/[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 1.10 by afe, Wed Oct 13 18:52:17 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}
18  include both straightforward examples of idealized geophysical  \label{www:tutorials}
19  fluid simulations and more involved cases encompassing  
20  large scale modeling and  This section illustrates an example of MITgcm simulating a laboratory
21  automatic differentiation. Both hydrostatic and non-hydrostatic  experiment on much smaller scales than those commonly considered in  
22  experiments are presented, as well as experiments employing  geophysical
23  Cartesian, spherical-polar and cube-sphere coordinate systems.  fluid dynamics.
 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.  
24    
25  \section{Barotropic Ocean Gyre In Cartesian Coordinates}  \subsection{Overview}
 \label{sect:eg-baro}  
26  \label{www:tutorials}  \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}  \subsection{Equations Solved}
45  \label{www:tutorials}  \label{www:tutorials}
 The model is configured in hydrostatic form. The implicit free surface form of the  
46    
47    
48  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
49  \label{www:tutorials}  \label{www:tutorials}
50    
51   The domain is discretised with   The domain is discretised with
52  a uniform grid spacing in the horizontal set to  a uniform cylindrical grid spacing in the horizontal set to
53   $\Delta x=\Delta y=20$~km, so   $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
54  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
55  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.
56    \\
57  \subsubsection{Numerical Stability Criteria}  something about heat flux
 \label{www:tutorials}  
   
58    
59  \subsection{Code Configuration}  \subsection{Code Configuration}
60  \label{www:tutorials}  \label{www:tutorials}
61  \label{SEC:eg-baro-code_config}  \label{SEC:eg-baro-code_config}
62    
63  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
64  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/rotatingi\_tank/}.  The experiment files
65  \begin{itemize}  \begin{itemize}
66  \item {\it input/data}  \item {\it input/data}
67  \item {\it input/data.pkg}  \item {\it input/data.pkg}
68  \item {\it input/eedata},  \item {\it input/eedata},
69  \item {\it input/windx.sin\_y},  \item {\it input/bathyPol.bin},
70  \item {\it input/topog.box},  \item {\it input/thetaPol.bin},
71  \item {\it code/CPP\_EEOPTIONS.h}  \item {\it code/CPP\_EEOPTIONS.h}
72  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
73  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
74  \end{itemize}  \end{itemize}
75    
76  contain the code customizations and parameter settings for this  contain the code customizations and parameter settings for this
77  experiments. Below we describe the customizations  experiments. Below we describe the customizations
78  to these files associated with this experiment.  to these files associated with this experiment.
# Line 78  are Line 86  are
86    
87  \begin{itemize}  \begin{itemize}
88    
89  \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
90  the Laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$,
91  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  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 $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
98    
99  \item Lines 15 and 16  \item Lines 27 and 28
100  \begin{verbatim}  \begin{verbatim}
101  rigidLid=.FALSE.,  rigidLid=.TRUE.,
102  implicitFreeSurface=.TRUE.,  implicitFreeSurface=.FALSE.,
103  \end{verbatim}  \end{verbatim}
104  these lines suppress the rigid lid formulation of the surface  
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  pressure inverter and activate the implicit free surface form
108  of the pressure inverter.  of the pressure inverter.
109    
110  \item Line 27,  \item Line 44,
111  \begin{verbatim}  \begin{verbatim}
112  startTime=0,  nIter=0,
113  \end{verbatim}  \end{verbatim}
114  this line indicates that the experiment should start from $t=0$  this line indicates that the experiment should start from $t=0$
115  and implicitly suppresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
116  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
117    
118  \item Line 29,  \item Line 47,
119  \begin{verbatim}  \begin{verbatim}
120  endTime=12000,  deltaT=0.1,
121  \end{verbatim}  \end{verbatim}
122  this line indicates that the experiment should start finish at $t=12000s$.  This line sets the integration timestep to $0.1s$.  This is an unsually
123  A restart file will be written at this time that will enable the  small value among the examples due to the small physical scale of the
124  simulation to be continued from this point.  experiment.
125    
126  \item Line 30,  \item Line 58,
127  \begin{verbatim}  \begin{verbatim}
128  deltaTmom=1200,  usingCylindricalGrid=.TRUE.,
 \end{verbatim}  
 This line sets the momentum equation timestep to $1200s$.  
   
 \item Line 39,  
 \begin{verbatim}  
 usingCartesianGrid=.TRUE.,  
129  \end{verbatim}  \end{verbatim}
130  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
131  Cartesian coordinate system.  cylindrical coordinate system.
132    
133  \item Line 41,  \item Line 60,
134  \begin{verbatim}  \begin{verbatim}
135  delX=60*20E3,  dXspacing=3,
136  \end{verbatim}  \end{verbatim}
137  This line sets the horizontal grid spacing between each x-coordinate line  This line sets the azimuthal grid spacing between each $x$-coordinate line
138  in the discrete grid. The syntax indicates that the discrete grid  in the discrete grid. The syntax indicates that the discrete grid
139  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 $3^{\circ}$.
140  ($20$~km).                                                                                  
141    
142  \item Line 42,  
143    \item Line 61,
144  \begin{verbatim}  \begin{verbatim}
145  delY=60*20E3,  dYspacing=0.01,
146  \end{verbatim}  \end{verbatim}
147  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
148  in the discrete grid to $20 \times 10^{3}m$ ($20$~km).  in the discrete grid to $1cm$.
149    
150  \item Line 43,  \item Line 62,
151  \begin{verbatim}  \begin{verbatim}
152  delZ=5000,  delZ=29*0.005,
153  \end{verbatim}  \end{verbatim}
154  This line sets the vertical grid spacing between each z-coordinate line  This line sets the vertical grid spacing between each z-coordinate line
155  in the discrete grid to $5000m$ ($5$~km).  in the discrete grid to $5000m$ ($5$~km).
156    
157  \item Line 46,  \item Line 68,
158  \begin{verbatim}  \begin{verbatim}
159  bathyFile='topog.box'  bathyFile='bathyPol.bin',
160  \end{verbatim}  \end{verbatim}
161  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
162  bathymetry is read. This file is a two-dimensional ($x,y$) map of  ``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  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 x  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  coordinate varying fastest. The points are ordered from low coordinate
167  to high coordinate for both axes. The units and orientation of the  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  depths in this file are the same as used in the MITgcm code. In this
169  experiment, a depth of $0m$ indicates a solid wall and a depth  experiment, a depth of $0m$ indicates an area outside of the tank
170  of $-5000m$ indicates open ocean. The matlab program  and a depth
171  {\it input/gendata.m} shows an example of how to generate a  f $-0.145m$ indicates the tank itself.
 bathymetry file.  
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 49,  \item Line qqq
184  \begin{verbatim}  \begin{verbatim}
185  zonalWindFile='windx.sin_y'   tCyl  = 0
186  \end{verbatim}  \end{verbatim}
187  This line specifies the name of the file from which the x-direction  This line specifies the temperature in degrees Celsius of the interior
188  surface wind stress is read. This file is also a two-dimensional  wall of the tank -- usually a bucket of ice water.
189  ($x,y$) 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.    
190    
191  \end{itemize}  \end{itemize}
192    
# Line 177  code to generate a valid {\bf zonalWindF Line 194  code to generate a valid {\bf zonalWindF
194  that are described in the MITgcm Getting Started and MITgcm Parameters  that are described in the MITgcm Getting Started and MITgcm Parameters
195  notes.  notes.
196    
197  %%\begin{small}  \begin{small}
198  %%\input{part3/case_studies/barotropic_gyre/input/data}  \input{part3/case_studies/rotating_tank/input/data}
199  %%\end{small}  \end{small}
200    
201  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
202  \label{www:tutorials}  \label{www:tutorials}
# Line 193  customizations for this experiment. Line 210  customizations for this experiment.
210  This file uses standard default values and does not contain  This file uses standard default values and does not contain
211  customizations for this experiment.  customizations for this experiment.
212    
213  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/thetaPol.bin}}
214  \label{www:tutorials}  \label{www:tutorials}
215    
216  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
217  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of initial values of $\theta$ in degrees Celsius.  This particular
218  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
219  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.  
220    
221  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathyPol.bin}}
222  \label{www:tutorials}  \label{www:tutorials}
223    
224    
225  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
226  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
227  $0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep  $0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
228  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
229  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.  
230    
231  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
232  \label{www:tutorials}  \label{www:tutorials}
# Line 224  Two lines are customized in this file fo Line 236  Two lines are customized in this file fo
236  \begin{itemize}  \begin{itemize}
237    
238  \item Line 39,  \item Line 39,
239  \begin{verbatim} sNx=60, \end{verbatim} this line sets  \begin{verbatim} sNx=120, \end{verbatim} this line sets
240  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
241  axis aligned with the x-coordinate.  axis aligned with the x-coordinate.
242    
243  \item Line 40,  \item Line 40,
244  \begin{verbatim} sNy=60, \end{verbatim} this line sets  \begin{verbatim} sNy=31, \end{verbatim} this line sets
245  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
246  axis aligned with the y-coordinate.  axis aligned with the y-coordinate.
247    
248  \end{itemize}  \end{itemize}
249    
250  \begin{small}  \begin{small}
251  \input{part3/case_studies/barotropic_gyre/code/SIZE.h}  \input{part3/case_studies/rotating_tank/code/SIZE.h}
252  \end{small}  \end{small}
253    
254  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
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