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revision 1.3 by cnh, Mon Oct 22 11:55:47 2001 UTC revision 1.13 by molod, Tue Apr 4 20:23:08 2006 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  \section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
17  example MITgcm numerical experiments. The example experiments  \label{sect:eg-baro}
18  include both straightforward examples of idealised geophysical  \label{www:tutorials}
19  fluid simulations and more involved cases encompassing  \begin{rawhtml}
20  large scale modeling and  <!-- CMIREDIR:eg-baro: -->
21  automatic differentiation. Both hydrostatic and non-hydrostatic  \end{rawhtml}
 experiments are presented, as well as experiments employing  
 cartesian, spherical-polar and cube-sphere coordinate systems.  
 These ``case study'' documents include information describing  
 the experimental configuration and detailed information on how to  
 configure the MITgcm code and input files for each experiment.  
22    
 \subsection{Experiment Overview}  
23    
24  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
25  a barotropic, wind-forced, ocean gyre circulation. The experiment  a Barotropic, wind-forced, ocean gyre circulation. The experiment
26  is a numerical rendition of the gyre circulation problem simliar  is a numerical rendition of the gyre circulation problem similar
27  to the problems described analytically by Stommel in 1966  to the problems described analytically by Stommel in 1966
28  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
29    
# Line 40  In this experiment the model Line 31  In this experiment the model
31  is configured to represent a rectangular enclosed box of fluid,  is configured to represent a rectangular enclosed box of fluid,
32  $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
33  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
34  in the ``north-south'' direction. Topologically the grid is cartesian and  in the ``north-south'' direction. Topologically the grid is Cartesian and
35  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
36  equation  equation
37    
38  \begin{equation}  \begin{equation}
39  \label{EQ:fcori}  \label{EQ:eg-baro-fcori}
40  f(y) = f_{0}+\beta y  f(y) = f_{0}+\beta y
41  \end{equation}  \end{equation}
42    
43  \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
44  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
45  (\ref{EQ:fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.  (\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
46  \\  \\
47  \\  \\
48   The sinusoidal wind-stress variations are defined according to   The sinusoidal wind-stress variations are defined according to
49    
50  \begin{equation}  \begin{equation}
51  \label{EQ:taux}  \label{EQ:eg-baro-taux}
52  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})  \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
53  \end{equation}  \end{equation}
54    
# Line 65  simulated domain. For this experiment $f Line 56  simulated domain. For this experiment $f
56  $\tau_0$ is set to $0.1N m^{-2}$.  $\tau_0$ is set to $0.1N m^{-2}$.
57  \\  \\
58  \\  \\
59  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:eg-baro-simulation_config}
60  summarises the configuration simulated.  summarizes the configuration simulated.
61    
62    %% === eh3 ===
63  \begin{figure}  \begin{figure}
64  \begin{center}  %% \begin{center}
65   \resizebox{7.5in}{5.5in}{  %%  \resizebox{7.5in}{5.5in}{
66     \includegraphics*[0.2in,0.7in][10.5in,10.5in]  %%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
67      {part3/case_studies/barotropic_gyre/simulation_config.eps} }  %%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
68  \end{center}  %% \end{center}
69    \centerline{
70      \scalefig{.95}
71      \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
72    }
73  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
74  for barotropic gyre numerical experiment. The domain is enclosed bu solid  for barotropic gyre numerical experiment. The domain is enclosed bu solid
75  walls at $x=$~0,1200km and at $y=$~0,1200km.}  walls at $x=$~0,1200km and at $y=$~0,1200km.}
76  \label{FIG:simulation_config}  \label{FIG:eg-baro-simulation_config}
77  \end{figure}  \end{figure}
78    
79  \subsection{Equations Solved}  \subsection{Equations Solved}
80    \label{www:tutorials}
81  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
82  pressure equation described in Marshall et. al \cite{Marshall97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
83  employed.  employed.
84  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
85  dissipation. The wind-stress momentum input is added to the momentum equation  dissipation. The wind-stress momentum input is added to the momentum equation
86  for the ``zonal flow'', $u$. Other terms in the model  for the ``zonal flow'', $u$. Other terms in the model
87  are explicitly switched off for this experiement configuration (see section  are explicitly switched off for this experiment configuration (see section
88  \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
89  configuration as follows  configuration as follows
90    
91  \begin{eqnarray}  \begin{eqnarray}
92  \label{EQ:model_equations}  \label{EQ:eg-baro-model_equations}
93  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
94                g\frac{\partial \eta}{\partial x} -                g\frac{\partial \eta}{\partial x} -
95                A_{h}\nabla_{h}^2u                A_{h}\nabla_{h}^2u
# Line 115  flow vector $\vec{u}$. Line 112  flow vector $\vec{u}$.
112    
113    
114  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
115    \label{www:tutorials}
116    
117   The domain is discretised with   The domain is discretised with
118  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 121  that there are sixty grid cells in the $
121  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.
122    
123  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
124    \label{www:tutorials}
125    
126  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
127  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},
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 139  layer is well resolved. Line 138  layer is well resolved.
138    
139  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
140  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
141  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
142    
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 153  for stability. Line 152  for stability.
152  \\  \\
153    
154  \noindent The numerical stability for inertial oscillations    \noindent The numerical stability for inertial oscillations  
155  \cite{Adcroft_thesis}  \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 164  S_{i} = f^{2} {\delta t}^2 Line 163  S_{i} = f^{2} {\delta t}^2
163  limit for stability.  limit for stability.
164  \\  \\
165    
166  \noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum  \noindent The advective CFL \cite{adcroft:95} for an extreme maximum
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{www:tutorials}
179    \label{SEC:eg-baro-code_config}
180    
181  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
182  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/exp0/}.  The experiment files
# Line 190  directory {\it verification/exp0/}.  The Line 190  directory {\it verification/exp0/}.  The
190  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
191  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
192  \end{itemize}  \end{itemize}
193  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
194  experiements. Below we describe the customisations  experiments. Below we describe the customizations
195  to these files associated with this experiment.  to these files associated with this experiment.
196    
197  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
198    \label{www:tutorials}
199    
200  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
201  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 204  are
204  \begin{itemize}  \begin{itemize}
205    
206  \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
207  the laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $400 m^2s^{-1}$
208  \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
209  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
210    
# Line 221  of the pressure inverter. Line 222  of the pressure inverter.
222  startTime=0,  startTime=0,
223  \end{verbatim}  \end{verbatim}
224  this line indicates that the experiment should start from $t=0$  this line indicates that the experiment should start from $t=0$
225  and implicitly supresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
226  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
227    
228  \item Line 29,  \item Line 29,
# Line 243  This line sets the momentum equation tim Line 244  This line sets the momentum equation tim
244  usingCartesianGrid=.TRUE.,  usingCartesianGrid=.TRUE.,
245  \end{verbatim}  \end{verbatim}
246  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
247  cartesian coordinate system.  Cartesian coordinate system.
248    
249  \item Line 41,  \item Line 41,
250  \begin{verbatim}  \begin{verbatim}
# Line 306  notes. Line 307  notes.
307  \end{small}  \end{small}
308    
309  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
310    \label{www:tutorials}
311    
312  This file uses standard default values and does not contain  This file uses standard default values and does not contain
313  customisations for this experiment.  customizations for this experiment.
314    
315  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
316    \label{www:tutorials}
317    
318  This file uses standard default values and does not contain  This file uses standard default values and does not contain
319  customisations for this experiment.  customizations for this experiment.
320    
321  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
322    \label{www:tutorials}
323    
324  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
325  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 330  in MITgcm. The included matlab program {
330  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
331    
332  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
333    \label{www:tutorials}
334    
335    
336  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 342  The included matlab program {\it input/g
342  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
343    
344  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
345    \label{www:tutorials}
346    
347  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
348    
# Line 359  axis aligned with the y-coordinate. Line 365  axis aligned with the y-coordinate.
365  \end{small}  \end{small}
366    
367  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
368    \label{www:tutorials}
369    
370  This file uses standard default values and does not contain  This file uses standard default values and does not contain
371  customisations for this experiment.  customizations for this experiment.
372    
373    
374  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
375    \label{www:tutorials}
376    
377  This file uses standard default values and does not contain  This file uses standard default values and does not contain
378  customisations for this experiment.  customizations for this experiment.
379    
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