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\bodytext{bgcolor="#FFFFFFFF"} |
\bodytext{bgcolor="#FFFFFFFF"} |
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%\begin{center} |
%\begin{center} |
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%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical |
%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical |
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%Coordinates} |
%Coordinates} |
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% |
% |
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%\vspace*{4mm} |
%\vspace*{4mm} |
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% |
% |
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%\vspace*{3mm} |
%\vspace*{3mm} |
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%{\large June 2004} |
%{\large May 2001} |
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%\end{center} |
%\end{center} |
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This is the first in a series of tutorials describing |
\section{A Rotating Tank in Cylindrical Coordinates} |
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example MITgcm numerical experiments. The example experiments |
\label{sect:eg-tank} |
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include both straightforward examples of idealized geophysical |
\label{www:tutorials} |
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fluid simulations and more involved cases encompassing |
|
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large scale modeling and |
This section illustrates an example of MITgcm simulating a laboratory |
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automatic differentiation. Both hydrostatic and non-hydrostatic |
experiment on much smaller scales than those common to geophysical |
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experiments are presented, as well as experiments employing |
fluid dynamics. |
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Cartesian, spherical-polar and cube-sphere coordinate systems. |
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These ``case study'' documents include information describing |
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the experimental configuration and detailed information on how to |
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configure the MITgcm code and input files for each experiment. |
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\section{Barotropic Ocean Gyre In Cartesian Coordinates} |
\subsection{Overview} |
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\label{sect:eg-baro} |
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\label{www:tutorials} |
\label{www:tutorials} |
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This example experiment demonstrates using the MITgcm to simulate |
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a laboratory experiment with a rotating tank of water with an ice |
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bucket in the center. The simulation is configured for a laboratory |
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scale on a |
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$3^{\circ}$ $\times$ 20cm |
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cyclindrical grid with twenty-nine vertical |
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levels. |
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\\ |
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\subsection{Equations Solved} |
\subsection{Equations Solved} |
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\label{www:tutorials} |
\label{www:tutorials} |
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The model is configured in hydrostatic form. The implicit free surface form of the |
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\subsection{Discrete Numerical Configuration} |
\subsection{Discrete Numerical Configuration} |
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\subsubsection{Numerical Stability Criteria} |
\subsubsection{Numerical Stability Criteria} |
| 55 |
\label{www:tutorials} |
\label{www:tutorials} |
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The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$. |
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This value is chosen to yield a Munk layer width \cite{adcroft:95}, |
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\begin{eqnarray} |
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\label{EQ:eg-baro-munk_layer} |
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M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
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\end{eqnarray} |
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\noindent of $\approx 100$km. This is greater than the model |
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resolution $\Delta x$, ensuring that the frictional boundary |
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layer is well resolved. |
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\\ |
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\noindent The model is stepped forward with a |
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time step $\delta t=1200$secs. With this time step the stability |
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parameter to the horizontal Laplacian friction \cite{adcroft:95} |
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\begin{eqnarray} |
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\label{EQ:eg-baro-laplacian_stability} |
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S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} |
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\end{eqnarray} |
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\noindent evaluates to 0.012, which is well below the 0.3 upper limit |
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for stability. |
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\\ |
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\noindent The numerical stability for inertial oscillations |
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\cite{adcroft:95} |
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\begin{eqnarray} |
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\label{EQ:eg-baro-inertial_stability} |
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S_{i} = f^{2} {\delta t}^2 |
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\end{eqnarray} |
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\noindent evaluates to $0.0144$, which is well below the $0.5$ upper |
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limit for stability. |
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\\ |
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\noindent The advective CFL \cite{adcroft:95} for an extreme maximum |
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horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ |
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\begin{eqnarray} |
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\label{EQ:eg-baro-cfl_stability} |
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S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} |
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\end{eqnarray} |
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\noindent evaluates to 0.12. This is approaching the stability limit |
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of 0.5 and limits $\delta t$ to $1200s$. |
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\subsection{Code Configuration} |
\subsection{Code Configuration} |
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\label{www:tutorials} |
\label{www:tutorials} |
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\label{SEC:eg-baro-code_config} |
\label{SEC:eg-baro-code_config} |
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The model configuration for this experiment resides under the |
The model configuration for this experiment resides under the |
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directory {\it verification/exp0/}. The experiment files |
directory {\it verification/rotatingi\_tank/}. The experiment files |
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\begin{itemize} |
\begin{itemize} |
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\item {\it input/data} |
\item {\it input/data} |
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\item {\it input/data.pkg} |
\item {\it input/data.pkg} |
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\item {\it input/eedata}, |
\item {\it input/eedata}, |
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\item {\it input/windx.sin\_y}, |
\item {\it input/bathyPol.bin}, |
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\item {\it input/topog.box}, |
\item {\it input/thetaPol.bin}, |
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\item {\it code/CPP\_EEOPTIONS.h} |
\item {\it code/CPP\_EEOPTIONS.h} |
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\item {\it code/CPP\_OPTIONS.h}, |
\item {\it code/CPP\_OPTIONS.h}, |
| 122 |
\item {\it code/SIZE.h}. |
\item {\it code/SIZE.h}. |
| 123 |
\end{itemize} |
\end{itemize} |
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contain the code customizations and parameter settings for this |
contain the code customizations and parameter settings for this |
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experiments. Below we describe the customizations |
experiments. Below we describe the customizations |
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to these files associated with this experiment. |
to these files associated with this experiment. |
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|
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\begin{itemize} |
\begin{itemize} |
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\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 |
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the Laplacian friction coefficient to $400 m^2s^{-1}$ |
the Laplacian friction coefficient to $0.000006 m^2s^{-1}$, which is ususally |
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low because of the small scale, presumably.... qqq |
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\item Line X, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the |
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coriolis term, and represents a tank spinning at qqq |
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\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 |
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$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ |
$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ |
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|
| 147 |
\item Lines 15 and 16 |
\item Lines 15 and 16 |
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\begin{verbatim} |
\begin{verbatim} |
| 149 |
rigidLid=.FALSE., |
rigidLid=.TRUE., |
| 150 |
implicitFreeSurface=.TRUE., |
implicitFreeSurface=.FALSE., |
| 151 |
\end{verbatim} |
\end{verbatim} |
| 152 |
these lines suppress the rigid lid formulation of the surface |
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these lines do the opposite of the following: |
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suppress the rigid lid formulation of the surface |
| 155 |
pressure inverter and activate the implicit free surface form |
pressure inverter and activate the implicit free surface form |
| 156 |
of the pressure inverter. |
of the pressure inverter. |
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and implicitly suppresses searching for checkpoint files associated |
and implicitly suppresses searching for checkpoint files associated |
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with restarting an numerical integration from a previously saved state. |
with restarting an numerical integration from a previously saved state. |
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\item Line 29, |
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\begin{verbatim} |
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endTime=12000, |
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\end{verbatim} |
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this line indicates that the experiment should start finish at $t=12000s$. |
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A restart file will be written at this time that will enable the |
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simulation to be continued from this point. |
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\item Line 30, |
\item Line 30, |
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\begin{verbatim} |
\begin{verbatim} |
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deltaTmom=1200, |
deltaT=0.1, |
| 169 |
\end{verbatim} |
\end{verbatim} |
| 170 |
This line sets the momentum equation timestep to $1200s$. |
This line sets the integration timestep to $0.1s$. This is an unsually |
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small value among the examples due to the small physical scale of the |
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experiment. |
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\item Line 39, |
\item Line 39, |
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\begin{verbatim} |
\begin{verbatim} |
| 176 |
usingCartesianGrid=.TRUE., |
usingCylindricalGrid=.TRUE., |
| 177 |
\end{verbatim} |
\end{verbatim} |
| 178 |
This line requests that the simulation be performed in a |
This line requests that the simulation be performed in a |
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Cartesian coordinate system. |
cylindrical coordinate system. |
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\item Line 41, |
\item Line qqq, |
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\begin{verbatim} |
\begin{verbatim} |
| 183 |
delX=60*20E3, |
dXspacing=3, |
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\end{verbatim} |
\end{verbatim} |
| 185 |
This line sets the horizontal grid spacing between each x-coordinate line |
This line sets the azimuthal grid spacing between each x-coordinate line |
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in the discrete grid. The syntax indicates that the discrete grid |
in the discrete grid. The syntax indicates that the discrete grid |
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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 $3^{\circ}$. |
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($20$~km). |
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\item Line 42, |
\item Line qqq, |
| 192 |
\begin{verbatim} |
\begin{verbatim} |
| 193 |
delY=60*20E3, |
dYspacing=0.01, |
| 194 |
\end{verbatim} |
\end{verbatim} |
| 195 |
This line sets the horizontal grid spacing between each y-coordinate line |
This line sets the radial grid spacing between each $\rho$-coordinate line |
| 196 |
in the discrete grid to $20 \times 10^{3}m$ ($20$~km). |
in the discrete grid to $1cm$. |
| 197 |
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|
| 198 |
\item Line 43, |
\item Line 43, |
| 199 |
\begin{verbatim} |
\begin{verbatim} |
| 200 |
delZ=5000, |
delZ=29*0.005, |
| 201 |
\end{verbatim} |
\end{verbatim} |
| 202 |
This line sets the vertical grid spacing between each z-coordinate line |
This line sets the vertical grid spacing between each z-coordinate line |
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in the discrete grid to $5000m$ ($5$~km). |
in the discrete grid to $5000m$ ($5$~km). |
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\item Line 46, |
\item Line 46, |
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\begin{verbatim} |
\begin{verbatim} |
| 207 |
bathyFile='topog.box' |
bathyFile='bathyPol.bin', |
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\end{verbatim} |
\end{verbatim} |
| 209 |
This line specifies the name of the file from which the domain |
This line specifies the name of the file from which the domain |
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bathymetry is read. This file is a two-dimensional ($x,y$) map of |
``bathymetry'' (tank depth) is read. This file is a two-dimensional |
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($x,y$) map of |
| 212 |
depths. This file is assumed to contain 64-bit binary numbers |
depths. This file is assumed to contain 64-bit binary numbers |
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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 $x$ |
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coordinate varying fastest. The points are ordered from low coordinate |
coordinate varying fastest. The points are ordered from low coordinate |
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to high coordinate for both axes. The units and orientation of the |
to high coordinate for both axes. The units and orientation of the |
| 216 |
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 |
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experiment, a depth of $0m$ indicates a solid wall and a depth |
experiment, a depth of $0m$ indicates an area outside of the tank |
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of $-5000m$ indicates open ocean. The matlab program |
and a depth |
| 219 |
{\it input/gendata.m} shows an example of how to generate a |
f $-0.145m$ indicates the tank itself. |
|
bathymetry file. |
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\item Line 49, |
\item Line 49, |
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\begin{verbatim} |
\begin{verbatim} |
| 223 |
zonalWindFile='windx.sin_y' |
hydrogThetaFile='thetaPol.bin', |
| 224 |
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\end{verbatim} |
| 225 |
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This line specifies the name of the file from which the initial values |
| 226 |
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of $\theta$ |
| 227 |
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are read. This file is a three-dimensional |
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($x,y,z$) map and is enumerated and formatted in the same manner as the |
| 229 |
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bathymetry file. |
| 230 |
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| 231 |
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\item Line qqq |
| 232 |
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\begin{verbatim} |
| 233 |
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tCyl = 0 |
| 234 |
\end{verbatim} |
\end{verbatim} |
| 235 |
This line specifies the name of the file from which the x-direction |
This line specifies the temperature in degrees Celsius of the interior |
| 236 |
surface wind stress is read. This file is also a two-dimensional |
wall of the tank -- usually a bucket of ice water. |
| 237 |
($x,y$) map and is enumerated and formatted in the same manner as the |
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bathymetry file. The matlab program {\it input/gendata.m} includes example |
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code to generate a valid {\bf zonalWindFile} file. |
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| 239 |
\end{itemize} |
\end{itemize} |
| 240 |
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| 242 |
that are described in the MITgcm Getting Started and MITgcm Parameters |
that are described in the MITgcm Getting Started and MITgcm Parameters |
| 243 |
notes. |
notes. |
| 244 |
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| 245 |
%%\begin{small} |
\begin{small} |
| 246 |
%%\input{part3/case_studies/barotropic_gyre/input/data} |
\input{part3/case_studies/rotating_tank/input/data} |
| 247 |
%%\end{small} |
\end{small} |
| 248 |
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|
| 249 |
\subsubsection{File {\it input/data.pkg}} |
\subsubsection{File {\it input/data.pkg}} |
| 250 |
\label{www:tutorials} |
\label{www:tutorials} |
| 258 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 259 |
customizations for this experiment. |
customizations for this experiment. |
| 260 |
|
|
| 261 |
\subsubsection{File {\it input/windx.sin\_y}} |
\subsubsection{File {\it input/thetaPol.bin}} |
| 262 |
\label{www:tutorials} |
\label{www:tutorials} |
| 263 |
|
|
| 264 |
The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) |
The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) |
| 265 |
map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$. |
map of initial values of $\theta$ in degrees Celsius. |
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Although $\tau_{x}$ is only a function of $y$n in this experiment |
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this file must still define a complete two-dimensional map in order |
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to be compatible with the standard code for loading forcing fields |
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in MITgcm. The included matlab program {\it input/gendata.m} gives a complete |
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code for creating the {\it input/windx.sin\_y} file. |
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| 266 |
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| 267 |
\subsubsection{File {\it input/topog.box}} |
\subsubsection{File {\it input/bathyPol.bin}} |
| 268 |
\label{www:tutorials} |
\label{www:tutorials} |
| 269 |
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| 270 |
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| 271 |
The {\it input/topog.box} file specifies a two-dimensional ($x,y$) |
The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) |
| 272 |
map of depth values. For this experiment values are either |
map of depth values. For this experiment values are either |
| 273 |
$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep |
$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of |
| 274 |
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 |
| 275 |
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. |
|
| 276 |
|
|
| 277 |
\subsubsection{File {\it code/SIZE.h}} |
\subsubsection{File {\it code/SIZE.h}} |
| 278 |
\label{www:tutorials} |
\label{www:tutorials} |
| 282 |
\begin{itemize} |
\begin{itemize} |
| 283 |
|
|
| 284 |
\item Line 39, |
\item Line 39, |
| 285 |
\begin{verbatim} sNx=60, \end{verbatim} this line sets |
\begin{verbatim} sNx=120, \end{verbatim} this line sets |
| 286 |
the lateral domain extent in grid points for the |
the lateral domain extent in grid points for the |
| 287 |
axis aligned with the x-coordinate. |
axis aligned with the x-coordinate. |
| 288 |
|
|
| 289 |
\item Line 40, |
\item Line 40, |
| 290 |
\begin{verbatim} sNy=60, \end{verbatim} this line sets |
\begin{verbatim} sNy=31, \end{verbatim} this line sets |
| 291 |
the lateral domain extent in grid points for the |
the lateral domain extent in grid points for the |
| 292 |
axis aligned with the y-coordinate. |
axis aligned with the y-coordinate. |
| 293 |
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|
| 294 |
\end{itemize} |
\end{itemize} |
| 295 |
|
|
| 296 |
\begin{small} |
\begin{small} |
| 297 |
\input{part3/case_studies/barotropic_gyre/code/SIZE.h} |
\input{part3/case_studies/rotating_tank/code/SIZE.h} |
| 298 |
\end{small} |
\end{small} |
| 299 |
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|
| 300 |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
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