14 |
%\end{center} |
%\end{center} |
15 |
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|
16 |
\section{A Rotating Tank in Cylindrical Coordinates} |
\section{A Rotating Tank in Cylindrical Coordinates} |
17 |
\label{sect:eg-tank} |
\label{sec:eg-tank} |
18 |
\label{www:tutorials} |
%\label{www:tutorials} |
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|
\begin{rawhtml} |
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This section illustrates an example of MITgcm simulating a laboratory |
<!-- CMIREDIR:eg-tank: --> |
21 |
experiment on much smaller scales than those commonly considered in |
\end{rawhtml} |
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geophysical |
\begin{center} |
23 |
fluid dynamics. |
(in directory: {\it verification/rotating\_tank/}) |
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|
\end{center} |
25 |
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|
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\subsection{Overview} |
\subsection{Overview} |
27 |
\label{www:tutorials} |
%\label{www:tutorials} |
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This example configuration demonstrates using the MITgcm to simulate a |
30 |
This example configuration demonstrates using the MITgcm to simulate |
laboratory demonstration using a differentially heated rotating |
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a laboratory demonstration using a rotating tank of water with an ice |
annulus of water. The simulation is configured for a laboratory scale |
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bucket in the center. The simulation is configured for a laboratory |
on a $3^{\circ}\times1\mathrm{cm}$ cyclindrical grid with twenty-nine |
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scale on a |
vertical levels of 0.5cm each. This is a typical laboratory setup for |
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$3^{\circ}$ $\times$ 20cm |
illustration principles of GFD, as well as for a laboratory data |
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cyclindrical grid with twenty-nine vertical |
assimilation project. The files for this experiment can be found in |
36 |
levels. |
the verification directory under rotating\_tank. |
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\\ |
\\ |
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|
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example illustration from GFD lab here |
example illustration from GFD lab here |
40 |
\\ |
\\ |
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44 |
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45 |
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\subsection{Equations Solved} |
\subsection{Equations Solved} |
47 |
\label{www:tutorials} |
%\label{www:tutorials} |
48 |
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|
49 |
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|
50 |
\subsection{Discrete Numerical Configuration} |
\subsection{Discrete Numerical Configuration} |
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\label{www:tutorials} |
%\label{www:tutorials} |
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|
|
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The domain is discretised with |
The domain is discretised with a uniform cylindrical grid spacing in |
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a uniform cylindrical grid spacing in the horizontal set to |
the horizontal set to $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so |
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$\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so |
that there are 120 grid cells in the azimuthal direction and |
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that there are 120 grid cells in the azimuthal direction and thirty-one grid cells in the radial. Vertically the |
thirty-one grid cells in the radial, representing a tank 62cm in |
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model is configured with twenty-nine layers of uniform 0.5cm thickness. |
diameter. The bathymetry file sets the depth=0 in the nine lowest |
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radial rows to represent the central of the annulus. Vertically the |
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model is configured with twenty-nine layers of uniform 0.5cm |
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thickness. |
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\\ |
\\ |
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something about heat flux |
something about heat flux |
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|
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\subsection{Code Configuration} |
\subsection{Code Configuration} |
65 |
\label{www:tutorials} |
%\label{www:tutorials} |
66 |
\label{SEC:eg-baro-code_config} |
\label{sec:eg-tank-code_config} |
67 |
|
|
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The model configuration for this experiment resides under the |
The model configuration for this experiment resides under the |
69 |
directory {\it verification/rotatingi\_tank/}. The experiment files |
directory {\it verification/rotatingi\_tank/}. The experiment files |
83 |
to these files associated with this experiment. |
to these files associated with this experiment. |
84 |
|
|
85 |
\subsubsection{File {\it input/data}} |
\subsubsection{File {\it input/data}} |
86 |
\label{www:tutorials} |
%\label{www:tutorials} |
87 |
|
|
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This file, reproduced completely below, specifies the main parameters |
This file, reproduced completely below, specifies the main parameters |
89 |
for the experiment. The parameters that are significant for this configuration |
for the experiment. The parameters that are significant for this configuration |
91 |
|
|
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\begin{itemize} |
\begin{itemize} |
93 |
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|
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\item Line 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets |
\item Lines 9-10, \begin{verbatim} |
95 |
the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$, |
viscAh=5.0E-6, |
96 |
which is ususally |
viscAz=5.0E-6, |
97 |
low because of the small scale, presumably.... qqq |
\end{verbatim} |
98 |
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|
99 |
\item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the |
|
100 |
coriolis term, and represents a tank spinning at 2/s |
These lines set the Laplacian friction coefficient in the horizontal |
101 |
\item Line 20, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets |
and vertical, respectively. Note that they are several orders of |
102 |
$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ |
magnitude smaller than the other examples due to the small scale of |
103 |
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this example. |
104 |
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|
105 |
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\item Lines 13-16, \begin{verbatim} |
106 |
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diffKhT=2.5E-6, |
107 |
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diffKzT=2.5E-6, |
108 |
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diffKhS=1.0E-6, |
109 |
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diffKzS=1.0E-6, |
110 |
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111 |
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\end{verbatim} |
112 |
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113 |
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|
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These lines set horizontal and vertical diffusion coefficients for |
115 |
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temperature and salinity. Similarly to the friction coefficients, the |
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values are a couple of orders of magnitude less than most |
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configurations. |
118 |
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|
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\item Lines 27 and 28 |
|
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\item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the |
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coriolis term, and represents a tank spinning at about 2.4 rpm. |
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|
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\item Lines 23 and 24 |
124 |
\begin{verbatim} |
\begin{verbatim} |
125 |
rigidLid=.TRUE., |
rigidLid=.TRUE., |
126 |
implicitFreeSurface=.FALSE., |
implicitFreeSurface=.FALSE., |
127 |
\end{verbatim} |
\end{verbatim} |
128 |
|
|
129 |
qqq these lines do the opposite of the following: |
These lines activate the rigid lid formulation of the surface |
130 |
suppress the rigid lid formulation of the surface |
pressure inverter and suppress the implicit free surface form |
|
pressure inverter and activate the implicit free surface form |
|
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of the pressure inverter. |
of the pressure inverter. |
132 |
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|
133 |
\item Line 44, |
\item Line 40, |
134 |
\begin{verbatim} |
\begin{verbatim} |
135 |
nIter=0, |
nIter=0, |
136 |
\end{verbatim} |
\end{verbatim} |
137 |
this line indicates that the experiment should start from $t=0$ |
This line indicates that the experiment should start from $t=0$ and |
138 |
and implicitly suppresses searching for checkpoint files associated |
implicitly suppresses searching for checkpoint files associated with |
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with restarting an numerical integration from a previously saved state. |
restarting an numerical integration from a previously saved state. |
140 |
|
Instead, the file thetaPol.bin will be loaded to initialized the |
141 |
|
temperature fields as indicated below, and other variables will be |
142 |
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initialized to their defaults. |
143 |
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|
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\item Line 47, |
|
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|
\item Line 43, |
146 |
\begin{verbatim} |
\begin{verbatim} |
147 |
deltaT=0.1, |
deltaT=0.1, |
148 |
\end{verbatim} |
\end{verbatim} |
149 |
This line sets the integration timestep to $0.1s$. This is an unsually |
This line sets the integration timestep to $0.1s$. This is an |
150 |
small value among the examples due to the small physical scale of the |
unsually small value among the examples due to the small physical |
151 |
experiment. |
scale of the experiment. Using the ensemble Kalman filter to produce |
152 |
|
input fields can necessitate even shorter timesteps. |
153 |
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|
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\item Line 58, |
\item Line 56, |
155 |
\begin{verbatim} |
\begin{verbatim} |
156 |
usingCylindricalGrid=.TRUE., |
usingCylindricalGrid=.TRUE., |
157 |
\end{verbatim} |
\end{verbatim} |
158 |
This line requests that the simulation be performed in a |
This line requests that the simulation be performed in a |
159 |
cylindrical coordinate system. |
cylindrical coordinate system. |
160 |
|
|
161 |
\item Line 60, |
\item Line 57, |
162 |
\begin{verbatim} |
\begin{verbatim} |
163 |
dXspacing=3, |
dXspacing=3, |
164 |
\end{verbatim} |
\end{verbatim} |
165 |
This line sets the azimuthal grid spacing between each $x$-coordinate line |
This line sets the azimuthal grid spacing between each $x$-coordinate line |
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in the discrete grid. The syntax indicates that the discrete grid |
in the discrete grid. The syntax indicates that the discrete grid |
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should be comprise of $120$ grid lines each separated by $3^{\circ}$. |
should be comprised of $120$ grid lines each separated by $3^{\circ}$. |
168 |
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169 |
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|
\item Line 58, |
|
\item Line 61, |
|
171 |
\begin{verbatim} |
\begin{verbatim} |
172 |
dYspacing=0.01, |
dYspacing=0.01, |
173 |
\end{verbatim} |
\end{verbatim} |
|
This line sets the radial cylindrical grid spacing between each $a$-coordinate line |
|
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in the discrete grid to $1cm$. |
|
174 |
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|
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\item Line 62, |
This line sets the radial cylindrical grid spacing between each |
176 |
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$a$-coordinate line in the discrete grid to $1cm$. |
177 |
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|
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\item Line 59, |
179 |
\begin{verbatim} |
\begin{verbatim} |
180 |
delZ=29*0.005, |
delZ=29*0.005, |
181 |
\end{verbatim} |
\end{verbatim} |
|
This line sets the vertical grid spacing between each z-coordinate line |
|
|
in the discrete grid to $5000m$ ($5$~km). |
|
182 |
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|
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\item Line 68, |
This line sets the vertical grid spacing between each of 29 |
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z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm). |
185 |
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|
186 |
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\item Line 64, |
187 |
\begin{verbatim} |
\begin{verbatim} |
188 |
bathyFile='bathyPol.bin', |
bathyFile='bathyPol.bin', |
189 |
\end{verbatim} |
\end{verbatim} |
199 |
and a depth |
and a depth |
200 |
f $-0.145m$ indicates the tank itself. |
f $-0.145m$ indicates the tank itself. |
201 |
|
|
202 |
\item Line 67, |
\item Line 65, |
203 |
\begin{verbatim} |
\begin{verbatim} |
204 |
hydrogThetaFile='thetaPol.bin', |
hydrogThetaFile='thetaPol.bin', |
205 |
\end{verbatim} |
\end{verbatim} |
209 |
($x,y,z$) map and is enumerated and formatted in the same manner as the |
($x,y,z$) map and is enumerated and formatted in the same manner as the |
210 |
bathymetry file. |
bathymetry file. |
211 |
|
|
212 |
\item Line qqq |
\item Lines 66 and 67 |
213 |
\begin{verbatim} |
\begin{verbatim} |
214 |
tCyl = 0 |
tCylIn = 0 |
215 |
|
tCylOut = 20 |
216 |
\end{verbatim} |
\end{verbatim} |
217 |
This line specifies the temperature in degrees Celsius of the interior |
These line specify the temperatures in degrees Celsius of the interior |
218 |
wall of the tank -- usually a bucket of ice water. |
and exterior walls of the tank -- typically taken to be icewater on |
219 |
|
the inside and room temperature on the outside. |
220 |
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|
221 |
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|
222 |
\end{itemize} |
\end{itemize} |
223 |
|
|
224 |
\noindent other lines in the file {\it input/data} are standard values |
\noindent Other lines in the file {\it input/data} are standard values |
225 |
that are described in the MITgcm Getting Started and MITgcm Parameters |
that are described in the MITgcm Getting Started and MITgcm Parameters |
226 |
notes. |
notes. |
227 |
|
|
228 |
\begin{small} |
\begin{small} |
229 |
\input{part3/case_studies/rotating_tank/input/data} |
\input{s_examples/rotating_tank/input/data} |
230 |
\end{small} |
\end{small} |
231 |
|
|
232 |
\subsubsection{File {\it input/data.pkg}} |
\subsubsection{File {\it input/data.pkg}} |
233 |
\label{www:tutorials} |
%\label{www:tutorials} |
234 |
|
|
235 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
236 |
customizations for this experiment. |
customizations for this experiment. |
237 |
|
|
238 |
\subsubsection{File {\it input/eedata}} |
\subsubsection{File {\it input/eedata}} |
239 |
\label{www:tutorials} |
%\label{www:tutorials} |
240 |
|
|
241 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
242 |
customizations for this experiment. |
customizations for this experiment. |
243 |
|
|
244 |
\subsubsection{File {\it input/thetaPol.bin}} |
\subsubsection{File {\it input/thetaPol.bin}} |
245 |
\label{www:tutorials} |
%\label{www:tutorials} |
246 |
|
|
247 |
The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) |
The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) |
248 |
map of initial values of $\theta$ in degrees Celsius. This particular |
map of initial values of $\theta$ in degrees Celsius. This particular |
250 |
perturbations. |
perturbations. |
251 |
|
|
252 |
\subsubsection{File {\it input/bathyPol.bin}} |
\subsubsection{File {\it input/bathyPol.bin}} |
253 |
\label{www:tutorials} |
%\label{www:tutorials} |
254 |
|
|
255 |
|
|
256 |
The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) |
The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) |
260 |
in the same way as standard MITgcm two-dimensional, horizontal arrays. |
in the same way as standard MITgcm two-dimensional, horizontal arrays. |
261 |
|
|
262 |
\subsubsection{File {\it code/SIZE.h}} |
\subsubsection{File {\it code/SIZE.h}} |
263 |
\label{www:tutorials} |
%\label{www:tutorials} |
264 |
|
|
265 |
Two lines are customized in this file for the current experiment |
Two lines are customized in this file for the current experiment |
266 |
|
|
279 |
\end{itemize} |
\end{itemize} |
280 |
|
|
281 |
\begin{small} |
\begin{small} |
282 |
\input{part3/case_studies/rotating_tank/code/SIZE.h} |
\input{s_examples/rotating_tank/code/SIZE.h} |
283 |
\end{small} |
\end{small} |
284 |
|
|
285 |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
286 |
\label{www:tutorials} |
%\label{www:tutorials} |
287 |
|
|
288 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
289 |
customizations for this experiment. |
customizations for this experiment. |
290 |
|
|
291 |
|
|
292 |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
293 |
\label{www:tutorials} |
%\label{www:tutorials} |
294 |
|
|
295 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
296 |
customizations for this experiment. |
customizations for this experiment. |