s_examples/rotating_tank/tank.tex

% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.10 2004/10/13 18:52:17 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}
\begin{rawhtml}
<!-- CMIREDIR:eg-tank: -->
\end{rawhtml}

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

\subsection{Overview}
\label{www:tutorials}
                                                                                
                                                                                
This example configuration demonstrates using the MITgcm to simulate
a laboratory demonstration using 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.
\\
example illustration from GFD lab here
\\


\subsection{Equations Solved}
\label{www:tutorials}


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

 The domain is discretised with 
a uniform cylindrical grid spacing in the horizontal set to
 $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so 
that there are 120 grid cells in the azimuthal direction and thirty-one grid cells in the radial. Vertically the 
model is configured with twenty-nine layers of uniform 0.5cm thickness.
\\
something about heat flux

\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 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$, 
which is ususally 
low because of the small scale, presumably.... qqq

\item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the 
coriolis term, and represents a tank spinning at 2/s
\item Line 20, \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 27 and 28
\begin{verbatim}
rigidLid=.TRUE.,
implicitFreeSurface=.FALSE.,
\end{verbatim}

qqq 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 44,
\begin{verbatim}
nIter=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 47,
\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 58,
\begin{verbatim}
usingCylindricalGrid=.TRUE.,
\end{verbatim}
This line requests that the simulation be performed in a 
cylindrical coordinate system.

\item Line 60,
\begin{verbatim}
dXspacing=3,
\end{verbatim}
This line sets the azimuthal grid spacing between each $x$-coordinate line
in the discrete grid. The syntax indicates that the discrete grid
should be comprise of $120$ grid lines each separated by $3^{\circ}$.
                                                                                

\item Line 61,
\begin{verbatim}
dYspacing=0.01,
\end{verbatim}
This line sets the radial cylindrical grid spacing between each $a$-coordinate line
in the discrete grid to $1cm$.

\item Line 62,
\begin{verbatim}
delZ=29*0.005,
\end{verbatim}
This line sets the vertical grid spacing between each z-coordinate line
in the discrete grid to $5000m$ ($5$~km).

\item Line 68,
\begin{verbatim}
bathyFile='bathyPol.bin',
\end{verbatim}
This line specifies the name of the file from which the domain
``bathymetry'' (tank depth) is read. This file is a two-dimensional 
($a,\phi$) 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 $\phi$ 
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 an area outside of the tank
and a depth
f $-0.145m$ indicates the tank itself. 

\item Line 67,
\begin{verbatim}
hydrogThetaFile='thetaPol.bin',
\end{verbatim}
This line specifies the name of the file from which the initial values 
of temperature
are read. This file is a three-dimensional
($x,y,z$) map and is enumerated and formatted in the same manner as the 
bathymetry file. 

\item Line qqq
\begin{verbatim}
 tCyl  = 0
\end{verbatim}
This line specifies the temperature in degrees Celsius of the interior
wall of the tank -- usually a bucket of ice water.


\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.  This particular 
experiment is set to random values x around 20C to provide initial 
perturbations.

\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=120, \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=31, \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/rotating_tank/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	edhill	1.11	% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.10 2004/10/13 18:52:17 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	edhill	1.11	\begin{rawhtml}
20			<!-- CMIREDIR:eg-tank: -->
21			\end{rawhtml}
22	afe	1.2
23	afe	1.4	This section illustrates an example of MITgcm simulating a laboratory
24	afe	1.10	experiment on much smaller scales than those commonly considered in
25			geophysical
26	afe	1.4	fluid dynamics.
27
28			\subsection{Overview}
29			\label{www:tutorials}
30
31
32	afe	1.10	This example configuration demonstrates using the MITgcm to simulate
33			a laboratory demonstration using a rotating tank of water with an ice
34	afe	1.4	bucket in the center. The simulation is configured for a laboratory
35			scale on a
36			$3^{\circ}$ $\times$ 20cm
37			cyclindrical grid with twenty-nine vertical
38			levels.
39			\\
40	afe	1.10	example illustration from GFD lab here
41			\\
42	afe	1.4
43
44	afe	1.2
45	afe	1.3
46
47			\subsection{Equations Solved}
48			\label{www:tutorials}
49	afe	1.1
50	afe	1.3
51			\subsection{Discrete Numerical Configuration}
52			\label{www:tutorials}
53
54			The domain is discretised with
55	afe	1.10	a uniform cylindrical grid spacing in the horizontal set to
56			$\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
57			that there are 120 grid cells in the azimuthal direction and thirty-one grid cells in the radial. Vertically the
58			model is configured with twenty-nine layers of uniform 0.5cm thickness.
59			\\
60			something about heat flux
61	afe	1.2
62	afe	1.3	\subsection{Code Configuration}
63	afe	1.1	\label{www:tutorials}
64	afe	1.3	\label{SEC:eg-baro-code_config}
65	afe	1.1
66	afe	1.5	The model configuration for this experiment resides under the
67			directory {\it verification/rotatingi\_tank/}. The experiment files
68	afe	1.1	\begin{itemize}
69			\item {\it input/data}
70			\item {\it input/data.pkg}
71			\item {\it input/eedata},
72	afe	1.5	\item {\it input/bathyPol.bin},
73			\item {\it input/thetaPol.bin},
74	afe	1.1	\item {\it code/CPP\_EEOPTIONS.h}
75			\item {\it code/CPP\_OPTIONS.h},
76	afe	1.5	\item {\it code/SIZE.h}.
77	afe	1.1	\end{itemize}
78	afe	1.5
79	afe	1.3	contain the code customizations and parameter settings for this
80	afe	1.1	experiments. Below we describe the customizations
81			to these files associated with this experiment.
82
83			\subsubsection{File {\it input/data}}
84			\label{www:tutorials}
85
86			This file, reproduced completely below, specifies the main parameters
87			for the experiment. The parameters that are significant for this configuration
88			are
89
90			\begin{itemize}
91
92	afe	1.10	\item Line 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
93			the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$,
94			which is ususally
95	afe	1.6	low because of the small scale, presumably.... qqq
96
97	afe	1.10	\item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
98			coriolis term, and represents a tank spinning at 2/s
99			\item Line 20, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
100	afe	1.3	$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
101
102	afe	1.10	\item Lines 27 and 28
103	afe	1.3	\begin{verbatim}
104	afe	1.6	rigidLid=.TRUE.,
105			implicitFreeSurface=.FALSE.,
106	afe	1.3	\end{verbatim}
107	afe	1.6
108	afe	1.10	qqq these lines do the opposite of the following:
109	afe	1.6	suppress the rigid lid formulation of the surface
110	afe	1.3	pressure inverter and activate the implicit free surface form
111			of the pressure inverter.
112	afe	1.1
113	afe	1.10	\item Line 44,
114	afe	1.1	\begin{verbatim}
115	afe	1.10	nIter=0,
116	afe	1.1	\end{verbatim}
117	afe	1.3	this line indicates that the experiment should start from $t=0$
118			and implicitly suppresses searching for checkpoint files associated
119			with restarting an numerical integration from a previously saved state.
120	afe	1.2
121	afe	1.10	\item Line 47,
122	afe	1.1	\begin{verbatim}
123	afe	1.6	deltaT=0.1,
124	afe	1.1	\end{verbatim}
125	afe	1.6	This line sets the integration timestep to $0.1s$. This is an unsually
126			small value among the examples due to the small physical scale of the
127			experiment.
128	afe	1.1
129	afe	1.10	\item Line 58,
130	afe	1.1	\begin{verbatim}
131	afe	1.6	usingCylindricalGrid=.TRUE.,
132	afe	1.1	\end{verbatim}
133	afe	1.3	This line requests that the simulation be performed in a
134	afe	1.7	cylindrical coordinate system.
135	afe	1.1
136	afe	1.10	\item Line 60,
137	afe	1.1	\begin{verbatim}
138	afe	1.7	dXspacing=3,
139	afe	1.1	\end{verbatim}
140	afe	1.10	This line sets the azimuthal grid spacing between each $x$-coordinate line
141	afe	1.3	in the discrete grid. The syntax indicates that the discrete grid
142	afe	1.7	should be comprise of $120$ grid lines each separated by $3^{\circ}$.
143
144
145	afe	1.1
146	afe	1.10	\item Line 61,
147	afe	1.1	\begin{verbatim}
148	afe	1.7	dYspacing=0.01,
149	afe	1.1	\end{verbatim}
150	afe	1.10	This line sets the radial cylindrical grid spacing between each $a$-coordinate line
151	afe	1.7	in the discrete grid to $1cm$.
152	afe	1.1
153	afe	1.10	\item Line 62,
154	afe	1.1	\begin{verbatim}
155	afe	1.7	delZ=29*0.005,
156	afe	1.2	\end{verbatim}
157	afe	1.3	This line sets the vertical grid spacing between each z-coordinate line
158			in the discrete grid to $5000m$ ($5$~km).
159	afe	1.1
160	afe	1.10	\item Line 68,
161	afe	1.1	\begin{verbatim}
162	afe	1.7	bathyFile='bathyPol.bin',
163	afe	1.1	\end{verbatim}
164			This line specifies the name of the file from which the domain
165	afe	1.7	``bathymetry'' (tank depth) is read. This file is a two-dimensional
166	afe	1.10	($a,\phi$) map of
167	afe	1.1	depths. This file is assumed to contain 64-bit binary numbers
168	afe	1.10	giving the depth of the model at each grid cell, ordered with the $\phi$
169	afe	1.1	coordinate varying fastest. The points are ordered from low coordinate
170	afe	1.7	to high coordinate for both axes. The units and orientation of the
171	afe	1.1	depths in this file are the same as used in the MITgcm code. In this
172	afe	1.7	experiment, a depth of $0m$ indicates an area outside of the tank
173			and a depth
174			f $-0.145m$ indicates the tank itself.
175	afe	1.1
176	afe	1.10	\item Line 67,
177	afe	1.7	\begin{verbatim}
178			hydrogThetaFile='thetaPol.bin',
179			\end{verbatim}
180			This line specifies the name of the file from which the initial values
181	afe	1.10	of temperature
182	afe	1.7	are read. This file is a three-dimensional
183			($x,y,z$) map and is enumerated and formatted in the same manner as the
184			bathymetry file.
185	afe	1.1
186	afe	1.7	\item Line qqq
187	afe	1.1	\begin{verbatim}
188	afe	1.7	tCyl = 0
189	afe	1.1	\end{verbatim}
190	afe	1.7	This line specifies the temperature in degrees Celsius of the interior
191			wall of the tank -- usually a bucket of ice water.
192
193	afe	1.1
194			\end{itemize}
195
196			\noindent other lines in the file {\it input/data} are standard values
197			that are described in the MITgcm Getting Started and MITgcm Parameters
198			notes.
199
200	afe	1.2	\begin{small}
201	afe	1.5	\input{part3/case_studies/rotating_tank/input/data}
202	afe	1.2	\end{small}
203	afe	1.1
204			\subsubsection{File {\it input/data.pkg}}
205			\label{www:tutorials}
206
207			This file uses standard default values and does not contain
208	afe	1.3	customizations for this experiment.
209	afe	1.1
210			\subsubsection{File {\it input/eedata}}
211			\label{www:tutorials}
212
213			This file uses standard default values and does not contain
214	afe	1.3	customizations for this experiment.
215	afe	1.1
216	afe	1.6	\subsubsection{File {\it input/thetaPol.bin}}
217	afe	1.1	\label{www:tutorials}
218
219	afe	1.6	The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
220	afe	1.10	map of initial values of $\theta$ in degrees Celsius. This particular
221			experiment is set to random values x around 20C to provide initial
222			perturbations.
223	afe	1.1
224	afe	1.6	\subsubsection{File {\it input/bathyPol.bin}}
225	afe	1.1	\label{www:tutorials}
226
227
228	afe	1.6	The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
229	afe	1.1	map of depth values. For this experiment values are either
230	afe	1.6	$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
231			the tank. The file contains a raw binary stream of data that is enumerated
232	afe	1.1	in the same way as standard MITgcm two-dimensional, horizontal arrays.
233
234			\subsubsection{File {\it code/SIZE.h}}
235			\label{www:tutorials}
236
237			Two lines are customized in this file for the current experiment
238
239			\begin{itemize}
240
241			\item Line 39,
242	afe	1.7	\begin{verbatim} sNx=120, \end{verbatim} this line sets
243	afe	1.1	the lateral domain extent in grid points for the
244			axis aligned with the x-coordinate.
245
246			\item Line 40,
247	afe	1.7	\begin{verbatim} sNy=31, \end{verbatim} this line sets
248	afe	1.1	the lateral domain extent in grid points for the
249			axis aligned with the y-coordinate.
250
251			\end{itemize}
252
253			\begin{small}
254	afe	1.7	\input{part3/case_studies/rotating_tank/code/SIZE.h}
255	afe	1.1	\end{small}
256
257			\subsubsection{File {\it code/CPP\_OPTIONS.h}}
258			\label{www:tutorials}
259
260			This file uses standard default values and does not contain
261	afe	1.3	customizations for this experiment.
262	afe	1.1
263
264			\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
265			\label{www:tutorials}
266
267			This file uses standard default values and does not contain
268	afe	1.3	customizations for this experiment.
269	afe	1.2