/[MITgcm]/manual/s_examples/rotating_tank/tank.tex
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revision 1.9 by afe, Tue Jul 27 13:40:09 2004 UTC revision 1.16 by jmc, Tue Jan 15 20:16:44 2008 UTC
# Line 16  Line 16 
16  \section{A Rotating Tank in Cylindrical Coordinates}  \section{A Rotating Tank in Cylindrical Coordinates}
17  \label{sect:eg-tank}  \label{sect:eg-tank}
18  \label{www:tutorials}  \label{www:tutorials}
19    \begin{rawhtml}
20  This section illustrates an example of MITgcm simulating a laboratory  <!-- CMIREDIR:eg-tank: -->
21  experiment on much smaller scales than those common to geophysical  \end{rawhtml}
22  fluid dynamics.  \begin{center}
23    (in directory: {\it verification/rotating\_tank/})
24    \end{center}
25    
26  \subsection{Overview}  \subsection{Overview}
27  \label{www:tutorials}  \label{www:tutorials}
28                                                                                                                                                              
29                                                                                    This example configuration demonstrates using the MITgcm to simulate a
30  This example experiment demonstrates using the MITgcm to simulate  laboratory demonstration using a differentially heated rotating
31  a laboratory experiment with a rotating tank of water with an ice  annulus of water.  The simulation is configured for a laboratory scale
32  bucket in the center. The simulation is configured for a laboratory  on a $3^{\circ}\times1\mathrm{cm}$ cyclindrical grid with twenty-nine
33  scale on a  vertical levels of 0.5cm each.  This is a typical laboratory setup for
34  $3^{\circ}$ $\times$ 20cm  illustration principles of GFD, as well as for a laboratory data
35  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.
37    \\
38    
39    example illustration from GFD lab here
40  \\  \\
41    
42    
# Line 45  levels. Line 50  levels.
50  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
51  \label{www:tutorials}  \label{www:tutorials}
52    
53   The domain is discretised with   The domain is discretised with a uniform cylindrical grid spacing in
54  a uniform grid spacing in the horizontal set to  the horizontal set to $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
55   $\Delta x=\Delta y=20$~km, so  that there are 120 grid cells in the azimuthal direction and
56  that there are sixty grid cells in the $x$ and $y$ directions. Vertically the  thirty-one grid cells in the radial, representing a tank 62cm in
57  model is configured with a single layer with depth, $\Delta z$, of $5000$~m.  diameter.  The bathymetry file sets the depth=0 in the nine lowest
58    radial rows to represent the central of the annulus.  Vertically the
59    model is configured with twenty-nine layers of uniform 0.5cm
60    thickness.
61    \\
62    something about heat flux
63    
64  \subsection{Code Configuration}  \subsection{Code Configuration}
65  \label{www:tutorials}  \label{www:tutorials}
# Line 82  are Line 91  are
91    
92  \begin{itemize}  \begin{itemize}
93    
94  \item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets  \item Lines 9-10, \begin{verbatim}
95  the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally  viscAh=5.0E-6,
96  low because of the small scale, presumably.... qqq  viscAz=5.0E-6,
97    \end{verbatim}
98  \item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the  
99  coriolis term, and represents a tank spinning at qqq  
100  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  These lines set the Laplacian friction coefficient in the horizontal
101  $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  and vertical, respectively.  Note that they are several orders of
102    magnitude smaller than the other examples due to the small scale of
103    this example.
104    
105    \item Lines 13-16, \begin{verbatim}
106     diffKhT=2.5E-6,
107     diffKzT=2.5E-6,
108     diffKhS=1.0E-6,
109     diffKzS=1.0E-6,
110    
111    \end{verbatim}
112    
113    
114  \item Lines 15 and 16  These lines set horizontal and vertical diffusion coefficients for
115    temperature and salinity.  Similarly to the friction coefficients, the
116    values are a couple of orders of magnitude less than most
117     configurations.
118    
119    
120    \item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
121    coriolis term, and represents a tank spinning at about 2.4 rpm.
122    
123    \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  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  
131  of the pressure inverter.  of the pressure inverter.
132    
133  \item Line 27,  \item Line 40,
134  \begin{verbatim}  \begin{verbatim}
135  startTime=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
139  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    initialized to their defaults.
143    
144  \item Line 30,  
145    \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    
154  \item Line 39,  \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 qqq,  \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
166  in the discrete grid. The syntax indicates that the discrete grid  in the discrete grid. The syntax indicates that the discrete grid
167  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                                                                                                                                                                  
169    
170    \item Line 58,
 \item Line qqq,  
171  \begin{verbatim}  \begin{verbatim}
172  dYspacing=0.01,  dYspacing=0.01,
173  \end{verbatim}  \end{verbatim}
 This line sets the radial grid spacing between each $\rho$-coordinate line  
 in the discrete grid to $1cm$.  
174    
175  \item Line 43,  This line sets the radial cylindrical grid spacing between each
176    $a$-coordinate line in the discrete grid to $1cm$.
177    
178    \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    
183  \item Line 46,  This line sets the vertical grid spacing between each of 29
184    z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm).
185    
186    \item Line 64,
187  \begin{verbatim}  \begin{verbatim}
188  bathyFile='bathyPol.bin',  bathyFile='bathyPol.bin',
189  \end{verbatim}  \end{verbatim}
190  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
191  ``bathymetry'' (tank depth) is read. This file is a two-dimensional  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
192  ($x,y$) map of  ($a,\phi$) map of
193  depths. This file is assumed to contain 64-bit binary numbers  depths. This file is assumed to contain 64-bit binary numbers
194  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 $\phi$
195  coordinate varying fastest. The points are ordered from low coordinate  coordinate varying fastest. The points are ordered from low coordinate
196  to high coordinate for both axes.  The units and orientation of the  to high coordinate for both axes.  The units and orientation of the
197  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
# Line 165  experiment, a depth of $0m$ indicates an Line 199  experiment, a depth of $0m$ indicates an
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 49,  \item Line 65,
203  \begin{verbatim}  \begin{verbatim}
204  hydrogThetaFile='thetaPol.bin',  hydrogThetaFile='thetaPol.bin',
205  \end{verbatim}  \end{verbatim}
206  This line specifies the name of the file from which the initial values  This line specifies the name of the file from which the initial values
207  of $\theta$  of temperature
208  are read. This file is a three-dimensional  are read. This file is a three-dimensional
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    
221    
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    
# Line 209  customizations for this experiment. Line 245  customizations for this experiment.
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.  map of initial values of $\theta$ in degrees Celsius.  This particular
249    experiment is set to random values x around 20C to provide initial
250    perturbations.
251    
252  \subsubsection{File {\it input/bathyPol.bin}}  \subsubsection{File {\it input/bathyPol.bin}}
253  \label{www:tutorials}  \label{www:tutorials}
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