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% $Header: /u/gcmpack/manual/s_examples/rotating_tank/tank.tex,v 1.17 2010/08/27 13:25:32 jmc Exp $ |
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% $Name: $ |
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\bodytext{bgcolor="#FFFFFFFF"} |
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%\begin{center} |
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%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical |
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%Coordinates} |
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% |
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%\vspace*{4mm} |
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% |
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%\vspace*{3mm} |
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%{\large May 2001} |
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%\end{center} |
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\section{A Rotating Tank in Cylindrical Coordinates} |
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\label{sec:eg-tank} |
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%\label{www:tutorials} |
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\begin{rawhtml} |
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<!-- CMIREDIR:eg-tank: --> |
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\end{rawhtml} |
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\begin{center} |
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(in directory: {\it verification/rotating\_tank/}) |
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\end{center} |
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\subsection{Overview} |
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%\label{www:tutorials} |
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This example configuration demonstrates using the MITgcm to simulate a |
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laboratory demonstration using a differentially heated rotating |
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annulus of water. The simulation is configured for a laboratory scale |
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on a $3^{\circ}\times1\mathrm{cm}$ cyclindrical grid with twenty-nine |
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vertical levels of 0.5cm each. This is a typical laboratory setup for |
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illustration principles of GFD, as well as for a laboratory data |
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assimilation project. The files for this experiment can be found in |
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the verification directory under rotating\_tank. |
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\\ |
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|
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example illustration from GFD lab here |
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\\ |
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\subsection{Equations Solved} |
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%\label{www:tutorials} |
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\subsection{Discrete Numerical Configuration} |
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%\label{www:tutorials} |
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The domain is discretised with a uniform cylindrical grid spacing in |
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the horizontal set to $\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so |
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that there are 120 grid cells in the azimuthal direction and |
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thirty-one grid cells in the radial, representing a tank 62cm in |
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diameter. The bathymetry file sets the depth=0 in the nine lowest |
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radial rows to represent the central of the annulus. Vertically the |
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model is configured with twenty-nine layers of uniform 0.5cm |
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thickness. |
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\\ |
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something about heat flux |
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\subsection{Code Configuration} |
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%\label{www:tutorials} |
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\label{sec:eg-tank-code_config} |
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The model configuration for this experiment resides under the |
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directory {\it verification/rotatingi\_tank/}. The experiment files |
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\begin{itemize} |
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\item {\it input/data} |
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\item {\it input/data.pkg} |
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\item {\it input/eedata}, |
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\item {\it input/bathyPol.bin}, |
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\item {\it input/thetaPol.bin}, |
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\item {\it code/CPP\_EEOPTIONS.h} |
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\item {\it code/CPP\_OPTIONS.h}, |
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\item {\it code/SIZE.h}. |
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\end{itemize} |
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|
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contain the code customizations and parameter settings for this |
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experiments. Below we describe the customizations |
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to these files associated with this experiment. |
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\subsubsection{File {\it input/data}} |
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%\label{www:tutorials} |
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This file, reproduced completely below, specifies the main parameters |
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for the experiment. The parameters that are significant for this configuration |
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are |
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\begin{itemize} |
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\item Lines 9-10, \begin{verbatim} |
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viscAh=5.0E-6, |
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viscAz=5.0E-6, |
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\end{verbatim} |
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These lines set the Laplacian friction coefficient in the horizontal |
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and vertical, respectively. Note that they are several orders of |
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magnitude smaller than the other examples due to the small scale of |
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this example. |
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\item Lines 13-16, \begin{verbatim} |
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diffKhT=2.5E-6, |
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diffKzT=2.5E-6, |
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diffKhS=1.0E-6, |
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diffKzS=1.0E-6, |
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\end{verbatim} |
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These lines set horizontal and vertical diffusion coefficients for |
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temperature and salinity. Similarly to the friction coefficients, the |
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values are a couple of orders of magnitude less than most |
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configurations. |
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|
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\item Line 17, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the |
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coriolis term, and represents a tank spinning at about 2.4 rpm. |
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\item Lines 23 and 24 |
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\begin{verbatim} |
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rigidLid=.TRUE., |
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implicitFreeSurface=.FALSE., |
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\end{verbatim} |
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These lines activate the rigid lid formulation of the surface |
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pressure inverter and suppress the implicit free surface form |
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of the pressure inverter. |
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\item Line 40, |
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\begin{verbatim} |
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nIter=0, |
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\end{verbatim} |
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This line indicates that the experiment should start from $t=0$ and |
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implicitly suppresses searching for checkpoint files associated with |
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restarting an numerical integration from a previously saved state. |
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Instead, the file thetaPol.bin will be loaded to initialized the |
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temperature fields as indicated below, and other variables will be |
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initialized to their defaults. |
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\item Line 43, |
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\begin{verbatim} |
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deltaT=0.1, |
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\end{verbatim} |
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This line sets the integration timestep to $0.1s$. This is an |
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unsually small value among the examples due to the small physical |
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scale of the experiment. Using the ensemble Kalman filter to produce |
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input fields can necessitate even shorter timesteps. |
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\item Line 56, |
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\begin{verbatim} |
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usingCylindricalGrid=.TRUE., |
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\end{verbatim} |
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This line requests that the simulation be performed in a |
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cylindrical coordinate system. |
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\item Line 57, |
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\begin{verbatim} |
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dXspacing=3, |
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\end{verbatim} |
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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 |
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should be comprised of $120$ grid lines each separated by $3^{\circ}$. |
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\item Line 58, |
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\begin{verbatim} |
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dYspacing=0.01, |
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\end{verbatim} |
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This line sets the radial cylindrical grid spacing between each |
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$a$-coordinate line in the discrete grid to $1cm$. |
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\item Line 59, |
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\begin{verbatim} |
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delZ=29*0.005, |
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\end{verbatim} |
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This line sets the vertical grid spacing between each of 29 |
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z-coordinate lines in the discrete grid to $0.005m$ ($5$~mm). |
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\item Line 64, |
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\begin{verbatim} |
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bathyFile='bathyPol.bin', |
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\end{verbatim} |
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This line specifies the name of the file from which the domain |
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``bathymetry'' (tank depth) is read. This file is a two-dimensional |
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($a,\phi$) map of |
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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 $\phi$ |
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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 |
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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 an area outside of the tank |
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and a depth |
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f $-0.145m$ indicates the tank itself. |
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\item Line 65, |
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\begin{verbatim} |
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hydrogThetaFile='thetaPol.bin', |
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\end{verbatim} |
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This line specifies the name of the file from which the initial values |
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of temperature |
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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 |
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bathymetry file. |
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\item Lines 66 and 67 |
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\begin{verbatim} |
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tCylIn = 0 |
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tCylOut = 20 |
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\end{verbatim} |
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These line specify the temperatures in degrees Celsius of the interior |
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and exterior walls of the tank -- typically taken to be icewater on |
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the inside and room temperature on the outside. |
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\end{itemize} |
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\noindent Other lines in the file {\it input/data} are standard values |
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that are described in the MITgcm Getting Started and MITgcm Parameters |
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notes. |
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\begin{small} |
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\input{s_examples/rotating_tank/input/data} |
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\end{small} |
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\subsubsection{File {\it input/data.pkg}} |
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%\label{www:tutorials} |
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This file uses standard default values and does not contain |
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customizations for this experiment. |
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\subsubsection{File {\it input/eedata}} |
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%\label{www:tutorials} |
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This file uses standard default values and does not contain |
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customizations for this experiment. |
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|
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\subsubsection{File {\it input/thetaPol.bin}} |
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%\label{www:tutorials} |
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|
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The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) |
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map of initial values of $\theta$ in degrees Celsius. This particular |
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experiment is set to random values x around 20C to provide initial |
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perturbations. |
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|
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\subsubsection{File {\it input/bathyPol.bin}} |
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%\label{www:tutorials} |
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The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) |
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map of depth values. For this experiment values are either |
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$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of |
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the tank. The file contains a raw binary stream of data that is enumerated |
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in the same way as standard MITgcm two-dimensional, horizontal arrays. |
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\subsubsection{File {\it code/SIZE.h}} |
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%\label{www:tutorials} |
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Two lines are customized in this file for the current experiment |
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\begin{itemize} |
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\item Line 39, |
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\begin{verbatim} sNx=120, \end{verbatim} this line sets |
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the lateral domain extent in grid points for the |
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axis aligned with the x-coordinate. |
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\item Line 40, |
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\begin{verbatim} sNy=31, \end{verbatim} this line sets |
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the lateral domain extent in grid points for the |
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axis aligned with the y-coordinate. |
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\end{itemize} |
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\begin{small} |
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\input{s_examples/rotating_tank/code/SIZE.h} |
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\end{small} |
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\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
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%\label{www:tutorials} |
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This file uses standard default values and does not contain |
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customizations for this experiment. |
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\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
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%\label{www:tutorials} |
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|
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This file uses standard default values and does not contain |
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customizations for this experiment. |
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|