s_examples/rotating_tank/tank.tex

% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.5 2004/07/26 18:41:32 afe Exp $
% $Name:  $

\bodytext{bgcolor="#FFFFFFFF"}

%\begin{center} 
%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical
%Coordinates}
%
%\vspace*{4mm}
%
%\vspace*{3mm}
%{\large May 2001}
%\end{center}

\section{A Rotating Tank in Cylindrical Coordinates}
\label{sect:eg-tank}
\label{www:tutorials}

This section illustrates an example of MITgcm simulating a laboratory
experiment on much smaller scales than those common to geophysical
fluid dynamics.

\subsection{Overview}
\label{www:tutorials}
                                                                                
                                                                                
This example experiment demonstrates using the MITgcm to simulate
a laboratory experiment with a rotating tank of water with an ice
bucket in the center. The simulation is configured for a laboratory
scale on a
$3^{\circ}$ $\times$ 20cm
cyclindrical grid with twenty-nine vertical
levels.
\\


This example experiment demonstrates using the MITgcm to simulate
a Barotropic, wind-forced, ocean gyre circulation. The experiment 
is a numerical rendition of the gyre circulation problem similar
to the problems described analytically by Stommel in 1966 
\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.

In this experiment the model 
is configured to represent a rectangular enclosed box of fluid,
$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
in the ``north-south'' direction. Topologically the grid is Cartesian and 
the coriolis parameter $f$ is defined according to a mid-latitude beta-plane 
equation

\begin{equation}
\label{EQ:eg-baro-fcori}
f(y) = f_{0}+\beta y
\end{equation}
 
\noindent where $y$ is the distance along the ``north-south'' axis of the 
simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in 
(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. 
\\
\\
 The sinusoidal wind-stress variations are defined according to 

\begin{equation}
\label{EQ:eg-baro-taux}
\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
\end{equation}
 
\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and 
$\tau_0$ is set to $0.1N m^{-2}$. 
\\
\\
Figure \ref{FIG:eg-baro-simulation_config}
summarizes the configuration simulated.

%% === eh3 ===
\begin{figure}
%% \begin{center}
%%  \resizebox{7.5in}{5.5in}{
%%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
%%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
%% \end{center}
\centerline{
  \scalefig{.95}
  \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
}
\caption{Schematic of simulation domain and wind-stress forcing function 
for barotropic gyre numerical experiment. The domain is enclosed bu solid
walls at $x=$~0,1200km and at $y=$~0,1200km.}
\label{FIG:eg-baro-simulation_config}
\end{figure}

\subsection{Equations Solved}
\label{www:tutorials}
The model is configured in hydrostatic form. The implicit free surface form of the
pressure equation described in Marshall et. al \cite{marshall:97a} is
employed.
A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
dissipation. The wind-stress momentum input is added to the momentum equation
for the ``zonal flow'', $u$. Other terms in the model
are explicitly switched off for this experiment configuration (see section
\ref{SEC:code_config} ), yielding an active set of equations solved in this
configuration as follows 

\begin{eqnarray}
\label{EQ:eg-baro-model_equations}
\frac{Du}{Dt} - fv +
              g\frac{\partial \eta}{\partial x} -
              A_{h}\nabla_{h}^2u
& = &
\frac{\tau_{x}}{\rho_{0}\Delta z}
\\
\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
              A_{h}\nabla_{h}^2v
& = &
0
\\
\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
&=&
0
\end{eqnarray}

\noindent where $u$ and $v$ and the $x$ and $y$ components of the
flow vector $\vec{u}$.
\\


\subsection{Discrete Numerical Configuration}
\label{www:tutorials}

 The domain is discretised with 
a uniform grid spacing in the horizontal set to
 $\Delta x=\Delta y=20$~km, so 
that there are sixty grid cells in the $x$ and $y$ directions. Vertically the 
model is configured with a single layer with depth, $\Delta z$, of $5000$~m. 

\subsubsection{Numerical Stability Criteria}
\label{www:tutorials}

The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
This value is chosen to yield a Munk layer width \cite{adcroft:95},

\begin{eqnarray}
\label{EQ:eg-baro-munk_layer}
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
\end{eqnarray}

\noindent  of $\approx 100$km. This is greater than the model
resolution $\Delta x$, ensuring that the frictional boundary
layer is well resolved.
\\

\noindent The model is stepped forward with a 
time step $\delta t=1200$secs. With this time step the stability 
parameter to the horizontal Laplacian friction \cite{adcroft:95}


\begin{eqnarray}
\label{EQ:eg-baro-laplacian_stability}
S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
\end{eqnarray}

\noindent evaluates to 0.012, which is well below the 0.3 upper limit
for stability. 
\\

\noindent The numerical stability for inertial oscillations  
\cite{adcroft:95} 

\begin{eqnarray}
\label{EQ:eg-baro-inertial_stability}
S_{i} = f^{2} {\delta t}^2
\end{eqnarray}

\noindent evaluates to $0.0144$, which is well below the $0.5$ upper 
limit for stability.
\\

\noindent The advective CFL \cite{adcroft:95} for an extreme maximum 
horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$

\begin{eqnarray}
\label{EQ:eg-baro-cfl_stability}
S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
\end{eqnarray}

\noindent evaluates to 0.12. This is approaching the stability limit
of 0.5 and limits $\delta t$ to $1200s$.

\subsection{Code Configuration}
\label{www:tutorials}
\label{SEC:eg-baro-code_config}

The model configuration for this experiment resides under the
directory {\it verification/rotatingi\_tank/}.  The experiment files
\begin{itemize}
\item {\it input/data}
\item {\it input/data.pkg}
\item {\it input/eedata},
\item {\it input/bathyPol.bin},
\item {\it input/thetaPol.bin},
\item {\it code/CPP\_EEOPTIONS.h}
\item {\it code/CPP\_OPTIONS.h},
\item {\it code/SIZE.h}.
\end{itemize}

contain the code customizations and parameter settings for this 
experiments. Below we describe the customizations
to these files associated with this experiment.

\subsubsection{File {\it input/data}}
\label{www:tutorials}

This file, reproduced completely below, specifies the main parameters 
for the experiment. The parameters that are significant for this configuration
are

\begin{itemize}

\item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally 
low because of the small scale, presumably.... qqq

\item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the 
coriolis term, and represents a tank spinning at qqq
\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$

\item Lines 15 and 16
\begin{verbatim}
rigidLid=.TRUE.,
implicitFreeSurface=.FALSE.,
\end{verbatim}

these lines do the opposite of the following: 
suppress the rigid lid formulation of the surface
pressure inverter and activate the implicit free surface form
of the pressure inverter.

\item Line 27,
\begin{verbatim}
startTime=0,
\end{verbatim}
this line indicates that the experiment should start from $t=0$
and implicitly suppresses searching for checkpoint files associated
with restarting an numerical integration from a previously saved state.

\item Line 30,
\begin{verbatim}
deltaT=0.1,
\end{verbatim}
This line sets the integration timestep to $0.1s$.  This is an unsually
small value among the examples due to the small physical scale of the 
experiment.

\item Line 39,
\begin{verbatim}
usingCylindricalGrid=.TRUE.,
\end{verbatim}
This line requests that the simulation be performed in a 
Cartesian coordinate system.

\item Line 41,
\begin{verbatim}
delX=60*20E3,
\end{verbatim}
This line sets the horizontal grid spacing between each x-coordinate line
in the discrete grid. The syntax indicates that the discrete grid
should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
($20$~km).

\item Line 42,
\begin{verbatim}
delY=60*20E3,
\end{verbatim}
This line sets the horizontal grid spacing between each y-coordinate line
in the discrete grid to $20 \times 10^{3}m$ ($20$~km).

\item Line 43,
\begin{verbatim}
delZ=5000,
\end{verbatim}
This line sets the vertical grid spacing between each z-coordinate line
in the discrete grid to $5000m$ ($5$~km).

\item Line 46,
\begin{verbatim}
bathyFile='topog.box'
\end{verbatim}
This line specifies the name of the file from which the domain
bathymetry is read. This file is a two-dimensional ($x,y$) map of
depths. This file is assumed to contain 64-bit binary numbers 
giving the depth of the model at each grid cell, ordered with the x 
coordinate varying fastest. The points are ordered from low coordinate
to high coordinate for both axes. The units and orientation of the
depths in this file are the same as used in the MITgcm code. In this
experiment, a depth of $0m$ indicates a solid wall and a depth
of $-5000m$ indicates open ocean. The matlab program
{\it input/gendata.m} shows an example of how to generate a
bathymetry file.


\item Line 49,
\begin{verbatim}
zonalWindFile='windx.sin_y'
\end{verbatim}
This line specifies the name of the file from which the x-direction
surface wind stress is read. This file is also a two-dimensional
($x,y$) map and is enumerated and formatted in the same manner as the 
bathymetry file. The matlab program {\it input/gendata.m} includes example 
code to generate a valid {\bf zonalWindFile} file.  

\end{itemize}

\noindent other lines in the file {\it input/data} are standard values
that are described in the MITgcm Getting Started and MITgcm Parameters
notes.

\begin{small}
\input{part3/case_studies/rotating_tank/input/data}
\end{small}

\subsubsection{File {\it input/data.pkg}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.

\subsubsection{File {\it input/eedata}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.

\subsubsection{File {\it input/thetaPol.bin}}
\label{www:tutorials}

The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) 
map of initial values of $\theta$ in degrees Celsius.

\subsubsection{File {\it input/bathyPol.bin}}
\label{www:tutorials}


The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) 
map of depth values. For this experiment values are either
$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
the tank. The file contains a raw binary stream of data that is enumerated
in the same way as standard MITgcm two-dimensional, horizontal arrays.

\subsubsection{File {\it code/SIZE.h}}
\label{www:tutorials}

Two lines are customized in this file for the current experiment

\begin{itemize}

\item Line 39, 
\begin{verbatim} sNx=60, \end{verbatim} this line sets
the lateral domain extent in grid points for the
axis aligned with the x-coordinate.

\item Line 40, 
\begin{verbatim} sNy=60, \end{verbatim} this line sets
the lateral domain extent in grid points for the
axis aligned with the y-coordinate.

\end{itemize}

\begin{small}
\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
\end{small}

\subsubsection{File {\it code/CPP\_OPTIONS.h}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.


\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
\label{www:tutorials}

This file uses standard default values and does not contain
customizations for this experiment.

1	afe	1.6	% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.5 2004/07/26 18:41:32 afe Exp $
2	afe	1.1	% $Name: $
3
4			\bodytext{bgcolor="#FFFFFFFF"}
5
6			%\begin{center}
7	afe	1.3	%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical
8			%Coordinates}
9	afe	1.1	%
10			%\vspace*{4mm}
11			%
12			%\vspace*{3mm}
13	afe	1.3	%{\large May 2001}
14	afe	1.1	%\end{center}
15
16	afe	1.3	\section{A Rotating Tank in Cylindrical Coordinates}
17			\label{sect:eg-tank}
18	afe	1.2	\label{www:tutorials}
19
20	afe	1.4	This section illustrates an example of MITgcm simulating a laboratory
21			experiment on much smaller scales than those common to geophysical
22			fluid dynamics.
23
24			\subsection{Overview}
25			\label{www:tutorials}
26
27
28			This example experiment demonstrates using the MITgcm to simulate
29			a laboratory experiment with a rotating tank of water with an ice
30			bucket in the center. The simulation is configured for a laboratory
31			scale on a
32			$3^{\circ}$ $\times$ 20cm
33			cyclindrical grid with twenty-nine vertical
34			levels.
35			\\
36
37
38	afe	1.2
39			This example experiment demonstrates using the MITgcm to simulate
40	afe	1.3	a Barotropic, wind-forced, ocean gyre circulation. The experiment
41			is a numerical rendition of the gyre circulation problem similar
42			to the problems described analytically by Stommel in 1966
43			\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
44
45			In this experiment the model
46			is configured to represent a rectangular enclosed box of fluid,
47			$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
48			by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
49			in the ``north-south'' direction. Topologically the grid is Cartesian and
50			the coriolis parameter $f$ is defined according to a mid-latitude beta-plane
51			equation
52
53			\begin{equation}
54			\label{EQ:eg-baro-fcori}
55			f(y) = f_{0}+\beta y
56			\end{equation}
57
58			\noindent where $y$ is the distance along the ``north-south'' axis of the
59			simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in
60			(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$.
61			\\
62			\\
63			The sinusoidal wind-stress variations are defined according to
64
65			\begin{equation}
66			\label{EQ:eg-baro-taux}
67			\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
68			\end{equation}
69
70			\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and
71			$\tau_0$ is set to $0.1N m^{-2}$.
72			\\
73			\\
74			Figure \ref{FIG:eg-baro-simulation_config}
75			summarizes the configuration simulated.
76
77			%% === eh3 ===
78			\begin{figure}
79			%% \begin{center}
80			%% \resizebox{7.5in}{5.5in}{
81			%% \includegraphics*[0.2in,0.7in][10.5in,10.5in]
82			%% {part3/case_studies/barotropic_gyre/simulation_config.eps} }
83			%% \end{center}
84			\centerline{
85			\scalefig{.95}
86			\epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
87			}
88			\caption{Schematic of simulation domain and wind-stress forcing function
89			for barotropic gyre numerical experiment. The domain is enclosed bu solid
90			walls at $x=$~0,1200km and at $y=$~0,1200km.}
91			\label{FIG:eg-baro-simulation_config}
92			\end{figure}
93
94			\subsection{Equations Solved}
95			\label{www:tutorials}
96			The model is configured in hydrostatic form. The implicit free surface form of the
97			pressure equation described in Marshall et. al \cite{marshall:97a} is
98			employed.
99			A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
100			dissipation. The wind-stress momentum input is added to the momentum equation
101			for the ``zonal flow'', $u$. Other terms in the model
102			are explicitly switched off for this experiment configuration (see section
103			\ref{SEC:code_config} ), yielding an active set of equations solved in this
104			configuration as follows
105	afe	1.1
106	afe	1.2	\begin{eqnarray}
107	afe	1.3	\label{EQ:eg-baro-model_equations}
108			\frac{Du}{Dt} - fv +
109			g\frac{\partial \eta}{\partial x} -
110			A_{h}\nabla_{h}^2u
111			& = &
112			\frac{\tau_{x}}{\rho_{0}\Delta z}
113	afe	1.2	\\
114	afe	1.3	\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
115			A_{h}\nabla_{h}^2v
116	afe	1.2	& = &
117	afe	1.3	0
118	afe	1.2	\\
119			\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
120			&=&
121			0
122			\end{eqnarray}
123
124	afe	1.3	\noindent where $u$ and $v$ and the $x$ and $y$ components of the
125			flow vector $\vec{u}$.
126	afe	1.2	\\
127	afe	1.1
128	afe	1.3
129			\subsection{Discrete Numerical Configuration}
130			\label{www:tutorials}
131
132			The domain is discretised with
133			a uniform grid spacing in the horizontal set to
134			$\Delta x=\Delta y=20$~km, so
135			that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
136			model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
137
138	afe	1.1	\subsubsection{Numerical Stability Criteria}
139			\label{www:tutorials}
140
141	afe	1.3	The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
142	afe	1.2	This value is chosen to yield a Munk layer width \cite{adcroft:95},
143	afe	1.3
144	afe	1.2	\begin{eqnarray}
145	afe	1.3	\label{EQ:eg-baro-munk_layer}
146	afe	1.2	M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
147			\end{eqnarray}
148
149	afe	1.3	\noindent of $\approx 100$km. This is greater than the model
150			resolution $\Delta x$, ensuring that the frictional boundary
151			layer is well resolved.
152	afe	1.2	\\
153
154			\noindent The model is stepped forward with a
155	afe	1.3	time step $\delta t=1200$secs. With this time step the stability
156	afe	1.2	parameter to the horizontal Laplacian friction \cite{adcroft:95}
157
158
159	afe	1.3
160	afe	1.2	\begin{eqnarray}
161	afe	1.3	\label{EQ:eg-baro-laplacian_stability}
162			S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
163	afe	1.2	\end{eqnarray}
164
165	afe	1.3	\noindent evaluates to 0.012, which is well below the 0.3 upper limit
166			for stability.
167	afe	1.2	\\
168
169	afe	1.3	\noindent The numerical stability for inertial oscillations
170	afe	1.2	\cite{adcroft:95}
171
172			\begin{eqnarray}
173	afe	1.3	\label{EQ:eg-baro-inertial_stability}
174			S_{i} = f^{2} {\delta t}^2
175	afe	1.2	\end{eqnarray}
176
177	afe	1.3	\noindent evaluates to $0.0144$, which is well below the $0.5$ upper
178			limit for stability.
179	afe	1.2	\\
180
181	afe	1.3	\noindent The advective CFL \cite{adcroft:95} for an extreme maximum
182			horizontal flow speed of $ \| \vec{u} \| = 2 ms^{-1}$
183	afe	1.2
184			\begin{eqnarray}
185	afe	1.3	\label{EQ:eg-baro-cfl_stability}
186			S_{a} = \frac{\| \vec{u} \| \delta t}{ \Delta x}
187	afe	1.2	\end{eqnarray}
188
189	afe	1.3	\noindent evaluates to 0.12. This is approaching the stability limit
190			of 0.5 and limits $\delta t$ to $1200s$.
191	afe	1.2
192	afe	1.3	\subsection{Code Configuration}
193	afe	1.1	\label{www:tutorials}
194	afe	1.3	\label{SEC:eg-baro-code_config}
195	afe	1.1
196	afe	1.5	The model configuration for this experiment resides under the
197			directory {\it verification/rotatingi\_tank/}. The experiment files
198	afe	1.1	\begin{itemize}
199			\item {\it input/data}
200			\item {\it input/data.pkg}
201			\item {\it input/eedata},
202	afe	1.5	\item {\it input/bathyPol.bin},
203			\item {\it input/thetaPol.bin},
204	afe	1.1	\item {\it code/CPP\_EEOPTIONS.h}
205			\item {\it code/CPP\_OPTIONS.h},
206	afe	1.5	\item {\it code/SIZE.h}.
207	afe	1.1	\end{itemize}
208	afe	1.5
209	afe	1.3	contain the code customizations and parameter settings for this
210	afe	1.1	experiments. Below we describe the customizations
211			to these files associated with this experiment.
212
213			\subsubsection{File {\it input/data}}
214			\label{www:tutorials}
215
216			This file, reproduced completely below, specifies the main parameters
217			for the experiment. The parameters that are significant for this configuration
218			are
219
220			\begin{itemize}
221
222	afe	1.6	\item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
223			the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally
224			low because of the small scale, presumably.... qqq
225
226			\item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
227			coriolis term, and represents a tank spinning at qqq
228	afe	1.3	\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
229			$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
230
231			\item Lines 15 and 16
232			\begin{verbatim}
233	afe	1.6	rigidLid=.TRUE.,
234			implicitFreeSurface=.FALSE.,
235	afe	1.3	\end{verbatim}
236	afe	1.6
237			these lines do the opposite of the following:
238			suppress the rigid lid formulation of the surface
239	afe	1.3	pressure inverter and activate the implicit free surface form
240			of the pressure inverter.
241	afe	1.1
242			\item Line 27,
243			\begin{verbatim}
244	afe	1.3	startTime=0,
245	afe	1.1	\end{verbatim}
246	afe	1.3	this line indicates that the experiment should start from $t=0$
247			and implicitly suppresses searching for checkpoint files associated
248			with restarting an numerical integration from a previously saved state.
249	afe	1.2
250	afe	1.1	\item Line 30,
251			\begin{verbatim}
252	afe	1.6	deltaT=0.1,
253	afe	1.1	\end{verbatim}
254	afe	1.6	This line sets the integration timestep to $0.1s$. This is an unsually
255			small value among the examples due to the small physical scale of the
256			experiment.
257	afe	1.1
258	afe	1.3	\item Line 39,
259	afe	1.1	\begin{verbatim}
260	afe	1.6	usingCylindricalGrid=.TRUE.,
261	afe	1.1	\end{verbatim}
262	afe	1.3	This line requests that the simulation be performed in a
263			Cartesian coordinate system.
264	afe	1.1
265	afe	1.3	\item Line 41,
266	afe	1.1	\begin{verbatim}
267	afe	1.3	delX=60*20E3,
268	afe	1.1	\end{verbatim}
269	afe	1.3	This line sets the horizontal grid spacing between each x-coordinate line
270			in the discrete grid. The syntax indicates that the discrete grid
271			should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$
272			($20$~km).
273	afe	1.1
274			\item Line 42,
275			\begin{verbatim}
276	afe	1.3	delY=60*20E3,
277	afe	1.1	\end{verbatim}
278	afe	1.3	This line sets the horizontal grid spacing between each y-coordinate line
279			in the discrete grid to $20 \times 10^{3}m$ ($20$~km).
280	afe	1.1
281			\item Line 43,
282			\begin{verbatim}
283	afe	1.3	delZ=5000,
284	afe	1.2	\end{verbatim}
285	afe	1.3	This line sets the vertical grid spacing between each z-coordinate line
286			in the discrete grid to $5000m$ ($5$~km).
287	afe	1.1
288			\item Line 46,
289			\begin{verbatim}
290			bathyFile='topog.box'
291			\end{verbatim}
292			This line specifies the name of the file from which the domain
293			bathymetry is read. This file is a two-dimensional ($x,y$) map of
294			depths. This file is assumed to contain 64-bit binary numbers
295			giving the depth of the model at each grid cell, ordered with the x
296			coordinate varying fastest. The points are ordered from low coordinate
297			to high coordinate for both axes. The units and orientation of the
298			depths in this file are the same as used in the MITgcm code. In this
299			experiment, a depth of $0m$ indicates a solid wall and a depth
300	afe	1.3	of $-5000m$ indicates open ocean. The matlab program
301	afe	1.1	{\it input/gendata.m} shows an example of how to generate a
302			bathymetry file.
303
304
305	afe	1.3	\item Line 49,
306	afe	1.1	\begin{verbatim}
307			zonalWindFile='windx.sin_y'
308			\end{verbatim}
309			This line specifies the name of the file from which the x-direction
310			surface wind stress is read. This file is also a two-dimensional
311			($x,y$) map and is enumerated and formatted in the same manner as the
312			bathymetry file. The matlab program {\it input/gendata.m} includes example
313	afe	1.3	code to generate a valid {\bf zonalWindFile} file.
314	afe	1.1
315			\end{itemize}
316
317			\noindent other lines in the file {\it input/data} are standard values
318			that are described in the MITgcm Getting Started and MITgcm Parameters
319			notes.
320
321	afe	1.2	\begin{small}
322	afe	1.5	\input{part3/case_studies/rotating_tank/input/data}
323	afe	1.2	\end{small}
324	afe	1.1
325			\subsubsection{File {\it input/data.pkg}}
326			\label{www:tutorials}
327
328			This file uses standard default values and does not contain
329	afe	1.3	customizations for this experiment.
330	afe	1.1
331			\subsubsection{File {\it input/eedata}}
332			\label{www:tutorials}
333
334			This file uses standard default values and does not contain
335	afe	1.3	customizations for this experiment.
336	afe	1.1
337	afe	1.6	\subsubsection{File {\it input/thetaPol.bin}}
338	afe	1.1	\label{www:tutorials}
339
340	afe	1.6	The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
341			map of initial values of $\theta$ in degrees Celsius.
342	afe	1.1
343	afe	1.6	\subsubsection{File {\it input/bathyPol.bin}}
344	afe	1.1	\label{www:tutorials}
345
346
347	afe	1.6	The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
348	afe	1.1	map of depth values. For this experiment values are either
349	afe	1.6	$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
350			the tank. The file contains a raw binary stream of data that is enumerated
351	afe	1.1	in the same way as standard MITgcm two-dimensional, horizontal arrays.
352
353			\subsubsection{File {\it code/SIZE.h}}
354			\label{www:tutorials}
355
356			Two lines are customized in this file for the current experiment
357
358			\begin{itemize}
359
360			\item Line 39,
361			\begin{verbatim} sNx=60, \end{verbatim} this line sets
362			the lateral domain extent in grid points for the
363			axis aligned with the x-coordinate.
364
365			\item Line 40,
366			\begin{verbatim} sNy=60, \end{verbatim} this line sets
367			the lateral domain extent in grid points for the
368			axis aligned with the y-coordinate.
369
370			\end{itemize}
371
372			\begin{small}
373	afe	1.3	\input{part3/case_studies/barotropic_gyre/code/SIZE.h}
374	afe	1.1	\end{small}
375
376			\subsubsection{File {\it code/CPP\_OPTIONS.h}}
377			\label{www:tutorials}
378
379			This file uses standard default values and does not contain
380	afe	1.3	customizations for this experiment.
381	afe	1.1
382
383			\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
384			\label{www:tutorials}
385
386			This file uses standard default values and does not contain
387	afe	1.3	customizations for this experiment.
388	afe	1.2