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This example experiment demonstrates using the MITgcm to simulate |
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a Barotropic, wind-forced, ocean gyre circulation. The experiment |
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is a numerical rendition of the gyre circulation problem similar |
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to the problems described analytically by Stommel in 1966 |
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\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}. |
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In this experiment the model |
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is configured to represent a rectangular enclosed box of fluid, |
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$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced |
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by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally |
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in the ``north-south'' direction. Topologically the grid is Cartesian and |
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the coriolis parameter $f$ is defined according to a mid-latitude beta-plane |
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equation |
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\begin{equation} |
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\label{EQ:eg-baro-fcori} |
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f(y) = f_{0}+\beta y |
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\end{equation} |
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| 39 |
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\noindent where $y$ is the distance along the ``north-south'' axis of the |
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simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in |
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(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. |
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\\ |
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\\ |
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The sinusoidal wind-stress variations are defined according to |
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\begin{equation} |
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\label{EQ:eg-baro-taux} |
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\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) |
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\end{equation} |
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\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and |
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$\tau_0$ is set to $0.1N m^{-2}$. |
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\\ |
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\\ |
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Figure \ref{FIG:eg-baro-simulation_config} |
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summarizes the configuration simulated. |
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%% === eh3 === |
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\begin{figure} |
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%% \begin{center} |
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%% \resizebox{7.5in}{5.5in}{ |
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%% \includegraphics*[0.2in,0.7in][10.5in,10.5in] |
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%% {part3/case_studies/barotropic_gyre/simulation_config.eps} } |
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%% \end{center} |
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\centerline{ |
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\scalefig{.95} |
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\epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps} |
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} |
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\caption{Schematic of simulation domain and wind-stress forcing function |
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for barotropic gyre numerical experiment. The domain is enclosed bu solid |
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walls at $x=$~0,1200km and at $y=$~0,1200km.} |
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\label{FIG:eg-baro-simulation_config} |
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\end{figure} |
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| 40 |
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| 41 |
\subsection{Equations Solved} |
\subsection{Equations Solved} |
| 42 |
\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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pressure equation described in Marshall et. al \cite{marshall:97a} is |
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employed. |
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A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous |
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dissipation. The wind-stress momentum input is added to the momentum equation |
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for the ``zonal flow'', $u$. Other terms in the model |
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are explicitly switched off for this experiment configuration (see section |
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\ref{SEC:code_config} ), yielding an active set of equations solved in this |
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configuration as follows |
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\begin{eqnarray} |
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\label{EQ:eg-baro-model_equations} |
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\frac{Du}{Dt} - fv + |
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g\frac{\partial \eta}{\partial x} - |
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A_{h}\nabla_{h}^2u |
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& = & |
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\frac{\tau_{x}}{\rho_{0}\Delta z} |
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\\ |
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\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} - |
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A_{h}\nabla_{h}^2v |
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& = & |
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0 |
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\\ |
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\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u} |
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&=& |
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0 |
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\end{eqnarray} |
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\noindent where $u$ and $v$ and the $x$ and $y$ components of the |
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flow vector $\vec{u}$. |
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\\ |
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| 43 |
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| 44 |
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| 45 |
\subsection{Discrete Numerical Configuration} |
\subsection{Discrete Numerical Configuration} |
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usingCylindricalGrid=.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. |
| 180 |
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\item Line 41, |
\item Line qqq, |
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\begin{verbatim} |
\begin{verbatim} |
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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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| 190 |
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| 191 |
\item Line 42, |
\item Line qqq, |
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\begin{verbatim} |
\begin{verbatim} |
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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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\item Line 43, |
\item Line 43, |
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\begin{verbatim} |
\begin{verbatim} |
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delZ=5000, |
delZ=29*0.005, |
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\end{verbatim} |
\end{verbatim} |
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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} |
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bathyFile='topog.box' |
bathyFile='bathyPol.bin', |
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\end{verbatim} |
\end{verbatim} |
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This line specifies the name of the file from which the domain |
This line specifies the name of the file from which the domain |
| 210 |
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 |
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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 |
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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 |
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{\it input/gendata.m} shows an example of how to generate a |
f $-0.145m$ indicates the tank itself. |
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bathymetry file. |
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\item Line 49, |
\item Line 49, |
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\begin{verbatim} |
\begin{verbatim} |
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zonalWindFile='windx.sin_y' |
hydrogThetaFile='thetaPol.bin', |
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\end{verbatim} |
\end{verbatim} |
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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 |
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surface wind stress is read. This file is also a two-dimensional |
of $\theta$ |
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($x,y$) map and is enumerated and formatted in the same manner as the |
are read. This file is a three-dimensional |
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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 |
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code to generate a valid {\bf zonalWindFile} file. |
bathymetry file. |
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\item Line qqq |
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\begin{verbatim} |
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tCyl = 0 |
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\end{verbatim} |
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This line specifies the temperature in degrees Celsius of the interior |
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wall of the tank -- usually a bucket of ice water. |
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\end{itemize} |
\end{itemize} |
| 240 |
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| 282 |
\begin{itemize} |
\begin{itemize} |
| 283 |
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\item Line 39, |
\item Line 39, |
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\begin{verbatim} sNx=60, \end{verbatim} this line sets |
\begin{verbatim} sNx=120, \end{verbatim} this line sets |
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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. |
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\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. |
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\end{itemize} |
\end{itemize} |
| 295 |
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| 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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