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revision 1.1 by afe, Tue Jun 22 15:07:37 2004 UTC revision 1.9 by afe, Tue Jul 27 13:40:09 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 common to geophysical
22  experiments are presented, as well as experiments employing  fluid dynamics.
 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.  
23    
24  \section{Barotropic Ocean Gyre In Cartesian Coordinates}  \subsection{Overview}
 \label{sect:eg-baro}  
25  \label{www:tutorials}  \label{www:tutorials}
26                                                                                    
27                                                                                    
28    This example experiment demonstrates using the MITgcm to simulate
29    a laboratory experiment with a rotating tank of water with an ice
30    bucket in the center. The simulation is configured for a laboratory
31    scale on a
32    $3^{\circ}$ $\times$ 20cm
33    cyclindrical grid with twenty-nine vertical
34    levels.
35    \\
36    
37    
38    
39    
40    
41  \subsection{Equations Solved}  \subsection{Equations Solved}
42  \label{www:tutorials}  \label{www:tutorials}
 The model is configured in hydrostatic form. The implicit free surface form of the  
43    
44    
45  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
# Line 45  a uniform grid spacing in the horizontal Line 51  a uniform grid spacing in the horizontal
51  that there are sixty grid cells in the $x$ and $y$ directions. Vertically the  that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
52  model is configured with a single layer with depth, $\Delta z$, of $5000$~m.  model is configured with a single layer with depth, $\Delta z$, of $5000$~m.
53    
 \subsubsection{Numerical Stability Criteria}  
 \label{www:tutorials}  
   
54    
55  \subsection{Code Configuration}  \subsection{Code Configuration}
56  \label{www:tutorials}  \label{www:tutorials}
57  \label{SEC:eg-baro-code_config}  \label{SEC:eg-baro-code_config}
58    
59  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
60  directory {\it verification/exp0/}.  The experiment files  directory {\it verification/rotatingi\_tank/}.  The experiment files
61  \begin{itemize}  \begin{itemize}
62  \item {\it input/data}  \item {\it input/data}
63  \item {\it input/data.pkg}  \item {\it input/data.pkg}
64  \item {\it input/eedata},  \item {\it input/eedata},
65  \item {\it input/windx.sin\_y},  \item {\it input/bathyPol.bin},
66  \item {\it input/topog.box},  \item {\it input/thetaPol.bin},
67  \item {\it code/CPP\_EEOPTIONS.h}  \item {\it code/CPP\_EEOPTIONS.h}
68  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
69  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
70  \end{itemize}  \end{itemize}
71    
72  contain the code customizations and parameter settings for this  contain the code customizations and parameter settings for this
73  experiments. Below we describe the customizations  experiments. Below we describe the customizations
74  to these files associated with this experiment.  to these files associated with this experiment.
# Line 78  are Line 82  are
82    
83  \begin{itemize}  \begin{itemize}
84    
85  \item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets  \item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets
86  the Laplacian friction coefficient to $400 m^2s^{-1}$  the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally
87    low because of the small scale, presumably.... qqq
88    
89    \item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
90    coriolis term, and represents a tank spinning at qqq
91  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
92  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
93    
94  \item Lines 15 and 16  \item Lines 15 and 16
95  \begin{verbatim}  \begin{verbatim}
96  rigidLid=.FALSE.,  rigidLid=.TRUE.,
97  implicitFreeSurface=.TRUE.,  implicitFreeSurface=.FALSE.,
98  \end{verbatim}  \end{verbatim}
99  these lines suppress the rigid lid formulation of the surface  
100    these lines do the opposite of the following:
101    suppress the rigid lid formulation of the surface
102  pressure inverter and activate the implicit free surface form  pressure inverter and activate the implicit free surface form
103  of the pressure inverter.  of the pressure inverter.
104    
# Line 100  this line indicates that the experiment Line 110  this line indicates that the experiment
110  and implicitly suppresses searching for checkpoint files associated  and implicitly suppresses searching for checkpoint files associated
111  with restarting an numerical integration from a previously saved state.  with restarting an numerical integration from a previously saved state.
112    
 \item Line 29,  
 \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.  
   
113  \item Line 30,  \item Line 30,
114  \begin{verbatim}  \begin{verbatim}
115  deltaTmom=1200,  deltaT=0.1,
116  \end{verbatim}  \end{verbatim}
117  This line sets the momentum equation timestep to $1200s$.  This line sets the integration timestep to $0.1s$.  This is an unsually
118    small value among the examples due to the small physical scale of the
119    experiment.
120    
121  \item Line 39,  \item Line 39,
122  \begin{verbatim}  \begin{verbatim}
123  usingCartesianGrid=.TRUE.,  usingCylindricalGrid=.TRUE.,
124  \end{verbatim}  \end{verbatim}
125  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
126  Cartesian coordinate system.  cylindrical coordinate system.
127    
128  \item Line 41,  \item Line qqq,
129  \begin{verbatim}  \begin{verbatim}
130  delX=60*20E3,  dXspacing=3,
131  \end{verbatim}  \end{verbatim}
132  This line sets the horizontal grid spacing between each x-coordinate line  This line sets the azimuthal grid spacing between each x-coordinate line
133  in the discrete grid. The syntax indicates that the discrete grid  in the discrete grid. The syntax indicates that the discrete grid
134  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 $3^{\circ}$.
135  ($20$~km).                                                                                  
136    
137    
138  \item Line 42,  \item Line qqq,
139  \begin{verbatim}  \begin{verbatim}
140  delY=60*20E3,  dYspacing=0.01,
141  \end{verbatim}  \end{verbatim}
142  This line sets the horizontal grid spacing between each y-coordinate line  This line sets the radial grid spacing between each $\rho$-coordinate line
143  in the discrete grid to $20 \times 10^{3}m$ ($20$~km).  in the discrete grid to $1cm$.
144    
145  \item Line 43,  \item Line 43,
146  \begin{verbatim}  \begin{verbatim}
147  delZ=5000,  delZ=29*0.005,
148  \end{verbatim}  \end{verbatim}
149  This line sets the vertical grid spacing between each z-coordinate line  This line sets the vertical grid spacing between each z-coordinate line
150  in the discrete grid to $5000m$ ($5$~km).  in the discrete grid to $5000m$ ($5$~km).
151    
152  \item Line 46,  \item Line 46,
153  \begin{verbatim}  \begin{verbatim}
154  bathyFile='topog.box'  bathyFile='bathyPol.bin',
155  \end{verbatim}  \end{verbatim}
156  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
157  bathymetry is read. This file is a two-dimensional ($x,y$) map of  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
158    ($x,y$) map of
159  depths. This file is assumed to contain 64-bit binary numbers  depths. This file is assumed to contain 64-bit binary numbers
160  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 $x$
161  coordinate varying fastest. The points are ordered from low coordinate  coordinate varying fastest. The points are ordered from low coordinate
162  to high coordinate for both axes. The units and orientation of the  to high coordinate for both axes.  The units and orientation of the
163  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
164  experiment, a depth of $0m$ indicates a solid wall and a depth  experiment, a depth of $0m$ indicates an area outside of the tank
165  of $-5000m$ indicates open ocean. The matlab program  and a depth
166  {\it input/gendata.m} shows an example of how to generate a  f $-0.145m$ indicates the tank itself.
 bathymetry file.  
   
167    
168  \item Line 49,  \item Line 49,
169  \begin{verbatim}  \begin{verbatim}
170  zonalWindFile='windx.sin_y'  hydrogThetaFile='thetaPol.bin',
171  \end{verbatim}  \end{verbatim}
172  This line specifies the name of the file from which the x-direction  This line specifies the name of the file from which the initial values
173  surface wind stress is read. This file is also a two-dimensional  of $\theta$
174  ($x,y$) map and is enumerated and formatted in the same manner as the  are read. This file is a three-dimensional
175  bathymetry file. The matlab program {\it input/gendata.m} includes example  ($x,y,z$) map and is enumerated and formatted in the same manner as the
176  code to generate a valid {\bf zonalWindFile} file.    bathymetry file.
177    
178    \item Line qqq
179    \begin{verbatim}
180     tCyl  = 0
181    \end{verbatim}
182    This line specifies the temperature in degrees Celsius of the interior
183    wall of the tank -- usually a bucket of ice water.
184    
185    
186  \end{itemize}  \end{itemize}
187    
# Line 177  code to generate a valid {\bf zonalWindF Line 189  code to generate a valid {\bf zonalWindF
189  that are described in the MITgcm Getting Started and MITgcm Parameters  that are described in the MITgcm Getting Started and MITgcm Parameters
190  notes.  notes.
191    
192  %%\begin{small}  \begin{small}
193  %%\input{part3/case_studies/barotropic_gyre/input/data}  \input{part3/case_studies/rotating_tank/input/data}
194  %%\end{small}  \end{small}
195    
196  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
197  \label{www:tutorials}  \label{www:tutorials}
# Line 193  customizations for this experiment. Line 205  customizations for this experiment.
205  This file uses standard default values and does not contain  This file uses standard default values and does not contain
206  customizations for this experiment.  customizations for this experiment.
207    
208  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/thetaPol.bin}}
209  \label{www:tutorials}  \label{www:tutorials}
210    
211  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
212  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of initial values of $\theta$ in degrees Celsius.
 Although $\tau_{x}$ is only a function of $y$n in this experiment  
 this file must still define a complete two-dimensional map in order  
 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.  
213    
214  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathyPol.bin}}
215  \label{www:tutorials}  \label{www:tutorials}
216    
217    
218  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$)
219  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
220  $0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep  $0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of
221  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
222  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.  
223    
224  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
225  \label{www:tutorials}  \label{www:tutorials}
# Line 224  Two lines are customized in this file fo Line 229  Two lines are customized in this file fo
229  \begin{itemize}  \begin{itemize}
230    
231  \item Line 39,  \item Line 39,
232  \begin{verbatim} sNx=60, \end{verbatim} this line sets  \begin{verbatim} sNx=120, \end{verbatim} this line sets
233  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
234  axis aligned with the x-coordinate.  axis aligned with the x-coordinate.
235    
236  \item Line 40,  \item Line 40,
237  \begin{verbatim} sNy=60, \end{verbatim} this line sets  \begin{verbatim} sNy=31, \end{verbatim} this line sets
238  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
239  axis aligned with the y-coordinate.  axis aligned with the y-coordinate.
240    
241  \end{itemize}  \end{itemize}
242    
243  \begin{small}  \begin{small}
244  \input{part3/case_studies/barotropic_gyre/code/SIZE.h}  \input{part3/case_studies/rotating_tank/code/SIZE.h}
245  \end{small}  \end{small}
246    
247  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
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