/[MITgcm]/manual/s_examples/rotating_tank/tank.tex
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revision 1.8 by afe, Mon Jul 26 21:25:34 2004 UTC revision 1.10 by afe, Wed Oct 13 18:52:17 2004 UTC
# Line 18  Line 18 
18  \label{www:tutorials}  \label{www:tutorials}
19    
20  This section illustrates an example of MITgcm simulating a laboratory  This section illustrates an example of MITgcm simulating a laboratory
21  experiment on much smaller scales than those common to geophysical  experiment on much smaller scales than those commonly considered in  
22    geophysical
23  fluid dynamics.  fluid dynamics.
24    
25  \subsection{Overview}  \subsection{Overview}
26  \label{www:tutorials}  \label{www:tutorials}
27                                                                                                                                                                    
28                                                                                                                                                                    
29  This example experiment demonstrates using the MITgcm to simulate  This example configuration demonstrates using the MITgcm to simulate
30  a laboratory experiment with a rotating tank of water with an ice  a laboratory demonstration using a rotating tank of water with an ice
31  bucket in the center. The simulation is configured for a laboratory  bucket in the center. The simulation is configured for a laboratory
32  scale on a  scale on a
33  $3^{\circ}$ $\times$ 20cm  $3^{\circ}$ $\times$ 20cm
34  cyclindrical grid with twenty-nine vertical  cyclindrical grid with twenty-nine vertical
35  levels.  levels.
36  \\  \\
37    example illustration from GFD lab here
38    \\
39    
40    
41    
# Line 46  levels. Line 49  levels.
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.
   
 \subsubsection{Numerical Stability Criteria}  
 \label{www:tutorials}  
   
 The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  
 This value is chosen to yield a Munk layer width \cite{adcroft:95},  
   
 \begin{eqnarray}  
 \label{EQ:eg-baro-munk_layer}  
 M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  
 \end{eqnarray}  
   
 \noindent  of $\approx 100$km. This is greater than the model  
 resolution $\Delta x$, ensuring that the frictional boundary  
 layer is well resolved.  
56  \\  \\
57    something about heat flux
 \noindent The model is stepped forward with a  
 time step $\delta t=1200$secs. With this time step the stability  
 parameter to the horizontal Laplacian friction \cite{adcroft:95}  
   
   
   
 \begin{eqnarray}  
 \label{EQ:eg-baro-laplacian_stability}  
 S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  
 \end{eqnarray}  
   
 \noindent evaluates to 0.012, which is well below the 0.3 upper limit  
 for stability.  
 \\  
   
 \noindent The numerical stability for inertial oscillations    
 \cite{adcroft:95}  
   
 \begin{eqnarray}  
 \label{EQ:eg-baro-inertial_stability}  
 S_{i} = f^{2} {\delta t}^2  
 \end{eqnarray}  
   
 \noindent evaluates to $0.0144$, which is well below the $0.5$ upper  
 limit for stability.  
 \\  
   
 \noindent The advective CFL \cite{adcroft:95} for an extreme maximum  
 horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$  
   
 \begin{eqnarray}  
 \label{EQ:eg-baro-cfl_stability}  
 S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  
 \end{eqnarray}  
   
 \noindent evaluates to 0.12. This is approaching the stability limit  
 of 0.5 and limits $\delta t$ to $1200s$.  
58    
59  \subsection{Code Configuration}  \subsection{Code Configuration}
60  \label{www:tutorials}  \label{www:tutorials}
# Line 135  are Line 86  are
86    
87  \begin{itemize}  \begin{itemize}
88    
89  \item Line X, \begin{verbatim} viscAh=5.0E-6, \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 $0.000006 m^2s^{-1}$, which is ususally  the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$,
91    which is ususally
92  low because of the small scale, presumably.... qqq  low because of the small scale, presumably.... qqq
93    
94  \item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the  \item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
95  coriolis term, and represents a tank spinning at qqq  coriolis term, and represents a tank spinning at 2/s
96  \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  \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=.TRUE.,  rigidLid=.TRUE.,
102  implicitFreeSurface=.FALSE.,  implicitFreeSurface=.FALSE.,
103  \end{verbatim}  \end{verbatim}
104    
105  these lines do the opposite of the following:  qqq these lines do the opposite of the following:
106  suppress the rigid lid formulation of the surface  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 30,  \item Line 47,
119  \begin{verbatim}  \begin{verbatim}
120  deltaT=0.1,  deltaT=0.1,
121  \end{verbatim}  \end{verbatim}
# Line 171  This line sets the integration timestep Line 123  This line sets the integration timestep
123  small value among the examples due to the small physical scale of the  small value among the examples due to the small physical scale of the
124  experiment.  experiment.
125    
126  \item Line 39,  \item Line 58,
127  \begin{verbatim}  \begin{verbatim}
128  usingCylindricalGrid=.TRUE.,  usingCylindricalGrid=.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  cylindrical coordinate system.  cylindrical coordinate system.
132    
133  \item Line qqq,  \item Line 60,
134  \begin{verbatim}  \begin{verbatim}
135  dXspacing=3,  dXspacing=3,
136  \end{verbatim}  \end{verbatim}
137  This line sets the azimuthal 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 $120$ grid lines each separated by $3^{\circ}$.  should be comprise of $120$ grid lines each separated by $3^{\circ}$.
140                                                                                                                                                                    
141    
142    
143  \item Line qqq,  \item Line 61,
144  \begin{verbatim}  \begin{verbatim}
145  dYspacing=0.01,  dYspacing=0.01,
146  \end{verbatim}  \end{verbatim}
147  This line sets the radial grid spacing between each $\rho$-coordinate line  This line sets the radial cylindrical grid spacing between each $a$-coordinate line
148  in the discrete grid to $1cm$.  in the discrete grid to $1cm$.
149    
150  \item Line 43,  \item Line 62,
151  \begin{verbatim}  \begin{verbatim}
152  delZ=29*0.005,  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='bathyPol.bin',  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'' (tank depth) is read. This file is a two-dimensional  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
163  ($x,y$) map of  ($a,\phi$) 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
# Line 218  experiment, a depth of $0m$ indicates an Line 170  experiment, a depth of $0m$ indicates an
170  and a depth  and a depth
171  f $-0.145m$ indicates the tank itself.  f $-0.145m$ indicates the tank itself.
172    
173  \item Line 49,  \item Line 67,
174  \begin{verbatim}  \begin{verbatim}
175  hydrogThetaFile='thetaPol.bin',  hydrogThetaFile='thetaPol.bin',
176  \end{verbatim}  \end{verbatim}
177  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
178  of $\theta$  of temperature
179  are read. This file is a three-dimensional  are read. This file is a three-dimensional
180  ($x,y,z$) 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
181  bathymetry file.  bathymetry file.
# Line 262  customizations for this experiment. Line 214  customizations for this experiment.
214  \label{www:tutorials}  \label{www:tutorials}
215    
216  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
217  map of initial values of $\theta$ in degrees Celsius.  map of initial values of $\theta$ in degrees Celsius.  This particular
218    experiment is set to random values x around 20C to provide initial
219    perturbations.
220    
221  \subsubsection{File {\it input/bathyPol.bin}}  \subsubsection{File {\it input/bathyPol.bin}}
222  \label{www:tutorials}  \label{www:tutorials}
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