s_examples/rotating_tank/tank.tex

% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.8 2004/07/26 21:25:34 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.
\\


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


\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. 


\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 
cylindrical coordinate system.

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

\item Line 43,
\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 46,
\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 
($x,y$) 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 an area outside of the tank
and a depth
f $-0.145m$ indicates the tank itself. 

\item Line 49,
\begin{verbatim}
hydrogThetaFile='thetaPol.bin',
\end{verbatim}
This line specifies the name of the file from which the initial values 
of $\theta$ 
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.

\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	% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.8 2004/07/26 21:25:34 afe Exp $
2	% $Name: $
3
4	\bodytext{bgcolor="#FFFFFFFF"}
5
6	%\begin{center}
7	%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical
8	%Coordinates}
9	%
10	%\vspace*{4mm}
11	%
12	%\vspace*{3mm}
13	%{\large May 2001}
14	%\end{center}
15
16	\section{A Rotating Tank in Cylindrical Coordinates}
17	\label{sect:eg-tank}
18	\label{www:tutorials}
19
20	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
39
40
41	\subsection{Equations Solved}
42	\label{www:tutorials}
43
44
45	\subsection{Discrete Numerical Configuration}
46	\label{www:tutorials}
47
48	The domain is discretised with
49	a uniform grid spacing in the horizontal set to
50	$\Delta x=\Delta y=20$~km, so
51	that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
52	model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
53
54
55	\subsection{Code Configuration}
56	\label{www:tutorials}
57	\label{SEC:eg-baro-code_config}
58
59	The model configuration for this experiment resides under the
60	directory {\it verification/rotatingi\_tank/}. The experiment files
61	\begin{itemize}
62	\item {\it input/data}
63	\item {\it input/data.pkg}
64	\item {\it input/eedata},
65	\item {\it input/bathyPol.bin},
66	\item {\it input/thetaPol.bin},
67	\item {\it code/CPP\_EEOPTIONS.h}
68	\item {\it code/CPP\_OPTIONS.h},
69	\item {\it code/SIZE.h}.
70	\end{itemize}
71
72	contain the code customizations and parameter settings for this
73	experiments. Below we describe the customizations
74	to these files associated with this experiment.
75
76	\subsubsection{File {\it input/data}}
77	\label{www:tutorials}
78
79	This file, reproduced completely below, specifies the main parameters
80	for the experiment. The parameters that are significant for this configuration
81	are
82
83	\begin{itemize}
84
85	\item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
86	the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally
87	low because of the small scale, presumably.... qqq
88
89	\item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
90	coriolis term, and represents a tank spinning at qqq
91	\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
92	$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
93
94	\item Lines 15 and 16
95	\begin{verbatim}
96	rigidLid=.TRUE.,
97	implicitFreeSurface=.FALSE.,
98	\end{verbatim}
99
100	these lines do the opposite of the following:
101	suppress the rigid lid formulation of the surface
102	pressure inverter and activate the implicit free surface form
103	of the pressure inverter.
104
105	\item Line 27,
106	\begin{verbatim}
107	startTime=0,
108	\end{verbatim}
109	this line indicates that the experiment should start from $t=0$
110	and implicitly suppresses searching for checkpoint files associated
111	with restarting an numerical integration from a previously saved state.
112
113	\item Line 30,
114	\begin{verbatim}
115	deltaT=0.1,
116	\end{verbatim}
117	This line sets the integration timestep to $0.1s$. This is an unsually
118	small value among the examples due to the small physical scale of the
119	experiment.
120
121	\item Line 39,
122	\begin{verbatim}
123	usingCylindricalGrid=.TRUE.,
124	\end{verbatim}
125	This line requests that the simulation be performed in a
126	cylindrical coordinate system.
127
128	\item Line qqq,
129	\begin{verbatim}
130	dXspacing=3,
131	\end{verbatim}
132	This line sets the azimuthal grid spacing between each x-coordinate line
133	in the discrete grid. The syntax indicates that the discrete grid
134	should be comprise of $120$ grid lines each separated by $3^{\circ}$.
135
136
137
138	\item Line qqq,
139	\begin{verbatim}
140	dYspacing=0.01,
141	\end{verbatim}
142	This line sets the radial grid spacing between each $\rho$-coordinate line
143	in the discrete grid to $1cm$.
144
145	\item Line 43,
146	\begin{verbatim}
147	delZ=29*0.005,
148	\end{verbatim}
149	This line sets the vertical grid spacing between each z-coordinate line
150	in the discrete grid to $5000m$ ($5$~km).
151
152	\item Line 46,
153	\begin{verbatim}
154	bathyFile='bathyPol.bin',
155	\end{verbatim}
156	This line specifies the name of the file from which the domain
157	``bathymetry'' (tank depth) is read. This file is a two-dimensional
158	($x,y$) map of
159	depths. This file is assumed to contain 64-bit binary numbers
160	giving the depth of the model at each grid cell, ordered with the $x$
161	coordinate varying fastest. The points are ordered from low coordinate
162	to high coordinate for both axes. The units and orientation of the
163	depths in this file are the same as used in the MITgcm code. In this
164	experiment, a depth of $0m$ indicates an area outside of the tank
165	and a depth
166	f $-0.145m$ indicates the tank itself.
167
168	\item Line 49,
169	\begin{verbatim}
170	hydrogThetaFile='thetaPol.bin',
171	\end{verbatim}
172	This line specifies the name of the file from which the initial values
173	of $\theta$
174	are read. This file is a three-dimensional
175	($x,y,z$) map and is enumerated and formatted in the same manner as the
176	bathymetry file.
177
178	\item Line qqq
179	\begin{verbatim}
180	tCyl = 0
181	\end{verbatim}
182	This line specifies the temperature in degrees Celsius of the interior
183	wall of the tank -- usually a bucket of ice water.
184
185
186	\end{itemize}
187
188	\noindent other lines in the file {\it input/data} are standard values
189	that are described in the MITgcm Getting Started and MITgcm Parameters
190	notes.
191
192	\begin{small}
193	\input{part3/case_studies/rotating_tank/input/data}
194	\end{small}
195
196	\subsubsection{File {\it input/data.pkg}}
197	\label{www:tutorials}
198
199	This file uses standard default values and does not contain
200	customizations for this experiment.
201
202	\subsubsection{File {\it input/eedata}}
203	\label{www:tutorials}
204
205	This file uses standard default values and does not contain
206	customizations for this experiment.
207
208	\subsubsection{File {\it input/thetaPol.bin}}
209	\label{www:tutorials}
210
211	The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
212	map of initial values of $\theta$ in degrees Celsius.
213
214	\subsubsection{File {\it input/bathyPol.bin}}
215	\label{www:tutorials}
216
217
218	The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
219	map of depth values. For this experiment values are either
220	$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
221	the tank. The file contains a raw binary stream of data that is enumerated
222	in the same way as standard MITgcm two-dimensional, horizontal arrays.
223
224	\subsubsection{File {\it code/SIZE.h}}
225	\label{www:tutorials}
226
227	Two lines are customized in this file for the current experiment
228
229	\begin{itemize}
230
231	\item Line 39,
232	\begin{verbatim} sNx=120, \end{verbatim} this line sets
233	the lateral domain extent in grid points for the
234	axis aligned with the x-coordinate.
235
236	\item Line 40,
237	\begin{verbatim} sNy=31, \end{verbatim} this line sets
238	the lateral domain extent in grid points for the
239	axis aligned with the y-coordinate.
240
241	\end{itemize}
242
243	\begin{small}
244	\input{part3/case_studies/rotating_tank/code/SIZE.h}
245	\end{small}
246
247	\subsubsection{File {\it code/CPP\_OPTIONS.h}}
248	\label{www:tutorials}
249
250	This file uses standard default values and does not contain
251	customizations for this experiment.
252
253
254	\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
255	\label{www:tutorials}
256
257	This file uses standard default values and does not contain
258	customizations for this experiment.
259