--- manual/s_examples/barotropic_gyre/baro.tex	2001/08/08 16:15:49	1.1
+++ manual/s_examples/barotropic_gyre/baro.tex	2004/10/13 05:06:26	1.11
@@ -1,8 +1,6 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.1 2001/08/08 16:15:49 adcroft Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.11 2004/10/13 05:06:26 cnh Exp $
 % $Name:  $
 
-\section{Example: Barotropic Ocean Gyre In Cartesian Coordinates}
-
 \bodytext{bgcolor="#FFFFFFFF"}
 
 %\begin{center} 
@@ -15,25 +13,26 @@
 %{\large May 2001}
 %\end{center}
 
-\subsection{Introduction}
-
-This document is the first in a series of documents describing
+This is the first in a series of tutorials describing
 example MITgcm numerical experiments. The example experiments 
-include both straightforward examples of idealised geophysical 
+include both straightforward examples of idealized geophysical 
 fluid simulations and more involved cases encompassing
 large scale modeling and
 automatic differentiation. Both hydrostatic and non-hydrostatic 
-experiements are presented, as well as experiments employing
-cartesian, spherical-polar and cube-sphere coordinate systems.
+experiments are presented, as well as experiments employing
+Cartesian, spherical-polar and cube-sphere coordinate systems.
 These ``case study'' documents include information describing
 the experimental configuration and detailed information on how to
 configure the MITgcm code and input files for each experiment.
 
-\subsection{Experiment Overview}
+\section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates}
+\label{sect:eg-baro}
+\label{www:tutorials}
+
 
 This example experiment demonstrates using the MITgcm to simulate
-a barotropic, wind-forced, ocean gyre circulation. The experiment 
-is a numerical rendition of the gyre circulation problem simliar
+a Barotropic, wind-forced, ocean gyre circulation. The experiment 
+is a numerical rendition of the gyre circulation problem similar
 to the problems described analytically by Stommel in 1966 
 \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
 
@@ -41,24 +40,24 @@
 is configured to represent a rectangular enclosed box of fluid,
 $1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced
 by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
-in the ``north-south'' direction. Topologically the grid is cartesian and 
+in the ``north-south'' direction. Topologically the grid is Cartesian and 
 the coriolis parameter $f$ is defined according to a mid-latitude beta-plane 
 equation
 
 \begin{equation}
-\label{EQ:fcori}
+\label{EQ:eg-baro-fcori}
 f(y) = f_{0}+\beta y
 \end{equation}
  
 \noindent where $y$ is the distance along the ``north-south'' axis of the 
 simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in 
-(\ref{EQ:fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. 
+(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. 
 \\
 \\
  The sinusoidal wind-stress variations are defined according to 
 
 \begin{equation}
-\label{EQ:taux}
+\label{EQ:eg-baro-taux}
 \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y})
 \end{equation}
  
@@ -66,48 +65,48 @@
 $\tau_0$ is set to $0.1N m^{-2}$. 
 \\
 \\
-Figure \ref{FIG:simulation_config}
-summarises the configuration simulated.
+Figure \ref{FIG:eg-baro-simulation_config}
+summarizes the configuration simulated.
 
+%% === eh3 ===
 \begin{figure}
+%% \begin{center}
+%%  \resizebox{7.5in}{5.5in}{
+%%    \includegraphics*[0.2in,0.7in][10.5in,10.5in]
+%%     {part3/case_studies/barotropic_gyre/simulation_config.eps} }
+%% \end{center}
 \centerline{
- \resizebox{7.5in}{5.5in}{
-   \includegraphics*[0.2in,0.7in][10.5in,10.5in]
-    {part3/case_studies/barotropic_gyre/simulation_config.eps} }
+  \scalefig{.95}
+  \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps}
 }
 \caption{Schematic of simulation domain and wind-stress forcing function 
 for barotropic gyre numerical experiment. The domain is enclosed bu solid
 walls at $x=$~0,1200km and at $y=$~0,1200km.}
-\label{FIG:simulation_config}
+\label{FIG:eg-baro-simulation_config}
 \end{figure}
 
-\subsection{Discrete Numerical Configuration}
-
- The model is configured in hydrostatic form.  The domain is discretised with 
-a uniform grid spacing in the horizontal set to
- $\Delta x=\Delta y=20$~km, so 
-that there are sixty grid cells in the $x$ and $y$ directions. Vertically the 
-model is configured with a single layer with depth, $\Delta z$, of $5000$~m. 
-The implicit free surface form of the 
-pressure equation described in Marshall et. al \cite{Marshall97a} is 
-employed. 
-A horizontal laplacian operator $\nabla_{h}^2$ provides viscous
+\subsection{Equations Solved}
+\label{www:tutorials}
+The model is configured in hydrostatic form. The implicit free surface form of the
+pressure equation described in Marshall et. al \cite{marshall:97a} is
+employed.
+A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
 dissipation. The wind-stress momentum input is added to the momentum equation
 for the ``zonal flow'', $u$. Other terms in the model
-are explicitly switched off for this experiement configuration (see section
-\ref{SEC:code_config} ), yielding an active set of equations solved in this 
-configuration as follows
+are explicitly switched off for this experiment configuration (see section
+\ref{SEC:code_config} ), yielding an active set of equations solved in this
+configuration as follows 
 
 \begin{eqnarray}
-\label{EQ:model_equations}
-\frac{Du}{Dt} - fv + 
-              g\frac{\partial \eta}{\partial x} - 
-              A_{h}\nabla_{h}^2u 
+\label{EQ:eg-baro-model_equations}
+\frac{Du}{Dt} - fv +
+              g\frac{\partial \eta}{\partial x} -
+              A_{h}\nabla_{h}^2u
 & = &
 \frac{\tau_{x}}{\rho_{0}\Delta z}
 \\
 \frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} -
-              A_{h}\nabla_{h}^2v 
+              A_{h}\nabla_{h}^2v
 & = &
 0
 \\
@@ -117,16 +116,27 @@
 \end{eqnarray}
 
 \noindent where $u$ and $v$ and the $x$ and $y$ components of the
-flow vector $\vec{u}$. 
+flow vector $\vec{u}$.
 \\
 
+
+\subsection{Discrete Numerical Configuration}
+\label{www:tutorials}
+
+ The domain is discretised with 
+a uniform grid spacing in the horizontal set to
+ $\Delta x=\Delta y=20$~km, so 
+that there are sixty grid cells in the $x$ and $y$ directions. Vertically the 
+model is configured with a single layer with depth, $\Delta z$, of $5000$~m. 
+
 \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_thesis},
+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:munk_layer}
+\label{EQ:eg-baro-munk_layer}
 M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
 \end{eqnarray}
 
@@ -137,12 +147,12 @@
 
 \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_thesis}
+parameter to the horizontal Laplacian friction \cite{adcroft:95}
 
 
 
 \begin{eqnarray}
-\label{EQ:laplacian_stability}
+\label{EQ:eg-baro-laplacian_stability}
 S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
 \end{eqnarray}
 
@@ -151,10 +161,10 @@
 \\
 
 \noindent The numerical stability for inertial oscillations  
-\cite{Adcroft_thesis} 
+\cite{adcroft:95} 
 
 \begin{eqnarray}
-\label{EQ:inertial_stability}
+\label{EQ:eg-baro-inertial_stability}
 S_{i} = f^{2} {\delta t}^2
 \end{eqnarray}
 
@@ -162,11 +172,11 @@
 limit for stability.
 \\
 
-\noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum 
+\noindent The advective CFL \cite{adcroft:95} for an extreme maximum 
 horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$
 
 \begin{eqnarray}
-\label{EQ:cfl_stability}
+\label{EQ:eg-baro-cfl_stability}
 S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
 \end{eqnarray}
 
@@ -174,7 +184,8 @@
 of 0.5 and limits $\delta t$ to $1200s$.
 
 \subsection{Code Configuration}
-\label{SEC:code_config}
+\label{www:tutorials}
+\label{SEC:eg-baro-code_config}
 
 The model configuration for this experiment resides under the 
 directory {\it verification/exp0/}.  The experiment files 
@@ -188,11 +199,12 @@
 \item {\it code/CPP\_OPTIONS.h},
 \item {\it code/SIZE.h}. 
 \end{itemize}
-contain the code customisations and parameter settings for this 
-experiements. Below we describe the customisations
+contain the code customizations and parameter settings for this 
+experiments. Below we describe the customizations
 to these files associated with this experiment.
 
 \subsubsection{File {\it input/data}}
+\label{www:tutorials}
 
 This file, reproduced completely below, specifies the main parameters 
 for the experiment. The parameters that are significant for this configuration
@@ -201,7 +213,7 @@
 \begin{itemize}
 
 \item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets
-the laplacian friction coefficient to $400 m^2s^{-1}$
+the Laplacian friction coefficient to $400 m^2s^{-1}$
 \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets
 $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$
 
@@ -219,7 +231,7 @@
 startTime=0,
 \end{verbatim}
 this line indicates that the experiment should start from $t=0$
-and implicitly supresses searching for checkpoint files associated
+and implicitly suppresses searching for checkpoint files associated
 with restarting an numerical integration from a previously saved state.
 
 \item Line 29,
@@ -241,7 +253,7 @@
 usingCartesianGrid=.TRUE.,
 \end{verbatim}
 This line requests that the simulation be performed in a 
-cartesian coordinate system.
+Cartesian coordinate system.
 
 \item Line 41,
 \begin{verbatim}
@@ -304,16 +316,19 @@
 \end{small}
 
 \subsubsection{File {\it input/data.pkg}}
+\label{www:tutorials}
 
 This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
 
 \subsubsection{File {\it input/eedata}}
+\label{www:tutorials}
 
 This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
 
 \subsubsection{File {\it input/windx.sin\_y}}
+\label{www:tutorials}
 
 The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) 
 map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
@@ -324,6 +339,7 @@
 code for creating the {\it input/windx.sin\_y} file.
 
 \subsubsection{File {\it input/topog.box}}
+\label{www:tutorials}
 
 
 The {\it input/topog.box} file specifies a two-dimensional ($x,y$) 
@@ -335,6 +351,7 @@
 code for creating the {\it input/topog.box} file.
 
 \subsubsection{File {\it code/SIZE.h}}
+\label{www:tutorials}
 
 Two lines are customized in this file for the current experiment
 
@@ -357,13 +374,15 @@
 \end{small}
 
 \subsubsection{File {\it code/CPP\_OPTIONS.h}}
+\label{www:tutorials}
 
 This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
 
 
 \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
+\label{www:tutorials}
 
 This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.