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revision 1.7 by adcroft, Tue Nov 13 20:13:54 2001 UTC revision 1.13 by molod, Tue Apr 4 20:23:08 2006 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
 \section{Example: Barotropic Ocean Gyre In Cartesian Coordinates}  
 \label{sect:eg-baro}  
   
4  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
5    
6  %\begin{center}  %\begin{center}
# Line 16  Line 13 
13  %{\large May 2001}  %{\large May 2001}
14  %\end{center}  %\end{center}
15    
16  This is the first in a series of sections describing  \section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
17  example MITgcm numerical experiments. The example experiments  \label{sect:eg-baro}
18  include both straightforward examples of idealized geophysical  \label{www:tutorials}
19  fluid simulations and more involved cases encompassing  \begin{rawhtml}
20  large scale modeling and  <!-- CMIREDIR:eg-baro: -->
21  automatic differentiation. Both hydrostatic and non-hydrostatic  \end{rawhtml}
 experiments are presented, as well as experiments employing  
 Cartesian, spherical-polar and cube-sphere coordinate systems.  
 These ``case study'' documents include information describing  
 the experimental configuration and detailed information on how to  
 configure the MITgcm code and input files for each experiment.  
22    
 \subsection{Experiment Overview}  
23    
24  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
25  a Barotropic, wind-forced, ocean gyre circulation. The experiment  a Barotropic, wind-forced, ocean gyre circulation. The experiment
# Line 45  the coriolis parameter $f$ is defined ac Line 36  the coriolis parameter $f$ is defined ac
36  equation  equation
37    
38  \begin{equation}  \begin{equation}
39  \label{EQ:fcori}  \label{EQ:eg-baro-fcori}
40  f(y) = f_{0}+\beta y  f(y) = f_{0}+\beta y
41  \end{equation}  \end{equation}
42    
43  \noindent where $y$ is the distance along the ``north-south'' axis of the  \noindent where $y$ is the distance along the ``north-south'' axis of the
44  simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in  simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in
45  (\ref{EQ:fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.  (\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
46  \\  \\
47  \\  \\
48   The sinusoidal wind-stress variations are defined according to   The sinusoidal wind-stress variations are defined according to
49    
50  \begin{equation}  \begin{equation}
51  \label{EQ:taux}  \label{EQ:eg-baro-taux}
52  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
53  \end{equation}  \end{equation}
54    
# Line 65  simulated domain. For this experiment $f Line 56  simulated domain. For this experiment $f
56  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
57  \\  \\
58  \\  \\
59  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-baro-simulation_config}
60  summarizes the configuration simulated.  summarizes the configuration simulated.
61    
62    %% === eh3 ===
63  \begin{figure}  \begin{figure}
64  \begin{center}  %% \begin{center}
65   \resizebox{7.5in}{5.5in}{  %%  \resizebox{7.5in}{5.5in}{
66     \includegraphics*[0.2in,0.7in][10.5in,10.5in]  %%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
67      {part3/case_studies/barotropic_gyre/simulation_config.eps} }  %%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
68  \end{center}  %% \end{center}
69    \centerline{
70      \scalefig{.95}
71      \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
72    }
73  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
74  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
75  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
76  \label{FIG:simulation_config}  \label{FIG:eg-baro-simulation_config}
77  \end{figure}  \end{figure}
78    
79  \subsection{Equations Solved}  \subsection{Equations Solved}
80    \label{www:tutorials}
81  The model is configured in hydrostatic form. The implicit free surface form of the  The model is configured in hydrostatic form. The implicit free surface form of the
82  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
83  employed.  employed.
# Line 92  are explicitly switched off for this exp Line 89  are explicitly switched off for this exp
89  configuration as follows  configuration as follows
90    
91  \begin{eqnarray}  \begin{eqnarray}
92  \label{EQ:model_equations}  \label{EQ:eg-baro-model_equations}
93  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
94                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
95                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 115  flow vector $\vec{u}$. Line 112  flow vector $\vec{u}$.
112    
113    
114  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
115    \label{www:tutorials}
116    
117   The domain is discretised with   The domain is discretised with
118  a uniform grid spacing in the horizontal set to  a uniform grid spacing in the horizontal set to
# Line 123  that there are sixty grid cells in the $ Line 121  that there are sixty grid cells in the $
121  model is configured with a single layer with depth, $\Delta z$, of $5000$~m.  model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
122    
123  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
124    \label{www:tutorials}
125    
126  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
127  This value is chosen to yield a Munk layer width \cite{adcroft:95},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
128    
129  \begin{eqnarray}  \begin{eqnarray}
130  \label{EQ:munk_layer}  \label{EQ:eg-baro-munk_layer}
131  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
132  \end{eqnarray}  \end{eqnarray}
133    
# Line 144  parameter to the horizontal Laplacian fr Line 143  parameter to the horizontal Laplacian fr
143    
144    
145  \begin{eqnarray}  \begin{eqnarray}
146  \label{EQ:laplacian_stability}  \label{EQ:eg-baro-laplacian_stability}
147  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
148  \end{eqnarray}  \end{eqnarray}
149    
# Line 156  for stability. Line 155  for stability.
155  \cite{adcroft:95}  \cite{adcroft:95}
156    
157  \begin{eqnarray}  \begin{eqnarray}
158  \label{EQ:inertial_stability}  \label{EQ:eg-baro-inertial_stability}
159  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
160  \end{eqnarray}  \end{eqnarray}
161    
# Line 168  limit for stability. Line 167  limit for stability.
167  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
168    
169  \begin{eqnarray}  \begin{eqnarray}
170  \label{EQ:cfl_stability}  \label{EQ:eg-baro-cfl_stability}
171  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
172  \end{eqnarray}  \end{eqnarray}
173    
# Line 176  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 175  S_{a} = \frac{| \vec{u} | \delta t}{ \De
175  of 0.5 and limits $\delta t$ to $1200s$.  of 0.5 and limits $\delta t$ to $1200s$.
176    
177  \subsection{Code Configuration}  \subsection{Code Configuration}
178  \label{SEC:code_config}  \label{www:tutorials}
179    \label{SEC:eg-baro-code_config}
180    
181  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
182  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/exp0/}.  The experiment files
# Line 195  experiments. Below we describe the custo Line 195  experiments. Below we describe the custo
195  to these files associated with this experiment.  to these files associated with this experiment.
196    
197  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
198    \label{www:tutorials}
199    
200  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
201  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 306  notes. Line 307  notes.
307  \end{small}  \end{small}
308    
309  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
310    \label{www:tutorials}
311    
312  This file uses standard default values and does not contain  This file uses standard default values and does not contain
313  customizations for this experiment.  customizations for this experiment.
314    
315  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
316    \label{www:tutorials}
317    
318  This file uses standard default values and does not contain  This file uses standard default values and does not contain
319  customizations for this experiment.  customizations for this experiment.
320    
321  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
322    \label{www:tutorials}
323    
324  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
325  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
# Line 326  in MITgcm. The included matlab program { Line 330  in MITgcm. The included matlab program {
330  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
331    
332  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
333    \label{www:tutorials}
334    
335    
336  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
# Line 337  The included matlab program {\it input/g Line 342  The included matlab program {\it input/g
342  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
343    
344  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
345    \label{www:tutorials}
346    
347  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
348    
# Line 359  axis aligned with the y-coordinate. Line 365  axis aligned with the y-coordinate.
365  \end{small}  \end{small}
366    
367  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
368    \label{www:tutorials}
369    
370  This file uses standard default values and does not contain  This file uses standard default values and does not contain
371  customizations for this experiment.  customizations for this experiment.
372    
373    
374  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
375    \label{www:tutorials}
376    
377  This file uses standard default values and does not contain  This file uses standard default values and does not contain
378  customizations for this experiment.  customizations for this experiment.
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