/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.7 by adcroft, Tue Nov 13 20:13:54 2001 UTC revision 1.9 by adcroft, Thu May 16 15:54:37 2002 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  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  \begin{figure}  \begin{figure}
# Line 77  summarizes the configuration simulated. Line 77  summarizes the configuration simulated.
77  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
78  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
79  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
80  \label{FIG:simulation_config}  \label{FIG:eg-baro-simulation_config}
81  \end{figure}  \end{figure}
82    
83  \subsection{Equations Solved}  \subsection{Equations Solved}
84    \label{www:tutorials}
85  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
86  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
87  employed.  employed.
# Line 92  are explicitly switched off for this exp Line 93  are explicitly switched off for this exp
93  configuration as follows  configuration as follows
94    
95  \begin{eqnarray}  \begin{eqnarray}
96  \label{EQ:model_equations}  \label{EQ:eg-baro-model_equations}
97  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
98                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
99                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 115  flow vector $\vec{u}$. Line 116  flow vector $\vec{u}$.
116    
117    
118  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
119    \label{www:tutorials}
120    
121   The domain is discretised with   The domain is discretised with
122  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 125  that there are sixty grid cells in the $
125  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.
126    
127  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
128    \label{www:tutorials}
129    
130  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
131  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},
132    
133  \begin{eqnarray}  \begin{eqnarray}
134  \label{EQ:munk_layer}  \label{EQ:eg-baro-munk_layer}
135  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
136  \end{eqnarray}  \end{eqnarray}
137    
# Line 144  parameter to the horizontal Laplacian fr Line 147  parameter to the horizontal Laplacian fr
147    
148    
149  \begin{eqnarray}  \begin{eqnarray}
150  \label{EQ:laplacian_stability}  \label{EQ:eg-baro-laplacian_stability}
151  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
152  \end{eqnarray}  \end{eqnarray}
153    
# Line 156  for stability. Line 159  for stability.
159  \cite{adcroft:95}  \cite{adcroft:95}
160    
161  \begin{eqnarray}  \begin{eqnarray}
162  \label{EQ:inertial_stability}  \label{EQ:eg-baro-inertial_stability}
163  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
164  \end{eqnarray}  \end{eqnarray}
165    
# Line 168  limit for stability. Line 171  limit for stability.
171  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
172    
173  \begin{eqnarray}  \begin{eqnarray}
174  \label{EQ:cfl_stability}  \label{EQ:eg-baro-cfl_stability}
175  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
176  \end{eqnarray}  \end{eqnarray}
177    
# Line 176  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 179  S_{a} = \frac{| \vec{u} | \delta t}{ \De
179  of 0.5 and limits $\delta t$ to $1200s$.  of 0.5 and limits $\delta t$ to $1200s$.
180    
181  \subsection{Code Configuration}  \subsection{Code Configuration}
182  \label{SEC:code_config}  \label{www:tutorials}
183    \label{SEC:eg-baro-code_config}
184    
185  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
186  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/exp0/}.  The experiment files
# Line 195  experiments. Below we describe the custo Line 199  experiments. Below we describe the custo
199  to these files associated with this experiment.  to these files associated with this experiment.
200    
201  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
202    \label{www:tutorials}
203    
204  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
205  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 311  notes.
311  \end{small}  \end{small}
312    
313  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
314    \label{www:tutorials}
315    
316  This file uses standard default values and does not contain  This file uses standard default values and does not contain
317  customizations for this experiment.  customizations for this experiment.
318    
319  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
320    \label{www:tutorials}
321    
322  This file uses standard default values and does not contain  This file uses standard default values and does not contain
323  customizations for this experiment.  customizations for this experiment.
324    
325  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
326    \label{www:tutorials}
327    
328  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
329  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 334  in MITgcm. The included matlab program {
334  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
335    
336  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
337    \label{www:tutorials}
338    
339    
340  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 346  The included matlab program {\it input/g
346  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
347    
348  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
349    \label{www:tutorials}
350    
351  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
352    
# Line 359  axis aligned with the y-coordinate. Line 369  axis aligned with the y-coordinate.
369  \end{small}  \end{small}
370    
371  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
372    \label{www:tutorials}
373    
374  This file uses standard default values and does not contain  This file uses standard default values and does not contain
375  customizations for this experiment.  customizations for this experiment.
376    
377    
378  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
379    \label{www:tutorials}
380    
381  This file uses standard default values and does not contain  This file uses standard default values and does not contain
382  customizations for this experiment.  customizations for this experiment.
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