/[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 1.13 by afe, Wed Jun 15 14:54:58 2005 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    <!-- CMIREDIR:eg-tank: -->
21    \end{rawhtml}
22    
23  This section illustrates an example of MITgcm simulating a laboratory  This section illustrates an example of MITgcm simulating a laboratory
24  experiment on much smaller scales than those common to geophysical  experiment on much smaller scales than those commonly considered in  
25    geophysical
26  fluid dynamics.  fluid dynamics.
27    
28  \subsection{Overview}  \subsection{Overview}
29  \label{www:tutorials}  \label{www:tutorials}
30                                                                                                                                                              
31                                                                                    This example configuration demonstrates using the MITgcm to simulate a
32  This example experiment demonstrates using the MITgcm to simulate  laboratory demonstration using a differentially heated rotating
33  a laboratory experiment with a rotating tank of water with an ice  annulus of water.  The simulation is configured for a laboratory scale
34  bucket in the center. The simulation is configured for a laboratory  on a $3^{\circ}$ $\times$ 1cm cyclindrical grid with twenty-nine
35  scale on a  vertical levels of 0.5cm each.  This is a typical laboratory setup for
36  $3^{\circ}$ $\times$ 20cm  illustration principles of GFD, as well as for a laboratory data
37  cyclindrical grid with twenty-nine vertical  assimilation project.
38  levels.  \\
39    
40    example illustration from GFD lab here
41  \\  \\
42    
43    
# Line 45  levels. Line 51  levels.
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 a uniform cylindrical grid spacing in
55  a uniform grid spacing in the horizontal set to  the horizontal set to $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so
56   $\Delta x=\Delta y=20$~km, so  that there are 120 grid cells in the azimuthal direction and
57  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
58  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
59    radial rows to represent the central of the annulus.  Vertically the
60  \subsubsection{Numerical Stability Criteria}  model is configured with twenty-nine layers of uniform 0.5cm
61  \label{www:tutorials}  thickness.
   
 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.  
 \\  
   
 \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.  
62  \\  \\
63    something about heat flux
 \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 $1200s$.  
64    
65  \subsection{Code Configuration}  \subsection{Code Configuration}
66  \label{www:tutorials}  \label{www:tutorials}
# Line 135  are Line 92  are
92    
93  \begin{itemize}  \begin{itemize}
94    
95  \item Line X, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets  \item Lines 9-10, \begin{verbatim}
96  the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally  viscAh=5.0E-6,
97  low because of the small scale, presumably.... qqq  viscAz=5.0E-6,
98    \end{verbatim}
 \item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the  
 coriolis term, and represents a tank spinning at qqq  
 \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets  
 $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$  
99    
100  \item Lines 15 and 16  
101    These lines set the Laplacian friction coefficient in the horizontal
102    and vertical, respectively.  Note that they are several orders of
103    magnitude smaller than the other examples due to the small scale of
104    this example.
105    
106    \item Lines 13-16, \begin{verbatim}
107     diffKhT=2.5E-6,
108     diffKzT=2.5E-6,
109     diffKhS=1.0E-6,
110     diffKzS=1.0E-6,
111    
112    \end{verbatim}
113    
114    
115    These lines set horizontal and vertical diffusion coefficients for
116    temperature and salinity.  Similarly to the friction coefficients, the
117    values are a couple of orders of magnitude less than most
118     configurations.
119    
120    
121    \item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the
122    coriolis term, and represents a tank spinning at about 2.4 rpm.
123    
124    \item Lines 23 and 24
125  \begin{verbatim}  \begin{verbatim}
126  rigidLid=.TRUE.,  rigidLid=.TRUE.,
127  implicitFreeSurface=.FALSE.,  implicitFreeSurface=.FALSE.,
128  \end{verbatim}  \end{verbatim}
129    
130  these lines do the opposite of the following:  These lines activate  the rigid lid formulation of the surface
131  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  
132  of the pressure inverter.  of the pressure inverter.
133    
134  \item Line 27,  \item Line 40,
135  \begin{verbatim}  \begin{verbatim}
136  startTime=0,  nIter=0,
137  \end{verbatim}  \end{verbatim}
138  this line indicates that the experiment should start from $t=0$  This line indicates that the experiment should start from $t=0$ and
139  and implicitly suppresses searching for checkpoint files associated  implicitly suppresses searching for checkpoint files associated with
140  with restarting an numerical integration from a previously saved state.  restarting an numerical integration from a previously saved state.
141    Instead, the file thetaPol.bin will be loaded to initialized the
142    temperature fields as indicated below, and other variables will be
143    initialized to their defaults.
144    
145    
146  \item Line 30,  \item Line 43,
147  \begin{verbatim}  \begin{verbatim}
148  deltaT=0.1,  deltaT=0.1,
149  \end{verbatim}  \end{verbatim}
150  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
151  small value among the examples due to the small physical scale of the  unsually small value among the examples due to the small physical
152  experiment.  scale of the experiment.  Using the ensemble Kalman filter to produce
153    input fields can necessitate even shorter timesteps.
154    
155  \item Line 39,  \item Line 56,
156  \begin{verbatim}  \begin{verbatim}
157  usingCylindricalGrid=.TRUE.,  usingCylindricalGrid=.TRUE.,
158  \end{verbatim}  \end{verbatim}
159  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
160  cylindrical coordinate system.  cylindrical coordinate system.
161    
162  \item Line qqq,  \item Line 57,
163  \begin{verbatim}  \begin{verbatim}
164  dXspacing=3,  dXspacing=3,
165  \end{verbatim}  \end{verbatim}
166  This line sets the azimuthal grid spacing between each x-coordinate line  This line sets the azimuthal grid spacing between each $x$-coordinate line
167  in the discrete grid. The syntax indicates that the discrete grid  in the discrete grid. The syntax indicates that the discrete grid
168  should be comprise of $120$ grid lines each separated by $3^{\circ}$.  should be comprised of $120$ grid lines each separated by $3^{\circ}$.
169                                                                                                                                                                  
   
170    
171  \item Line qqq,  \item Line 58,
172  \begin{verbatim}  \begin{verbatim}
173  dYspacing=0.01,  dYspacing=0.01,
174  \end{verbatim}  \end{verbatim}
 This line sets the radial grid spacing between each $\rho$-coordinate line  
 in the discrete grid to $1cm$.  
175    
176  \item Line 43,  This line sets the radial cylindrical grid spacing between each
177    $a$-coordinate line in the discrete grid to $1cm$.
178    
179    \item Line 59,
180  \begin{verbatim}  \begin{verbatim}
181  delZ=29*0.005,  delZ=29*0.005,
182  \end{verbatim}  \end{verbatim}
 This line sets the vertical grid spacing between each z-coordinate line  
 in the discrete grid to $5000m$ ($5$~km).  
183    
184  \item Line 46,  This line sets the vertical grid spacing between each of 29
185    z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm).
186    
187    \item Line 64,
188  \begin{verbatim}  \begin{verbatim}
189  bathyFile='bathyPol.bin',  bathyFile='bathyPol.bin',
190  \end{verbatim}  \end{verbatim}
191  This line specifies the name of the file from which the domain  This line specifies the name of the file from which the domain
192  ``bathymetry'' (tank depth) is read. This file is a two-dimensional  ``bathymetry'' (tank depth) is read. This file is a two-dimensional
193  ($x,y$) map of  ($a,\phi$) map of
194  depths. This file is assumed to contain 64-bit binary numbers  depths. This file is assumed to contain 64-bit binary numbers
195  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 $\phi$
196  coordinate varying fastest. The points are ordered from low coordinate  coordinate varying fastest. The points are ordered from low coordinate
197  to high coordinate for both axes.  The units and orientation of the  to high coordinate for both axes.  The units and orientation of the
198  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 200  experiment, a depth of $0m$ indicates an
200  and a depth  and a depth
201  f $-0.145m$ indicates the tank itself.  f $-0.145m$ indicates the tank itself.
202    
203  \item Line 49,  \item Line 65,
204  \begin{verbatim}  \begin{verbatim}
205  hydrogThetaFile='thetaPol.bin',  hydrogThetaFile='thetaPol.bin',
206  \end{verbatim}  \end{verbatim}
207  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
208  of $\theta$  of temperature
209  are read. This file is a three-dimensional  are read. This file is a three-dimensional
210  ($x,y,z$) 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
211  bathymetry file.  bathymetry file.
212    
213  \item Line qqq  \item Lines 66 and 67
214  \begin{verbatim}  \begin{verbatim}
215   tCyl  = 0   tCylIn  = 0
216     tCylOut  = 20
217  \end{verbatim}  \end{verbatim}
218  This line specifies the temperature in degrees Celsius of the interior  These line specify the temperatures in degrees Celsius of the interior
219  wall of the tank -- usually a bucket of ice water.  and exterior walls of the tank -- typically taken to be icewater on
220    the inside and room temperature on the outside.
221    
222    
223  \end{itemize}  \end{itemize}
224    
225  \noindent other lines in the file {\it input/data} are standard values  \noindent Other lines in the file {\it input/data} are standard values
226  that are described in the MITgcm Getting Started and MITgcm Parameters  that are described in the MITgcm Getting Started and MITgcm Parameters
227  notes.  notes.
228    
# Line 262  customizations for this experiment. Line 246  customizations for this experiment.
246  \label{www:tutorials}  \label{www:tutorials}
247    
248  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)  The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$)
249  map of initial values of $\theta$ in degrees Celsius.  map of initial values of $\theta$ in degrees Celsius.  This particular
250    experiment is set to random values x around 20C to provide initial
251    perturbations.
252    
253  \subsubsection{File {\it input/bathyPol.bin}}  \subsubsection{File {\it input/bathyPol.bin}}
254  \label{www:tutorials}  \label{www:tutorials}
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