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revision 1.3 by cnh, Mon Oct 22 11:55:47 2001 UTC revision 1.12 by edhill, Sat Oct 16 03:40:13 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 idealised geophysical  include both straightforward examples of idealized geophysical
19  fluid simulations and more involved cases encompassing  fluid simulations and more involved cases encompassing
20  large scale modeling and  large scale modeling and
21  automatic differentiation. Both hydrostatic and non-hydrostatic  automatic differentiation. Both hydrostatic and non-hydrostatic
22  experiments are presented, as well as experiments employing  experiments are presented, as well as experiments employing
23  cartesian, spherical-polar and cube-sphere coordinate systems.  Cartesian, spherical-polar and cube-sphere coordinate systems.
24  These ``case study'' documents include information describing  These ``case study'' documents include information describing
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 Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
29    \label{sect:eg-baro}
30    \label{www:tutorials}
31    \begin{rawhtml}
32    <!-- CMIREDIR:eg-baro: -->
33    \end{rawhtml}
34    
35    
36  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
37  a barotropic, wind-forced, ocean gyre circulation. The experiment  a Barotropic, wind-forced, ocean gyre circulation. The experiment
38  is a numerical rendition of the gyre circulation problem simliar  is a numerical rendition of the gyre circulation problem similar
39  to the problems described analytically by Stommel in 1966  to the problems described analytically by Stommel in 1966
40  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
41    
# Line 40  In this experiment the model Line 43  In this experiment the model
43  is configured to represent a rectangular enclosed box of fluid,  is configured to represent a rectangular enclosed box of fluid,
44  $1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced  $1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
45  by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally  by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
46  in the ``north-south'' direction. Topologically the grid is cartesian and  in the ``north-south'' direction. Topologically the grid is Cartesian and
47  the coriolis parameter $f$ is defined according to a mid-latitude beta-plane  the coriolis parameter $f$ is defined according to a mid-latitude beta-plane
48  equation  equation
49    
50  \begin{equation}  \begin{equation}
51  \label{EQ:fcori}  \label{EQ:eg-baro-fcori}
52  f(y) = f_{0}+\beta y  f(y) = f_{0}+\beta y
53  \end{equation}  \end{equation}
54    
55  \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
56  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
57  (\ref{EQ:fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.  (\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
58  \\  \\
59  \\  \\
60   The sinusoidal wind-stress variations are defined according to   The sinusoidal wind-stress variations are defined according to
61    
62  \begin{equation}  \begin{equation}
63  \label{EQ:taux}  \label{EQ:eg-baro-taux}
64  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
65  \end{equation}  \end{equation}
66    
# Line 65  simulated domain. For this experiment $f Line 68  simulated domain. For this experiment $f
68  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
69  \\  \\
70  \\  \\
71  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-baro-simulation_config}
72  summarises the configuration simulated.  summarizes the configuration simulated.
73    
74    %% === eh3 ===
75  \begin{figure}  \begin{figure}
76  \begin{center}  %% \begin{center}
77   \resizebox{7.5in}{5.5in}{  %%  \resizebox{7.5in}{5.5in}{
78     \includegraphics*[0.2in,0.7in][10.5in,10.5in]  %%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
79      {part3/case_studies/barotropic_gyre/simulation_config.eps} }  %%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
80  \end{center}  %% \end{center}
81    \centerline{
82      \scalefig{.95}
83      \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
84    }
85  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
86  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
87  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
88  \label{FIG:simulation_config}  \label{FIG:eg-baro-simulation_config}
89  \end{figure}  \end{figure}
90    
91  \subsection{Equations Solved}  \subsection{Equations Solved}
92    \label{www:tutorials}
93  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
94  pressure equation described in Marshall et. al \cite{Marshall97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
95  employed.  employed.
96  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
97  dissipation. The wind-stress momentum input is added to the momentum equation  dissipation. The wind-stress momentum input is added to the momentum equation
98  for the ``zonal flow'', $u$. Other terms in the model  for the ``zonal flow'', $u$. Other terms in the model
99  are explicitly switched off for this experiement configuration (see section  are explicitly switched off for this experiment configuration (see section
100  \ref{SEC:code_config} ), yielding an active set of equations solved in this  \ref{SEC:code_config} ), yielding an active set of equations solved in this
101  configuration as follows  configuration as follows
102    
103  \begin{eqnarray}  \begin{eqnarray}
104  \label{EQ:model_equations}  \label{EQ:eg-baro-model_equations}
105  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
106                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
107                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 115  flow vector $\vec{u}$. Line 124  flow vector $\vec{u}$.
124    
125    
126  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
127    \label{www:tutorials}
128    
129   The domain is discretised with   The domain is discretised with
130  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 133  that there are sixty grid cells in the $
133  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.
134    
135  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
136    \label{www:tutorials}
137    
138  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
139  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
140    
141  \begin{eqnarray}  \begin{eqnarray}
142  \label{EQ:munk_layer}  \label{EQ:eg-baro-munk_layer}
143  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
144  \end{eqnarray}  \end{eqnarray}
145    
# Line 139  layer is well resolved. Line 150  layer is well resolved.
150    
151  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
152  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
153  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
154    
155    
156    
157  \begin{eqnarray}  \begin{eqnarray}
158  \label{EQ:laplacian_stability}  \label{EQ:eg-baro-laplacian_stability}
159  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
160  \end{eqnarray}  \end{eqnarray}
161    
# Line 153  for stability. Line 164  for stability.
164  \\  \\
165    
166  \noindent The numerical stability for inertial oscillations    \noindent The numerical stability for inertial oscillations  
167  \cite{Adcroft_thesis}  \cite{adcroft:95}
168    
169  \begin{eqnarray}  \begin{eqnarray}
170  \label{EQ:inertial_stability}  \label{EQ:eg-baro-inertial_stability}
171  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
172  \end{eqnarray}  \end{eqnarray}
173    
# Line 164  S_{i} = f^{2} {\delta t}^2 Line 175  S_{i} = f^{2} {\delta t}^2
175  limit for stability.  limit for stability.
176  \\  \\
177    
178  \noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum  \noindent The advective CFL \cite{adcroft:95} for an extreme maximum
179  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
180    
181  \begin{eqnarray}  \begin{eqnarray}
182  \label{EQ:cfl_stability}  \label{EQ:eg-baro-cfl_stability}
183  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
184  \end{eqnarray}  \end{eqnarray}
185    
# Line 176  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 187  S_{a} = \frac{| \vec{u} | \delta t}{ \De
187  of 0.5 and limits $\delta t$ to $1200s$.  of 0.5 and limits $\delta t$ to $1200s$.
188    
189  \subsection{Code Configuration}  \subsection{Code Configuration}
190  \label{SEC:code_config}  \label{www:tutorials}
191    \label{SEC:eg-baro-code_config}
192    
193  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
194  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/exp0/}.  The experiment files
# Line 190  directory {\it verification/exp0/}.  The Line 202  directory {\it verification/exp0/}.  The
202  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
203  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
204  \end{itemize}  \end{itemize}
205  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
206  experiements. Below we describe the customisations  experiments. Below we describe the customizations
207  to these files associated with this experiment.  to these files associated with this experiment.
208    
209  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
210    \label{www:tutorials}
211    
212  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
213  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 203  are Line 216  are
216  \begin{itemize}  \begin{itemize}
217    
218  \item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets  \item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
219  the laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $400 m^2s^{-1}$
220  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
221  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
222    
# Line 221  of the pressure inverter. Line 234  of the pressure inverter.
234  startTime=0,  startTime=0,
235  \end{verbatim}  \end{verbatim}
236  this line indicates that the experiment should start from $t=0$  this line indicates that the experiment should start from $t=0$
237  and implicitly supresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
238  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
239    
240  \item Line 29,  \item Line 29,
# Line 243  This line sets the momentum equation tim Line 256  This line sets the momentum equation tim
256  usingCartesianGrid=.TRUE.,  usingCartesianGrid=.TRUE.,
257  \end{verbatim}  \end{verbatim}
258  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
259  cartesian coordinate system.  Cartesian coordinate system.
260    
261  \item Line 41,  \item Line 41,
262  \begin{verbatim}  \begin{verbatim}
# Line 306  notes. Line 319  notes.
319  \end{small}  \end{small}
320    
321  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
322    \label{www:tutorials}
323    
324  This file uses standard default values and does not contain  This file uses standard default values and does not contain
325  customisations for this experiment.  customizations for this experiment.
326    
327  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
328    \label{www:tutorials}
329    
330  This file uses standard default values and does not contain  This file uses standard default values and does not contain
331  customisations for this experiment.  customizations for this experiment.
332    
333  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
334    \label{www:tutorials}
335    
336  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
337  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 342  in MITgcm. The included matlab program {
342  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
343    
344  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
345    \label{www:tutorials}
346    
347    
348  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 354  The included matlab program {\it input/g
354  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
355    
356  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
357    \label{www:tutorials}
358    
359  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
360    
# Line 359  axis aligned with the y-coordinate. Line 377  axis aligned with the y-coordinate.
377  \end{small}  \end{small}
378    
379  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
380    \label{www:tutorials}
381    
382  This file uses standard default values and does not contain  This file uses standard default values and does not contain
383  customisations for this experiment.  customizations for this experiment.
384    
385    
386  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
387    \label{www:tutorials}
388    
389  This file uses standard default values and does not contain  This file uses standard default values and does not contain
390  customisations for this experiment.  customizations for this experiment.
391    
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