }.
# Line 448  operator is $\frac{\partial}{\partial x} Line 464  operator is $\frac{\partial}{\partial x}
464  all boundaries.  all boundaries.
465  The variable  The variable
466  {\bf  {\bf
467  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
468  diffKhT  diffKhT
469  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
470  }  }
471  is read in the routine  is read in the routine
472  {\it  {\it
473  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
474  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
475  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
476  } and used in routine  } and used in routine
477  {\it  {\it
478  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
479  S/R CALC\_GT ({\it calc\_gt.F})  S/R CALC\_GT ({\it calc\_gt.F})
480  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
481  }.  }.
# Line 473  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 489  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
489  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
490  The variable  The variable
491  {\bf  {\bf
492  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
493  diffKzT  diffKzT
494  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
495  }  }
496  is read in the routine  is read in the routine
497  {\it  {\it
498  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
499  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
500  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
501  }.  }.
502  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
503  {\bf  {\bf
504  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
505  diffKrT  diffKrT
506  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
507  } which is used in routine  } which is used in routine
508  {\it  {\it
509  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
510  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
511  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
512  }.  }.
# Line 506  operator is $\frac{\partial}{\partial x} Line 522  operator is $\frac{\partial}{\partial x}
522  all boundaries.  all boundaries.
523  The variable  The variable
524  {\bf  {\bf
525  \begin{rawhtml} <A href=../../../code_reference/vdb/names/RC.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/RC.htm> \end{rawhtml}
526  diffKsT  diffKsT
527  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
528  }  }
529  is read in the routine  is read in the routine
530  {\it  {\it
531  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
532  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
533  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
534  } and used in routine  } and used in routine
535  {\it  {\it
536  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
537  S/R CALC\_GS ({\it calc\_gs.F})  S/R CALC\_GS ({\it calc\_gs.F})
538  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
539  }.  }.
# Line 532  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary Line 548  to 0.1 ${\rm m^{2}s^{-1}}$. The boundary
548  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.  operator is $\frac{\partial}{\partial z}$ = 0 on all boundaries.
549  The variable  The variable
550  {\bf  {\bf
551  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZT.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZT.htm> \end{rawhtml}
552  diffKzS  diffKzS
553  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
554  }  }
555  is read in the routine  is read in the routine
556  {\it  {\it
557  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
558  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
559  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
560  }.  }.
561  It is copied into model general vertical coordinate variable  It is copied into model general vertical coordinate variable
562  {\bf  {\bf
563  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/PD.htm> \end{rawhtml}
564  diffKrS  diffKrS
565  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
566  } which is used in routine  } which is used in routine
567  {\it  {\it
568  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
569  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})  S/R CALC\_DIFFUSIVITY ({\it calc\_diffusivity.F})
570  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
571  }.  }.
# Line 578  This line sets the thermal expansion coe Line 594  This line sets the thermal expansion coe
594  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.  to $2 \times 10^{-4}$ $^o$ C$^{-1}$.
595  The variable  The variable
596  {\bf  {\bf
597  \begin{rawhtml} <A href=../../../code_reference/vdb/names/ZV.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/ZV.htm> \end{rawhtml}
598  tAlpha  tAlpha
599  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
600  }  }
601  is read in the routine  is read in the routine
602  {\it  {\it
603  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
604  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
605  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
606  }.  }.
607  The routine  The routine
608  {\it  {\it
609  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
610  S/R FIND\_RHO ({\it find\_rho.F})  S/R FIND\_RHO ({\it find\_rho.F})
611  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
612  } makes use of {\bf tAlpha}.  } makes use of {\bf tAlpha}.
# Line 656  This line sets the  maximum number of it Line 672  This line sets the  maximum number of it
672  gradient solver will use to 40, {\bf irrespective of the convergence  gradient solver will use to 40, {\bf irrespective of the convergence
673  criteria being met}. Used in routine  criteria being met}. Used in routine
674  {\it  {\it
675  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
676  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
677  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
678  }.  }.
# Line 669  cg3dTargetResidual=1.E-9, Line 685  cg3dTargetResidual=1.E-9,
685  \end{verbatim}  \end{verbatim}
686  Sets the tolerance which the three-dimensional, conjugate  Sets the tolerance which the three-dimensional, conjugate
687  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
688  \ref{EQ:congrad_3d_resid} to $1 \times 10^{-9}$.  \ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.
689  The solver will iterate until the  The solver will iterate until the
690  tolerance falls below this value or until the maximum number of  tolerance falls below this value or until the maximum number of
691  solver iterations is reached. Used in routine  solver iterations is reached. Used in routine
692  {\it  {\it
693  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
694  S/R CG3D ({\it cg3d.F})  S/R CG3D ({\it cg3d.F})
695  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
696  }.  }.
# Line 743  to high coordinate for both axes. The ma Line 759  to high coordinate for both axes. The ma
759  surface heat flux file used in the example.  surface heat flux file used in the example.
760  The variable  The variable
761  {\bf  {\bf
762  \begin{rawhtml} <A href=../../../code_reference/vdb/names/179.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/names/179.htm> \end{rawhtml}
763  Qsurf  Qsurf
764  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
765  }  }
766  is read in the routine  is read in the routine
767  {\it  {\it
768  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
769  S/R INI\_PARMS ({\it ini\_parms.F})  S/R INI\_PARMS ({\it ini\_parms.F})
770  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
771  }  }
772  and applied in    and applied in  
773  {\it  {\it
774  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../code_reference/vdb/code/94.htm> \end{rawhtml}
775  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})  S/R EXTERNAL\_FORCING\_SURF ({\it external\_forcing\_surf.F})
776  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
777  } 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 788  S/R EXTERNAL\_FORCING\_SURF ({\it extern
788    
789    
790  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
791    \label{www:tutorials}
792    
793  This file uses standard default values and does not contain  This file uses standard default values and does not contain
794  customisations for this experiment.  customisations for this experiment.
795    
796  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
797    \label{www:tutorials}
798    
799  This file uses standard default values and does not contain  This file uses standard default values and does not contain
800  customisations for this experiment.  customisations for this experiment.
801    
802    
803  \subsubsection{File {\it input/Qsurf.bin}}  \subsubsection{File {\it input/Qsurf.bin}}
804    \label{www:tutorials}
805    
806  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)  The file {\it input/Qsurf.bin} specifies a two-dimensional ($x,y$)
807  map of heat flux values where  map of heat flux values where
# Line 801  directed upwards, according to the model Line 820  directed upwards, according to the model
820  \end{center}  \end{center}
821  \caption{  \caption{
822  }  }
823  \label{FIG:Qsurf}  \label{FIG:eg-bconv-Qsurf}
824  \end{figure}  \end{figure}
825    
826  \subsection{Running the example}  \subsection{Running the example}
827    \label{www:tutorials}
828    
829  \subsubsection{Code download}  \subsubsection{Code download}
830    \label{www:tutorials}
831    
832  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.
833  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.  Instructions for downloading the code can be found in \ref{sect:obtainingCode}.
834    
835  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
836    \label{www:tutorials}
837    
838   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
839    
# Line 819  Instructions for downloading the code ca Line 841  Instructions for downloading the code ca
841  {\it verification/convection/ }  {\it verification/convection/ }
842    
843  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
844    \label{www:tutorials}
845    
846   To run the experiment   To run the experiment
847    
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