/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.6 by adcroft, Tue Nov 13 19:01:42 2001 UTC revision 1.8 by cnh, Thu Feb 28 19:32:19 2002 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    
31    
32  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
33  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 44  the coriolis parameter $f$ is defined ac
44  equation  equation
45    
46  \begin{equation}  \begin{equation}
47  \label{EQ:fcori}  \label{EQ:eg-baro-fcori}
48  f(y) = f_{0}+\beta y  f(y) = f_{0}+\beta y
49  \end{equation}  \end{equation}
50    
51  \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
52  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
53  (\ref{EQ:fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.  (\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
54  \\  \\
55  \\  \\
56   The sinusoidal wind-stress variations are defined according to   The sinusoidal wind-stress variations are defined according to
57    
58  \begin{equation}  \begin{equation}
59  \label{EQ:taux}  \label{EQ:eg-baro-taux}
60  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
61  \end{equation}  \end{equation}
62    
# Line 65  simulated domain. For this experiment $f Line 64  simulated domain. For this experiment $f
64  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
65  \\  \\
66  \\  \\
67  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-baro-simulation_config}
68  summarizes the configuration simulated.  summarizes the configuration simulated.
69    
70  \begin{figure}  \begin{figure}
# Line 77  summarizes the configuration simulated. Line 76  summarizes the configuration simulated.
76  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
77  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
78  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
79  \label{FIG:simulation_config}  \label{FIG:eg-baro-simulation_config}
80  \end{figure}  \end{figure}
81    
82  \subsection{Equations Solved}  \subsection{Equations Solved}
# Line 92  are explicitly switched off for this exp Line 91  are explicitly switched off for this exp
91  configuration as follows  configuration as follows
92    
93  \begin{eqnarray}  \begin{eqnarray}
94  \label{EQ:model_equations}  \label{EQ:eg-baro-model_equations}
95  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
96                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
97                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 128  The Laplacian dissipation coefficient, $ Line 127  The Laplacian dissipation coefficient, $
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{SEC:eg-baro-code_config}
179    
180  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
181  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/exp0/}.  The experiment files
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