--- manual/s_examples/barotropic_gyre/baro.tex	2001/08/08 16:15:49	1.1
+++ manual/s_examples/barotropic_gyre/baro.tex	2001/11/13 18:19:18	1.5
@@ -1,7 +1,8 @@
-% $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 1.5 2001/11/13 18:19:18 adcroft Exp $
 % $Name:  $
 
 \section{Example: Barotropic Ocean Gyre In Cartesian Coordinates}
+\label{sec:eg-baro}
 
 \bodytext{bgcolor="#FFFFFFFF"}
 
@@ -15,16 +16,14 @@
 %{\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 sections 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.
@@ -32,8 +31,8 @@
 \subsection{Experiment Overview}
 
 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}.
 
@@ -41,7 +40,7 @@
 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
 
@@ -67,47 +66,41 @@
 \\
 \\
 Figure \ref{FIG:simulation_config}
-summarises the configuration simulated.
+summarizes the configuration simulated.
 
 \begin{figure}
-\centerline{
+\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}
 \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}
 \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}
+The model is configured in hydrostatic form. 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
 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 
+\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
 \\
@@ -117,13 +110,22 @@
 \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}
+
+ 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}
 
-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}
@@ -137,7 +139,7 @@
 
 \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}
 
 
 
@@ -151,7 +153,7 @@
 \\
 
 \noindent The numerical stability for inertial oscillations  
-\cite{Adcroft_thesis} 
+\cite{adcroft:95} 
 
 \begin{eqnarray}
 \label{EQ:inertial_stability}
@@ -162,7 +164,7 @@
 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}
@@ -188,8 +190,8 @@
 \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}}
@@ -201,7 +203,7 @@
 \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 +221,7 @@
 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 +243,7 @@
 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}
@@ -306,12 +308,12 @@
 \subsubsection{File {\it input/data.pkg}}
 
 This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
 
 \subsubsection{File {\it input/eedata}}
 
 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}}
 
@@ -359,11 +361,11 @@
 \subsubsection{File {\it code/CPP\_OPTIONS.h}}
 
 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}}
 
 This file uses standard default values and does not contain
-customisations for this experiment.
+customizations for this experiment.
 
