/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
ViewVC logotype

Diff of /manual/s_examples/barotropic_gyre/baro.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.3 by cnh, Mon Oct 22 11:55:47 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{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 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
35  is a numerical rendition of the gyre circulation problem simliar  is a numerical rendition of the gyre circulation problem similar
36  to the problems described analytically by Stommel in 1966  to the problems described analytically by Stommel in 1966
37  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
38    
# Line 40  In this experiment the model Line 40  In this experiment the model
40  is configured to represent a rectangular enclosed box of fluid,  is configured to represent a rectangular enclosed box of fluid,
41  $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
42  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
43  in the ``north-south'' direction. Topologically the grid is cartesian and  in the ``north-south'' direction. Topologically the grid is Cartesian and
44  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
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  summarises the configuration simulated.  summarizes the configuration simulated.
70    
71  \begin{figure}  \begin{figure}
72  \begin{center}  \begin{center}
# Line 77  summarises the configuration simulated. Line 77  summarises 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{Marshall97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
87  employed.  employed.
88  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
89  dissipation. The wind-stress momentum input is added to the momentum equation  dissipation. The wind-stress momentum input is added to the momentum equation
90  for the ``zonal flow'', $u$. Other terms in the model  for the ``zonal flow'', $u$. Other terms in the model
91  are explicitly switched off for this experiement configuration (see section  are explicitly switched off for this experiment configuration (see section
92  \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
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_thesis},  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 139  layer is well resolved. Line 142  layer is well resolved.
142    
143  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
144  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
145  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
146    
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 153  for stability. Line 156  for stability.
156  \\  \\
157    
158  \noindent The numerical stability for inertial oscillations    \noindent The numerical stability for inertial oscillations  
159  \cite{Adcroft_thesis}  \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 164  S_{i} = f^{2} {\delta t}^2 Line 167  S_{i} = f^{2} {\delta t}^2
167  limit for stability.  limit for stability.
168  \\  \\
169    
170  \noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum  \noindent The advective CFL \cite{adcroft:95} for an extreme maximum
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 190  directory {\it verification/exp0/}.  The Line 194  directory {\it verification/exp0/}.  The
194  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
195  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
196  \end{itemize}  \end{itemize}
197  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
198  experiements. Below we describe the customisations  experiments. Below we describe the customizations
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 203  are Line 208  are
208  \begin{itemize}  \begin{itemize}
209    
210  \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
211  the laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $400 m^2s^{-1}$
212  \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
213  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
214    
# Line 221  of the pressure inverter. Line 226  of the pressure inverter.
226  startTime=0,  startTime=0,
227  \end{verbatim}  \end{verbatim}
228  this line indicates that the experiment should start from $t=0$  this line indicates that the experiment should start from $t=0$
229  and implicitly supresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
230  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
231    
232  \item Line 29,  \item Line 29,
# Line 243  This line sets the momentum equation tim Line 248  This line sets the momentum equation tim
248  usingCartesianGrid=.TRUE.,  usingCartesianGrid=.TRUE.,
249  \end{verbatim}  \end{verbatim}
250  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
251  cartesian coordinate system.  Cartesian coordinate system.
252    
253  \item Line 41,  \item Line 41,
254  \begin{verbatim}  \begin{verbatim}
# 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  customisations 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  customisations 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  customisations 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  customisations for this experiment.  customizations for this experiment.
383    
Legend:
Removed from v.1.3  
changed lines
  Added in v.1.9
  ViewVC Help
Powered by ViewVC 1.1.22