s_examples/rotating_tank/tank.tex

% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.13 2005/06/15 14:54:58 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 differentially heated rotating
annulus of water.  The simulation is configured for a laboratory scale
on a $3^{\circ}\times1\mathrm{cm}$ cyclindrical grid with twenty-nine
vertical levels of 0.5cm each.  This is a typical laboratory setup for
illustration principles of GFD, as well as for a laboratory data
assimilation project.
\\

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, representing a tank 62cm in
diameter.  The bathymetry file sets the depth=0 in the nine lowest
radial rows to represent the central of the annulus.  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 Lines 9-10, \begin{verbatim} 
viscAh=5.0E-6, 
viscAz=5.0E-6,
\end{verbatim} 


These lines set the Laplacian friction coefficient in the horizontal
and vertical, respectively.  Note that they are several orders of
magnitude smaller than the other examples due to the small scale of
this example.

\item Lines 13-16, \begin{verbatim} 
 diffKhT=2.5E-6,
 diffKzT=2.5E-6,
 diffKhS=1.0E-6,
 diffKzS=1.0E-6,

\end{verbatim} 


These lines set horizontal and vertical diffusion coefficients for
temperature and salinity.  Similarly to the friction coefficients, the
values are a couple of orders of magnitude less than most
 configurations.


\item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the 
coriolis term, and represents a tank spinning at about 2.4 rpm.

\item Lines 23 and 24
\begin{verbatim}
rigidLid=.TRUE.,
implicitFreeSurface=.FALSE.,
\end{verbatim}

These lines activate  the rigid lid formulation of the surface
pressure inverter and suppress the implicit free surface form
of the pressure inverter.

\item Line 40,
\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.
Instead, the file thetaPol.bin will be loaded to initialized the
temperature fields as indicated below, and other variables will be
initialized to their defaults.


\item Line 43,
\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.  Using the ensemble Kalman filter to produce
input fields can necessitate even shorter timesteps.

\item Line 56,
\begin{verbatim}
usingCylindricalGrid=.TRUE.,
\end{verbatim}
This line requests that the simulation be performed in a 
cylindrical coordinate system.

\item Line 57,
\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 comprised of $120$ grid lines each separated by $3^{\circ}$.
                                                                               

\item Line 58,
\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 59,
\begin{verbatim}
delZ=29*0.005,
\end{verbatim}

This line sets the vertical grid spacing between each of 29
z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm).

\item Line 64,
\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 65,
\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 Lines 66 and 67
\begin{verbatim}
 tCylIn  = 0
 tCylOut  = 20
\end{verbatim}
These line specify the temperatures in degrees Celsius of the interior
and exterior walls of the tank -- typically taken to be icewater on
the inside and room temperature on the outside.


\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	% $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.13 2005/06/15 14:54:58 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	\begin{rawhtml}
20	<!-- CMIREDIR:eg-tank: -->
21	\end{rawhtml}
22
23	This section illustrates an example of MITgcm simulating a laboratory
24	experiment on much smaller scales than those commonly considered in
25	geophysical
26	fluid dynamics.
27
28	\subsection{Overview}
29	\label{www:tutorials}
30
31	This example configuration demonstrates using the MITgcm to simulate a
32	laboratory demonstration using a differentially heated rotating
33	annulus of water. The simulation is configured for a laboratory scale
34	on a $3^{\circ}\times1\mathrm{cm}$ cyclindrical grid with twenty-nine
35	vertical levels of 0.5cm each. This is a typical laboratory setup for
36	illustration principles of GFD, as well as for a laboratory data
37	assimilation project.
38	\\
39
40	example illustration from GFD lab here
41	\\
42
43
44
45
46
47	\subsection{Equations Solved}
48	\label{www:tutorials}
49
50
51	\subsection{Discrete Numerical Configuration}
52	\label{www:tutorials}
53
54	The domain is discretised with a uniform cylindrical grid spacing in
55	the horizontal set to $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
56	that there are 120 grid cells in the azimuthal direction and
57	thirty-one grid cells in the radial, representing a tank 62cm in
58	diameter. The bathymetry file sets the depth=0 in the nine lowest
59	radial rows to represent the central of the annulus. Vertically the
60	model is configured with twenty-nine layers of uniform 0.5cm
61	thickness.
62	\\
63	something about heat flux
64
65	\subsection{Code Configuration}
66	\label{www:tutorials}
67	\label{SEC:eg-baro-code_config}
68
69	The model configuration for this experiment resides under the
70	directory {\it verification/rotatingi\_tank/}. The experiment files
71	\begin{itemize}
72	\item {\it input/data}
73	\item {\it input/data.pkg}
74	\item {\it input/eedata},
75	\item {\it input/bathyPol.bin},
76	\item {\it input/thetaPol.bin},
77	\item {\it code/CPP\_EEOPTIONS.h}
78	\item {\it code/CPP\_OPTIONS.h},
79	\item {\it code/SIZE.h}.
80	\end{itemize}
81
82	contain the code customizations and parameter settings for this
83	experiments. Below we describe the customizations
84	to these files associated with this experiment.
85
86	\subsubsection{File {\it input/data}}
87	\label{www:tutorials}
88
89	This file, reproduced completely below, specifies the main parameters
90	for the experiment. The parameters that are significant for this configuration
91	are
92
93	\begin{itemize}
94
95	\item Lines 9-10, \begin{verbatim}
96	viscAh=5.0E-6,
97	viscAz=5.0E-6,
98	\end{verbatim}
99
100
101	These lines set the Laplacian friction coefficient in the horizontal
102	and vertical, respectively. Note that they are several orders of
103	magnitude smaller than the other examples due to the small scale of
104	this example.
105
106	\item Lines 13-16, \begin{verbatim}
107	diffKhT=2.5E-6,
108	diffKzT=2.5E-6,
109	diffKhS=1.0E-6,
110	diffKzS=1.0E-6,
111
112	\end{verbatim}
113
114
115	These lines set horizontal and vertical diffusion coefficients for
116	temperature and salinity. Similarly to the friction coefficients, the
117	values are a couple of orders of magnitude less than most
118	configurations.
119
120
121	\item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
122	coriolis term, and represents a tank spinning at about 2.4 rpm.
123
124	\item Lines 23 and 24
125	\begin{verbatim}
126	rigidLid=.TRUE.,
127	implicitFreeSurface=.FALSE.,
128	\end{verbatim}
129
130	These lines activate the rigid lid formulation of the surface
131	pressure inverter and suppress the implicit free surface form
132	of the pressure inverter.
133
134	\item Line 40,
135	\begin{verbatim}
136	nIter=0,
137	\end{verbatim}
138	This line indicates that the experiment should start from $t=0$ and
139	implicitly suppresses searching for checkpoint files associated with
140	restarting an numerical integration from a previously saved state.
141	Instead, the file thetaPol.bin will be loaded to initialized the
142	temperature fields as indicated below, and other variables will be
143	initialized to their defaults.
144
145
146	\item Line 43,
147	\begin{verbatim}
148	deltaT=0.1,
149	\end{verbatim}
150	This line sets the integration timestep to $0.1s$. This is an
151	unsually small value among the examples due to the small physical
152	scale of the experiment. Using the ensemble Kalman filter to produce
153	input fields can necessitate even shorter timesteps.
154
155	\item Line 56,
156	\begin{verbatim}
157	usingCylindricalGrid=.TRUE.,
158	\end{verbatim}
159	This line requests that the simulation be performed in a
160	cylindrical coordinate system.
161
162	\item Line 57,
163	\begin{verbatim}
164	dXspacing=3,
165	\end{verbatim}
166	This line sets the azimuthal grid spacing between each $x$-coordinate line
167	in the discrete grid. The syntax indicates that the discrete grid
168	should be comprised of $120$ grid lines each separated by $3^{\circ}$.
169
170
171	\item Line 58,
172	\begin{verbatim}
173	dYspacing=0.01,
174	\end{verbatim}
175
176	This line sets the radial cylindrical grid spacing between each
177	$a$-coordinate line in the discrete grid to $1cm$.
178
179	\item Line 59,
180	\begin{verbatim}
181	delZ=29*0.005,
182	\end{verbatim}
183
184	This line sets the vertical grid spacing between each of 29
185	z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm).
186
187	\item Line 64,
188	\begin{verbatim}
189	bathyFile='bathyPol.bin',
190	\end{verbatim}
191	This line specifies the name of the file from which the domain
192	``bathymetry'' (tank depth) is read. This file is a two-dimensional
193	($a,\phi$) map of
194	depths. This file is assumed to contain 64-bit binary numbers
195	giving the depth of the model at each grid cell, ordered with the $\phi$
196	coordinate varying fastest. The points are ordered from low coordinate
197	to high coordinate for both axes. The units and orientation of the
198	depths in this file are the same as used in the MITgcm code. In this
199	experiment, a depth of $0m$ indicates an area outside of the tank
200	and a depth
201	f $-0.145m$ indicates the tank itself.
202
203	\item Line 65,
204	\begin{verbatim}
205	hydrogThetaFile='thetaPol.bin',
206	\end{verbatim}
207	This line specifies the name of the file from which the initial values
208	of temperature
209	are read. This file is a three-dimensional
210	($x,y,z$) map and is enumerated and formatted in the same manner as the
211	bathymetry file.
212
213	\item Lines 66 and 67
214	\begin{verbatim}
215	tCylIn = 0
216	tCylOut = 20
217	\end{verbatim}
218	These line specify the temperatures in degrees Celsius of the interior
219	and exterior walls of the tank -- typically taken to be icewater on
220	the inside and room temperature on the outside.
221
222
223	\end{itemize}
224
225	\noindent Other lines in the file {\it input/data} are standard values
226	that are described in the MITgcm Getting Started and MITgcm Parameters
227	notes.
228
229	\begin{small}
230	\input{part3/case_studies/rotating_tank/input/data}
231	\end{small}
232
233	\subsubsection{File {\it input/data.pkg}}
234	\label{www:tutorials}
235
236	This file uses standard default values and does not contain
237	customizations for this experiment.
238
239	\subsubsection{File {\it input/eedata}}
240	\label{www:tutorials}
241
242	This file uses standard default values and does not contain
243	customizations for this experiment.
244
245	\subsubsection{File {\it input/thetaPol.bin}}
246	\label{www:tutorials}
247
248	The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
249	map of initial values of $\theta$ in degrees Celsius. This particular
250	experiment is set to random values x around 20C to provide initial
251	perturbations.
252
253	\subsubsection{File {\it input/bathyPol.bin}}
254	\label{www:tutorials}
255
256
257	The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
258	map of depth values. For this experiment values are either
259	$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
260	the tank. The file contains a raw binary stream of data that is enumerated
261	in the same way as standard MITgcm two-dimensional, horizontal arrays.
262
263	\subsubsection{File {\it code/SIZE.h}}
264	\label{www:tutorials}
265
266	Two lines are customized in this file for the current experiment
267
268	\begin{itemize}
269
270	\item Line 39,
271	\begin{verbatim} sNx=120, \end{verbatim} this line sets
272	the lateral domain extent in grid points for the
273	axis aligned with the x-coordinate.
274
275	\item Line 40,
276	\begin{verbatim} sNy=31, \end{verbatim} this line sets
277	the lateral domain extent in grid points for the
278	axis aligned with the y-coordinate.
279
280	\end{itemize}
281
282	\begin{small}
283	\input{part3/case_studies/rotating_tank/code/SIZE.h}
284	\end{small}
285
286	\subsubsection{File {\it code/CPP\_OPTIONS.h}}
287	\label{www:tutorials}
288
289	This file uses standard default values and does not contain
290	customizations for this experiment.
291
292
293	\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
294	\label{www:tutorials}
295
296	This file uses standard default values and does not contain
297	customizations for this experiment.
298