/[MITgcm]/manual/s_examples/deep_convection/convection.tex
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revision 1.9 by jmc, Fri Aug 27 13:25:31 2010 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}  \begin{rawhtml}
5  <!-- CMIREDIR:eg-bconv: -->  <!-- CMIREDIR:eg-bconv: -->
6  \end{rawhtml}  \end{rawhtml}
# Line 29  Line 29 
29  for the surface driven convection experiment. The domain is doubly periodic  for the surface driven convection experiment. The domain is doubly periodic
30  with an initially uniform temperature of 20 $^oC$.  with an initially uniform temperature of 20 $^oC$.
31  }  }
32  \label{FIG: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  This experiment, figure \ref{fig:eg-bconv-simulation_config}, showcasing MITgcm's non-hydrostatic
36  capability, was designed to explore  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. The files for this experiment can be found in the verification  period of oceanic deep convection. The files for this experiment can be found in the verification
# Line 48  directory under tutorial\_deep\_convecti Line 48  directory under tutorial\_deep\_convecti
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 60  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 82  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 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
94  \end{center}  \end{center}
95  \caption{  \caption{
96  }  }
97  \label{FIG: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 108  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 108  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
108  \end{center}  \end{center}
109  \caption{  \caption{
110  }  }
111  \label{FIG: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 118  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 128  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 177  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 188  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 209  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 221  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 238  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 278  the vertical domain extent in grid point Line 279  the vertical domain extent in grid point
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 693  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})
# Line 796  S/R EXTERNAL\_FORCING\_SURF ({\it extern Line 800  S/R EXTERNAL\_FORCING\_SURF ({\it extern
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 828  directed upwards, according to the model Line 832  directed upwards, according to the model
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 849  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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