/[MITgcm]/manual/s_examples/rotating_tank/tank.tex
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1 % $Header: /u/gcmpack/manual/part3/case_studies/rotating_tank/tank.tex,v 1.9 2004/07/27 13:40:09 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 commonly considered in
22 geophysical
23 fluid dynamics.
24
25 \subsection{Overview}
26 \label{www:tutorials}
27
28
29 This example configuration demonstrates using the MITgcm to simulate
30 a laboratory demonstration using a rotating tank of water with an ice
31 bucket in the center. The simulation is configured for a laboratory
32 scale on a
33 $3^{\circ}$ $\times$ 20cm
34 cyclindrical grid with twenty-nine vertical
35 levels.
36 \\
37 example illustration from GFD lab here
38 \\
39
40
41
42
43
44 \subsection{Equations Solved}
45 \label{www:tutorials}
46
47
48 \subsection{Discrete Numerical Configuration}
49 \label{www:tutorials}
50
51 The domain is discretised with
52 a uniform cylindrical grid spacing in the horizontal set to
53 $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
54 that there are 120 grid cells in the azimuthal direction and thirty-one grid cells in the radial. Vertically the
55 model is configured with twenty-nine layers of uniform 0.5cm thickness.
56 \\
57 something about heat flux
58
59 \subsection{Code Configuration}
60 \label{www:tutorials}
61 \label{SEC:eg-baro-code_config}
62
63 The model configuration for this experiment resides under the
64 directory {\it verification/rotatingi\_tank/}. The experiment files
65 \begin{itemize}
66 \item {\it input/data}
67 \item {\it input/data.pkg}
68 \item {\it input/eedata},
69 \item {\it input/bathyPol.bin},
70 \item {\it input/thetaPol.bin},
71 \item {\it code/CPP\_EEOPTIONS.h}
72 \item {\it code/CPP\_OPTIONS.h},
73 \item {\it code/SIZE.h}.
74 \end{itemize}
75
76 contain the code customizations and parameter settings for this
77 experiments. Below we describe the customizations
78 to these files associated with this experiment.
79
80 \subsubsection{File {\it input/data}}
81 \label{www:tutorials}
82
83 This file, reproduced completely below, specifies the main parameters
84 for the experiment. The parameters that are significant for this configuration
85 are
86
87 \begin{itemize}
88
89 \item Line 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
90 the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$,
91 which is ususally
92 low because of the small scale, presumably.... qqq
93
94 \item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
95 coriolis term, and represents a tank spinning at 2/s
96 \item Line 20, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
97 $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
98
99 \item Lines 27 and 28
100 \begin{verbatim}
101 rigidLid=.TRUE.,
102 implicitFreeSurface=.FALSE.,
103 \end{verbatim}
104
105 qqq these lines do the opposite of the following:
106 suppress the rigid lid formulation of the surface
107 pressure inverter and activate the implicit free surface form
108 of the pressure inverter.
109
110 \item Line 44,
111 \begin{verbatim}
112 nIter=0,
113 \end{verbatim}
114 this line indicates that the experiment should start from $t=0$
115 and implicitly suppresses searching for checkpoint files associated
116 with restarting an numerical integration from a previously saved state.
117
118 \item Line 47,
119 \begin{verbatim}
120 deltaT=0.1,
121 \end{verbatim}
122 This line sets the integration timestep to $0.1s$. This is an unsually
123 small value among the examples due to the small physical scale of the
124 experiment.
125
126 \item Line 58,
127 \begin{verbatim}
128 usingCylindricalGrid=.TRUE.,
129 \end{verbatim}
130 This line requests that the simulation be performed in a
131 cylindrical coordinate system.
132
133 \item Line 60,
134 \begin{verbatim}
135 dXspacing=3,
136 \end{verbatim}
137 This line sets the azimuthal grid spacing between each $x$-coordinate line
138 in the discrete grid. The syntax indicates that the discrete grid
139 should be comprise of $120$ grid lines each separated by $3^{\circ}$.
140
141
142
143 \item Line 61,
144 \begin{verbatim}
145 dYspacing=0.01,
146 \end{verbatim}
147 This line sets the radial cylindrical grid spacing between each $a$-coordinate line
148 in the discrete grid to $1cm$.
149
150 \item Line 62,
151 \begin{verbatim}
152 delZ=29*0.005,
153 \end{verbatim}
154 This line sets the vertical grid spacing between each z-coordinate line
155 in the discrete grid to $5000m$ ($5$~km).
156
157 \item Line 68,
158 \begin{verbatim}
159 bathyFile='bathyPol.bin',
160 \end{verbatim}
161 This line specifies the name of the file from which the domain
162 ``bathymetry'' (tank depth) is read. This file is a two-dimensional
163 ($a,\phi$) map of
164 depths. This file is assumed to contain 64-bit binary numbers
165 giving the depth of the model at each grid cell, ordered with the $\phi$
166 coordinate varying fastest. The points are ordered from low coordinate
167 to high coordinate for both axes. The units and orientation of the
168 depths in this file are the same as used in the MITgcm code. In this
169 experiment, a depth of $0m$ indicates an area outside of the tank
170 and a depth
171 f $-0.145m$ indicates the tank itself.
172
173 \item Line 67,
174 \begin{verbatim}
175 hydrogThetaFile='thetaPol.bin',
176 \end{verbatim}
177 This line specifies the name of the file from which the initial values
178 of temperature
179 are read. This file is a three-dimensional
180 ($x,y,z$) map and is enumerated and formatted in the same manner as the
181 bathymetry file.
182
183 \item Line qqq
184 \begin{verbatim}
185 tCyl = 0
186 \end{verbatim}
187 This line specifies the temperature in degrees Celsius of the interior
188 wall of the tank -- usually a bucket of ice water.
189
190
191 \end{itemize}
192
193 \noindent other lines in the file {\it input/data} are standard values
194 that are described in the MITgcm Getting Started and MITgcm Parameters
195 notes.
196
197 \begin{small}
198 \input{part3/case_studies/rotating_tank/input/data}
199 \end{small}
200
201 \subsubsection{File {\it input/data.pkg}}
202 \label{www:tutorials}
203
204 This file uses standard default values and does not contain
205 customizations for this experiment.
206
207 \subsubsection{File {\it input/eedata}}
208 \label{www:tutorials}
209
210 This file uses standard default values and does not contain
211 customizations for this experiment.
212
213 \subsubsection{File {\it input/thetaPol.bin}}
214 \label{www:tutorials}
215
216 The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
217 map of initial values of $\theta$ in degrees Celsius. This particular
218 experiment is set to random values x around 20C to provide initial
219 perturbations.
220
221 \subsubsection{File {\it input/bathyPol.bin}}
222 \label{www:tutorials}
223
224
225 The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
226 map of depth values. For this experiment values are either
227 $0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
228 the tank. The file contains a raw binary stream of data that is enumerated
229 in the same way as standard MITgcm two-dimensional, horizontal arrays.
230
231 \subsubsection{File {\it code/SIZE.h}}
232 \label{www:tutorials}
233
234 Two lines are customized in this file for the current experiment
235
236 \begin{itemize}
237
238 \item Line 39,
239 \begin{verbatim} sNx=120, \end{verbatim} this line sets
240 the lateral domain extent in grid points for the
241 axis aligned with the x-coordinate.
242
243 \item Line 40,
244 \begin{verbatim} sNy=31, \end{verbatim} this line sets
245 the lateral domain extent in grid points for the
246 axis aligned with the y-coordinate.
247
248 \end{itemize}
249
250 \begin{small}
251 \input{part3/case_studies/rotating_tank/code/SIZE.h}
252 \end{small}
253
254 \subsubsection{File {\it code/CPP\_OPTIONS.h}}
255 \label{www:tutorials}
256
257 This file uses standard default values and does not contain
258 customizations for this experiment.
259
260
261 \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
262 \label{www:tutorials}
263
264 This file uses standard default values and does not contain
265 customizations for this experiment.
266

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