/[MITgcm]/manual/s_examples/barotropic_gyre/baro.tex
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revision 1.3 by cnh, Mon Oct 22 11:55:47 2001 UTC revision 1.6 by adcroft, Tue Nov 13 19:01:42 2001 UTC
# Line 18  Line 18 
18    
19  This is the first in a series of sections describing  This is the first in a series of sections describing
20  example MITgcm numerical experiments. The example experiments  example MITgcm numerical experiments. The example experiments
21  include both straightforward examples of idealised geophysical  include both straightforward examples of idealized geophysical
22  fluid simulations and more involved cases encompassing  fluid simulations and more involved cases encompassing
23  large scale modeling and  large scale modeling and
24  automatic differentiation. Both hydrostatic and non-hydrostatic  automatic differentiation. Both hydrostatic and non-hydrostatic
25  experiments are presented, as well as experiments employing  experiments are presented, as well as experiments employing
26  cartesian, spherical-polar and cube-sphere coordinate systems.  Cartesian, spherical-polar and cube-sphere coordinate systems.
27  These ``case study'' documents include information describing  These ``case study'' documents include information describing
28  the experimental configuration and detailed information on how to  the experimental configuration and detailed information on how to
29  configure the MITgcm code and input files for each experiment.  configure the MITgcm code and input files for each experiment.
# Line 31  configure the MITgcm code and input file Line 31  configure the MITgcm code and input file
31  \subsection{Experiment Overview}  \subsection{Experiment Overview}
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    
# Line 66  $\tau_0$ is set to $0.1N m^{-2}$. Line 66  $\tau_0$ is set to $0.1N m^{-2}$.
66  \\  \\
67  \\  \\
68  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:simulation_config}
69  summarises the configuration simulated.  summarizes the configuration simulated.
70    
71  \begin{figure}  \begin{figure}
72  \begin{center}  \begin{center}
# Line 82  walls at $x=$~0,1200km and at $y=$~0,120 Line 82  walls at $x=$~0,1200km and at $y=$~0,120
82    
83  \subsection{Equations Solved}  \subsection{Equations Solved}
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{Marshall97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
86  employed.  employed.
87  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
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 experiement 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:code_config} ), yielding an active set of equations solved in this
92  configuration as follows  configuration as follows
93    
# Line 124  model is configured with a single layer Line 124  model is configured with a single layer
124    
125  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
126    
127  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
128  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},
129    
130  \begin{eqnarray}  \begin{eqnarray}
131  \label{EQ:munk_layer}  \label{EQ:munk_layer}
# Line 139  layer is well resolved. Line 139  layer is well resolved.
139    
140  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
141  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
142  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
143    
144    
145    
# Line 153  for stability. Line 153  for stability.
153  \\  \\
154    
155  \noindent The numerical stability for inertial oscillations    \noindent The numerical stability for inertial oscillations  
156  \cite{Adcroft_thesis}  \cite{adcroft:95}
157    
158  \begin{eqnarray}  \begin{eqnarray}
159  \label{EQ:inertial_stability}  \label{EQ:inertial_stability}
# Line 164  S_{i} = f^{2} {\delta t}^2 Line 164  S_{i} = f^{2} {\delta t}^2
164  limit for stability.  limit for stability.
165  \\  \\
166    
167  \noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum  \noindent The advective CFL \cite{adcroft:95} for an extreme maximum
168  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
169    
170  \begin{eqnarray}  \begin{eqnarray}
# 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}}
# Line 203  are Line 203  are
203  \begin{itemize}  \begin{itemize}
204    
205  \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
206  the laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $400 m^2s^{-1}$
207  \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
208  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
209    
# Line 221  of the pressure inverter. Line 221  of the pressure inverter.
221  startTime=0,  startTime=0,
222  \end{verbatim}  \end{verbatim}
223  this line indicates that the experiment should start from $t=0$  this line indicates that the experiment should start from $t=0$
224  and implicitly supresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
225  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
226    
227  \item Line 29,  \item Line 29,
# Line 243  This line sets the momentum equation tim Line 243  This line sets the momentum equation tim
243  usingCartesianGrid=.TRUE.,  usingCartesianGrid=.TRUE.,
244  \end{verbatim}  \end{verbatim}
245  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
246  cartesian coordinate system.  Cartesian coordinate system.
247    
248  \item Line 41,  \item Line 41,
249  \begin{verbatim}  \begin{verbatim}
# Line 308  notes. Line 308  notes.
308  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
309    
310  This file uses standard default values and does not contain  This file uses standard default values and does not contain
311  customisations for this experiment.  customizations for this experiment.
312    
313  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
314    
315  This file uses standard default values and does not contain  This file uses standard default values and does not contain
316  customisations for this experiment.  customizations for this experiment.
317    
318  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
319    
# Line 361  axis aligned with the y-coordinate. Line 361  axis aligned with the y-coordinate.
361  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
362    
363  This file uses standard default values and does not contain  This file uses standard default values and does not contain
364  customisations for this experiment.  customizations for this experiment.
365    
366    
367  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
368    
369  This file uses standard default values and does not contain  This file uses standard default values and does not contain
370  customisations for this experiment.  customizations for this experiment.
371    
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