/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.19 by jmc, Fri Aug 27 13:25:31 2010 UTC revision 1.20 by jmc, Mon Aug 30 23:09:19 2010 UTC
# Line 14  Line 14 
14  %\end{center}  %\end{center}
15    
16  \section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}  \section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
17  \label{www:tutorials}  %\label{www:tutorials}
18  \label{sect:eg-baro}  \label{sec:eg-baro}
19  \begin{rawhtml}  \begin{rawhtml}
20  <!-- CMIREDIR:eg-baro: -->  <!-- CMIREDIR:eg-baro: -->
21  \end{rawhtml}  \end{rawhtml}
# Line 39  the coriolis parameter $f$ is defined ac Line 39  the coriolis parameter $f$ is defined ac
39  equation  equation
40    
41  \begin{equation}  \begin{equation}
42  \label{EQ:eg-baro-fcori}  \label{eq:eg-baro-fcori}
43  f(y) = f_{0}+\beta y  f(y) = f_{0}+\beta y
44  \end{equation}  \end{equation}
45    
46  \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
47  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
48  (\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.  (\ref{eq:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
49  \\  \\
50  \\  \\
51   The sinusoidal wind-stress variations are defined according to   The sinusoidal wind-stress variations are defined according to
52    
53  \begin{equation}  \begin{equation}
54  \label{EQ:eg-baro-taux}  \label{eq:eg-baro-taux}
55  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
56  \end{equation}  \end{equation}
57    
# Line 59  simulated domain. For this experiment $f Line 59  simulated domain. For this experiment $f
59  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
60  \\  \\
61  \\  \\
62  Figure \ref{FIG:eg-baro-simulation_config}  Figure \ref{fig:eg-baro-simulation_config}
63  summarizes the configuration simulated.  summarizes the configuration simulated.
64    
65  %% === eh3 ===  %% === eh3 ===
# Line 76  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:eg-baro-simulation_config}  \label{fig:eg-baro-simulation_config}
80  \end{figure}  \end{figure}
81    
82  \subsection{Equations Solved}  \subsection{Equations Solved}
83  \label{www:tutorials}  %\label{www:tutorials}
84  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
85  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
86  employed.  employed.
# Line 88  A horizontal Laplacian operator $\nabla_ Line 88  A horizontal Laplacian operator $\nabla_
88  dissipation. The wind-stress momentum input is added to the momentum equation  dissipation. The wind-stress momentum input is added to the momentum equation
89  for the ``zonal flow'', $u$. Other terms in the model  for the ``zonal flow'', $u$. Other terms in the model
90  are explicitly switched off for this experiment configuration (see section  are explicitly switched off for this experiment configuration (see section
91  \ref{SEC:code_config} ), yielding an active set of equations solved in this  \ref{sec:eg-baro-code_config} ), yielding an active set of equations solved
92  configuration as follows  in this configuration as follows
93    
94  \begin{eqnarray}  \begin{eqnarray}
95  \label{EQ:eg-baro-model_equations}  \label{eq:eg-baro-model_equations}
96  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
97                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
98                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 115  flow vector $\vec{u}$. Line 115  flow vector $\vec{u}$.
115    
116    
117  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
118  \label{www:tutorials}  %\label{www:tutorials}
119    
120   The domain is discretised with   The domain is discretised with
121  a uniform grid spacing in the horizontal set to  a uniform grid spacing in the horizontal set to
# Line 124  that there are sixty grid cells in the $ Line 124  that there are sixty grid cells in the $
124  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.
125    
126  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
127  \label{www:tutorials}  %\label{www:tutorials}
128    
129  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
130  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},
131    
132  \begin{eqnarray}  \begin{eqnarray}
133  \label{EQ:eg-baro-munk_layer}  \label{eq:eg-baro-munk_layer}
134  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
135  \end{eqnarray}  \end{eqnarray}
136    
# Line 146  parameter to the horizontal Laplacian fr Line 146  parameter to the horizontal Laplacian fr
146    
147    
148  \begin{eqnarray}  \begin{eqnarray}
149  \label{EQ:eg-baro-laplacian_stability}  \label{eq:eg-baro-laplacian_stability}
150  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
151  \end{eqnarray}  \end{eqnarray}
152    
# Line 158  for stability. Line 158  for stability.
158  \cite{adcroft:95}  \cite{adcroft:95}
159    
160  \begin{eqnarray}  \begin{eqnarray}
161  \label{EQ:eg-baro-inertial_stability}  \label{eq:eg-baro-inertial_stability}
162  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
163  \end{eqnarray}  \end{eqnarray}
164    
# Line 170  limit for stability. Line 170  limit for stability.
170  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
171    
172  \begin{eqnarray}  \begin{eqnarray}
173  \label{EQ:eg-baro-cfl_stability}  \label{eq:eg-baro-cfl_stability}
174  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
175  \end{eqnarray}  \end{eqnarray}
176    
# Line 178  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 178  S_{a} = \frac{| \vec{u} | \delta t}{ \De
178  of 0.5 and limits $\delta t$ to $1200s$.  of 0.5 and limits $\delta t$ to $1200s$.
179    
180  \subsection{Code Configuration}  \subsection{Code Configuration}
181  \label{www:tutorials}  %\label{www:tutorials}
182  \label{SEC:eg-baro-code_config}  \label{sec:eg-baro-code_config}
183    
184  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
185  directory {\it verification/tutorial\_barotropic\_gyre/}.    directory {\it verification/tutorial\_barotropic\_gyre/}.  
# Line 199  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}  %\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 311  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}  %\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}  %\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}  %\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 334  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}  %\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 346  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}  %\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 369  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}  %\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}  %\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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