/[MITgcm]/manual/s_examples/rotating_tank/tank.tex
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revision 1.1 by afe, Tue Jun 22 15:07:37 2004 UTC revision 1.11 by edhill, Sat Oct 16 03:40:15 2004 UTC
# Line 4  Line 4 
4  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
5    
6  %\begin{center}  %\begin{center}
7  %{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical  %{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical
8  %Coordinates}  %Coordinates}
9  %  %
10  %\vspace*{4mm}  %\vspace*{4mm}
11  %  %
12  %\vspace*{3mm}  %\vspace*{3mm}
13  %{\large June 2004}  %{\large May 2001}
14  %\end{center}  %\end{center}
15    
16  This is the first in a series of tutorials describing  \section{A Rotating Tank in Cylindrical Coordinates}
17  example MITgcm numerical experiments. The example experiments  \label{sect:eg-tank}
 include both straightforward examples of idealized geophysical  
 fluid simulations and more involved cases encompassing  
 large scale modeling and  
 automatic differentiation. Both hydrostatic and non-hydrostatic  
 experiments are presented, as well as experiments employing  
 Cartesian, spherical-polar and cube-sphere coordinate systems.  
 These ``case study'' documents include information describing  
 the experimental configuration and detailed information on how to  
 configure the MITgcm code and input files for each experiment.  
   
 \section{Barotropic Ocean Gyre In Cartesian Coordinates}  
 \label{sect:eg-baro}  
18  \label{www:tutorials}  \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                                                                                    
32    This example configuration demonstrates using the MITgcm to simulate
33    a laboratory demonstration using a rotating tank of water with an ice
34    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    example illustration from GFD lab here
41    \\
42    
43    
44    
45    
46    
47  \subsection{Equations Solved}  \subsection{Equations Solved}
48  \label{www:tutorials}  \label{www:tutorials}
 The model is configured in hydrostatic form. The implicit free surface form of the  
49    
50    
51  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
52  \label{www:tutorials}  \label{www:tutorials}
53    
54   The domain is discretised with   The domain is discretised with
55  a uniform grid spacing in the horizontal set to  a uniform cylindrical grid spacing in the horizontal set to
56   $\Delta x=\Delta y=20$~km, so   $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
57  that there are sixty grid cells in the $x$ and $y$ directions. Vertically the  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 a single layer with depth, $\Delta z$, of $5000$~m.  model is configured with twenty-nine layers of uniform 0.5cm thickness.
59    \\
60  \subsubsection{Numerical Stability Criteria}  something about heat flux
 \label{www:tutorials}  
   
61    
62  \subsection{Code Configuration}  \subsection{Code Configuration}
63  \label{www:tutorials}  \label{www:tutorials}
64  \label{SEC:eg-baro-code_config}  \label{SEC:eg-baro-code_config}
65    
66  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
67  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/rotatingi\_tank/}.  The experiment files
68  \begin{itemize}  \begin{itemize}
69  \item {\it input/data}  \item {\it input/data}
70  \item {\it input/data.pkg}  \item {\it input/data.pkg}
71  \item {\it input/eedata},  \item {\it input/eedata},
72  \item {\it input/windx.sin\_y},  \item {\it input/bathyPol.bin},
73  \item {\it input/topog.box},  \item {\it input/thetaPol.bin},
74  \item {\it code/CPP\_EEOPTIONS.h}  \item {\it code/CPP\_EEOPTIONS.h}
75  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
76  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
77  \end{itemize}  \end{itemize}
78    
79  contain the code customizations and parameter settings for this  contain the code customizations and parameter settings for this
80  experiments. Below we describe the customizations  experiments. Below we describe the customizations
81  to these files associated with this experiment.  to these files associated with this experiment.
# Line 78  are Line 89  are
89    
90  \begin{itemize}  \begin{itemize}
91    
92  \item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets  \item Line 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
93  the Laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$,
94  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  which is ususally
95    low because of the small scale, presumably.... qqq
96    
97    \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  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
101    
102  \item Lines 15 and 16  \item Lines 27 and 28
103  \begin{verbatim}  \begin{verbatim}
104  rigidLid=.FALSE.,  rigidLid=.TRUE.,
105  implicitFreeSurface=.TRUE.,  implicitFreeSurface=.FALSE.,
106  \end{verbatim}  \end{verbatim}
107  these lines suppress the rigid lid formulation of the surface  
108    qqq these lines do the opposite of the following:
109    suppress the rigid lid formulation of the surface
110  pressure inverter and activate the implicit free surface form  pressure inverter and activate the implicit free surface form
111  of the pressure inverter.  of the pressure inverter.
112    
113  \item Line 27,  \item Line 44,
114  \begin{verbatim}  \begin{verbatim}
115  startTime=0,  nIter=0,
116  \end{verbatim}  \end{verbatim}
117  this line indicates that the experiment should start from $t=0$  this line indicates that the experiment should start from $t=0$
118  and implicitly suppresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
119  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
120    
121  \item Line 29,  \item Line 47,
 \begin{verbatim}  
 endTime=12000,  
 \end{verbatim}  
 this line indicates that the experiment should start finish at $t=12000s$.  
 A restart file will be written at this time that will enable the  
 simulation to be continued from this point.  
   
 \item Line 30,  
122  \begin{verbatim}  \begin{verbatim}
123  deltaTmom=1200,  deltaT=0.1,
124  \end{verbatim}  \end{verbatim}
125  This line sets the momentum equation timestep to $1200s$.  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    
129  \item Line 39,  \item Line 58,
130  \begin{verbatim}  \begin{verbatim}
131  usingCartesianGrid=.TRUE.,  usingCylindricalGrid=.TRUE.,
132  \end{verbatim}  \end{verbatim}
133  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
134  Cartesian coordinate system.  cylindrical coordinate system.
135    
136  \item Line 41,  \item Line 60,
137  \begin{verbatim}  \begin{verbatim}
138  delX=60*20E3,  dXspacing=3,
139  \end{verbatim}  \end{verbatim}
140  This line sets the horizontal grid spacing between each x-coordinate line  This line sets the azimuthal grid spacing between each $x$-coordinate line
141  in the discrete grid. The syntax indicates that the discrete grid  in the discrete grid. The syntax indicates that the discrete grid
142  should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$  should be comprise of $120$ grid lines each separated by $3^{\circ}$.
143  ($20$~km).                                                                                  
144    
145  \item Line 42,  
146    \item Line 61,
147  \begin{verbatim}  \begin{verbatim}
148  delY=60*20E3,  dYspacing=0.01,
149  \end{verbatim}  \end{verbatim}
150  This line sets the horizontal grid spacing between each y-coordinate line  This line sets the radial cylindrical grid spacing between each $a$-coordinate line
151  in the discrete grid to $20 \times 10^{3}m$ ($20$~km).  in the discrete grid to $1cm$.
152    
153  \item Line 43,  \item Line 62,
154  \begin{verbatim}  \begin{verbatim}
155  delZ=5000,  delZ=29*0.005,
156  \end{verbatim}  \end{verbatim}
157  This line sets the vertical grid spacing between each z-coordinate line  This line sets the vertical grid spacing between each z-coordinate line
158  in the discrete grid to $5000m$ ($5$~km).  in the discrete grid to $5000m$ ($5$~km).
159    
160  \item Line 46,  \item Line 68,
161  \begin{verbatim}  \begin{verbatim}
162  bathyFile='topog.box'  bathyFile='bathyPol.bin',
163  \end{verbatim}  \end{verbatim}
164  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
165  bathymetry is read. This file is a two-dimensional ($x,y$) map of  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
166    ($a,\phi$) map of
167  depths. This file is assumed to contain 64-bit binary numbers  depths. This file is assumed to contain 64-bit binary numbers
168  giving the depth of the model at each grid cell, ordered with the x  giving the depth of the model at each grid cell, ordered with the $\phi$
169  coordinate varying fastest. The points are ordered from low coordinate  coordinate varying fastest. The points are ordered from low coordinate
170  to high coordinate for both axes. The units and orientation of the  to high coordinate for both axes.  The units and orientation of the
171  depths in this file are the same as used in the MITgcm code. In this  depths in this file are the same as used in the MITgcm code. In this
172  experiment, a depth of $0m$ indicates a solid wall and a depth  experiment, a depth of $0m$ indicates an area outside of the tank
173  of $-5000m$ indicates open ocean. The matlab program  and a depth
174  {\it input/gendata.m} shows an example of how to generate a  f $-0.145m$ indicates the tank itself.
 bathymetry file.  
175    
176    \item Line 67,
177    \begin{verbatim}
178    hydrogThetaFile='thetaPol.bin',
179    \end{verbatim}
180    This line specifies the name of the file from which the initial values
181    of temperature
182    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    
186  \item Line 49,  \item Line qqq
187  \begin{verbatim}  \begin{verbatim}
188  zonalWindFile='windx.sin_y'   tCyl  = 0
189  \end{verbatim}  \end{verbatim}
190  This line specifies the name of the file from which the x-direction  This line specifies the temperature in degrees Celsius of the interior
191  surface wind stress is read. This file is also a two-dimensional  wall of the tank -- usually a bucket of ice water.
192  ($x,y$) map and is enumerated and formatted in the same manner as the  
 bathymetry file. The matlab program {\it input/gendata.m} includes example  
 code to generate a valid {\bf zonalWindFile} file.    
193    
194  \end{itemize}  \end{itemize}
195    
# Line 177  code to generate a valid {\bf zonalWindF Line 197  code to generate a valid {\bf zonalWindF
197  that are described in the MITgcm Getting Started and MITgcm Parameters  that are described in the MITgcm Getting Started and MITgcm Parameters
198  notes.  notes.
199    
200  %%\begin{small}  \begin{small}
201  %%\input{part3/case_studies/barotropic_gyre/input/data}  \input{part3/case_studies/rotating_tank/input/data}
202  %%\end{small}  \end{small}
203    
204  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
205  \label{www:tutorials}  \label{www:tutorials}
# Line 193  customizations for this experiment. Line 213  customizations for this experiment.
213  This file uses standard default values and does not contain  This file uses standard default values and does not contain
214  customizations for this experiment.  customizations for this experiment.
215    
216  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/thetaPol.bin}}
217  \label{www:tutorials}  \label{www:tutorials}
218    
219  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
220  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of initial values of $\theta$ in degrees Celsius.  This particular
221  Although $\tau_{x}$ is only a function of $y$n in this experiment  experiment is set to random values x around 20C to provide initial
222  this file must still define a complete two-dimensional map in order  perturbations.
 to be compatible with the standard code for loading forcing fields  
 in MITgcm. The included matlab program {\it input/gendata.m} gives a complete  
 code for creating the {\it input/windx.sin\_y} file.  
223    
224  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathyPol.bin}}
225  \label{www:tutorials}  \label{www:tutorials}
226    
227    
228  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
229  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
230  $0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep  $0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
231  ocean. The file contains a raw binary stream of data that is enumerated  the tank. The file contains a raw binary stream of data that is enumerated
232  in the same way as standard MITgcm two-dimensional, horizontal arrays.  in the same way as standard MITgcm two-dimensional, horizontal arrays.
 The included matlab program {\it input/gendata.m} gives a complete  
 code for creating the {\it input/topog.box} file.  
233    
234  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
235  \label{www:tutorials}  \label{www:tutorials}
# Line 224  Two lines are customized in this file fo Line 239  Two lines are customized in this file fo
239  \begin{itemize}  \begin{itemize}
240    
241  \item Line 39,  \item Line 39,
242  \begin{verbatim} sNx=60, \end{verbatim} this line sets  \begin{verbatim} sNx=120, \end{verbatim} this line sets
243  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
244  axis aligned with the x-coordinate.  axis aligned with the x-coordinate.
245    
246  \item Line 40,  \item Line 40,
247  \begin{verbatim} sNy=60, \end{verbatim} this line sets  \begin{verbatim} sNy=31, \end{verbatim} this line sets
248  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
249  axis aligned with the y-coordinate.  axis aligned with the y-coordinate.
250    
251  \end{itemize}  \end{itemize}
252    
253  \begin{small}  \begin{small}
254  \input{part3/case_studies/barotropic_gyre/code/SIZE.h}  \input{part3/case_studies/rotating_tank/code/SIZE.h}
255  \end{small}  \end{small}
256    
257  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
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