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revision 1.1 by helen, Wed Dec 19 14:34:39 2001 UTC revision 1.3 by adcroft, Thu May 16 15:54:37 2002 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 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
# 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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