/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.5 by adcroft, Tue Nov 13 18:19:18 2001 UTC revision 1.10 by edhill, Thu Jan 29 15:11:39 2004 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
 \section{Example: Barotropic Ocean Gyre In Cartesian Coordinates}  
 \label{sec: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  This is the first in a series of tutorials describing
17  example MITgcm numerical experiments. The example experiments  example MITgcm numerical experiments. The example experiments
18  include both straightforward examples of idealized geophysical  include both straightforward examples of idealized geophysical
19  fluid simulations and more involved cases encompassing  fluid simulations and more involved cases encompassing
# Line 28  These ``case study'' documents include i Line 25  These ``case study'' documents include i
25  the experimental configuration and detailed information on how to  the experimental configuration and detailed information on how to
26  configure the MITgcm code and input files for each experiment.  configure the MITgcm code and input files for each experiment.
27    
28  \subsection{Experiment Overview}  \section{Barotropic Ocean Gyre In Cartesian Coordinates}
29    \label{sect:eg-baro}
30    \label{www:tutorials}
31    
32    
33  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
34  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 45  the coriolis parameter $f$ is defined ac
45  equation  equation
46    
47  \begin{equation}  \begin{equation}
48  \label{EQ:fcori}  \label{EQ:eg-baro-fcori}
49  f(y) = f_{0}+\beta y  f(y) = f_{0}+\beta y
50  \end{equation}  \end{equation}
51    
52  \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
53  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
54  (\ref{EQ:fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.  (\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
55  \\  \\
56  \\  \\
57   The sinusoidal wind-stress variations are defined according to   The sinusoidal wind-stress variations are defined according to
58    
59  \begin{equation}  \begin{equation}
60  \label{EQ:taux}  \label{EQ:eg-baro-taux}
61  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
62  \end{equation}  \end{equation}
63    
# Line 65  simulated domain. For this experiment $f Line 65  simulated domain. For this experiment $f
65  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
66  \\  \\
67  \\  \\
68  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-baro-simulation_config}
69  summarizes the configuration simulated.  summarizes the configuration simulated.
70    
71    %% === eh3 ===
72  \begin{figure}  \begin{figure}
73  \begin{center}  %% \begin{center}
74   \resizebox{7.5in}{5.5in}{  %%  \resizebox{7.5in}{5.5in}{
75     \includegraphics*[0.2in,0.7in][10.5in,10.5in]  %%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
76      {part3/case_studies/barotropic_gyre/simulation_config.eps} }  %%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
77  \end{center}  %% \end{center}
78    \centerline{
79      \scalefig{.95}
80      \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
81    }
82  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
83  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
84  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
85  \label{FIG:simulation_config}  \label{FIG:eg-baro-simulation_config}
86  \end{figure}  \end{figure}
87    
88  \subsection{Equations Solved}  \subsection{Equations Solved}
89    \label{www:tutorials}
90  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
91  pressure equation described in Marshall et. al \cite{Marshall97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
92  employed.  employed.
93  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
94  dissipation. The wind-stress momentum input is added to the momentum equation  dissipation. The wind-stress momentum input is added to the momentum equation
# Line 92  are explicitly switched off for this exp Line 98  are explicitly switched off for this exp
98  configuration as follows  configuration as follows
99    
100  \begin{eqnarray}  \begin{eqnarray}
101  \label{EQ:model_equations}  \label{EQ:eg-baro-model_equations}
102  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
103                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
104                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 115  flow vector $\vec{u}$. Line 121  flow vector $\vec{u}$.
121    
122    
123  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
124    \label{www:tutorials}
125    
126   The domain is discretised with   The domain is discretised with
127  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 130  that there are sixty grid cells in the $
130  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.
131    
132  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
133    \label{www:tutorials}
134    
135  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
136  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},
137    
138  \begin{eqnarray}  \begin{eqnarray}
139  \label{EQ:munk_layer}  \label{EQ:eg-baro-munk_layer}
140  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
141  \end{eqnarray}  \end{eqnarray}
142    
# Line 144  parameter to the horizontal Laplacian fr Line 152  parameter to the horizontal Laplacian fr
152    
153    
154  \begin{eqnarray}  \begin{eqnarray}
155  \label{EQ:laplacian_stability}  \label{EQ:eg-baro-laplacian_stability}
156  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
157  \end{eqnarray}  \end{eqnarray}
158    
# Line 156  for stability. Line 164  for stability.
164  \cite{adcroft:95}  \cite{adcroft:95}
165    
166  \begin{eqnarray}  \begin{eqnarray}
167  \label{EQ:inertial_stability}  \label{EQ:eg-baro-inertial_stability}
168  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
169  \end{eqnarray}  \end{eqnarray}
170    
# Line 168  limit for stability. Line 176  limit for stability.
176  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
177    
178  \begin{eqnarray}  \begin{eqnarray}
179  \label{EQ:cfl_stability}  \label{EQ:eg-baro-cfl_stability}
180  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
181  \end{eqnarray}  \end{eqnarray}
182    
# Line 176  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 184  S_{a} = \frac{| \vec{u} | \delta t}{ \De
184  of 0.5 and limits $\delta t$ to $1200s$.  of 0.5 and limits $\delta t$ to $1200s$.
185    
186  \subsection{Code Configuration}  \subsection{Code Configuration}
187  \label{SEC:code_config}  \label{www:tutorials}
188    \label{SEC:eg-baro-code_config}
189    
190  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
191  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/exp0/}.  The experiment files
# Line 195  experiments. Below we describe the custo Line 204  experiments. Below we describe the custo
204  to these files associated with this experiment.  to these files associated with this experiment.
205    
206  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
207    \label{www:tutorials}
208    
209  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
210  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 316  notes.
316  \end{small}  \end{small}
317    
318  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
319    \label{www:tutorials}
320    
321  This file uses standard default values and does not contain  This file uses standard default values and does not contain
322  customizations for this experiment.  customizations for this experiment.
323    
324  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
325    \label{www:tutorials}
326    
327  This file uses standard default values and does not contain  This file uses standard default values and does not contain
328  customizations for this experiment.  customizations for this experiment.
329    
330  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
331    \label{www:tutorials}
332    
333  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
334  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 339  in MITgcm. The included matlab program {
339  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
340    
341  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
342    \label{www:tutorials}
343    
344    
345  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 351  The included matlab program {\it input/g
351  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
352    
353  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
354    \label{www:tutorials}
355    
356  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
357    
# Line 359  axis aligned with the y-coordinate. Line 374  axis aligned with the y-coordinate.
374  \end{small}  \end{small}
375    
376  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
377    \label{www:tutorials}
378    
379  This file uses standard default values and does not contain  This file uses standard default values and does not contain
380  customizations for this experiment.  customizations for this experiment.
381    
382    
383  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
384    \label{www:tutorials}
385    
386  This file uses standard default values and does not contain  This file uses standard default values and does not contain
387  customizations for this experiment.  customizations for this experiment.
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