--- manual/s_examples/baroclinic_gyre/fourlayer.tex	2001/10/25 12:06:56	1.8
+++ manual/s_examples/baroclinic_gyre/fourlayer.tex	2002/02/28 19:32:19	1.12
@@ -1,8 +1,8 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.8 2001/10/25 12:06:56 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.12 2002/02/28 19:32:19 cnh Exp $
 % $Name:  $
 
-\section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}
-\label{sec:eg-fourlayer}
+\section{Four Layer Baroclinic Ocean Gyre In Spherical Coordinates}
+\label{sect:eg-fourlayer}
 
 \bodytext{bgcolor="#FFFFFFFF"}
 
@@ -19,9 +19,9 @@
 This document describes an example experiment using MITgcm
 to simulate a baroclinic ocean gyre in spherical
 polar coordinates. The barotropic
-example experiment in section \ref{sec:eg-baro}
-ilustrated how to configure the code for a single layer 
-simulation in a cartesian grid. In this example a similar physical problem
+example experiment in section \ref{sect:eg-baro}
+illustrated how to configure the code for a single layer 
+simulation in a Cartesian grid. In this example a similar physical problem
 is simulated, but the code is now configured
 for four layers and in a spherical polar coordinate system.
 
@@ -29,7 +29,7 @@
 
 This example experiment demonstrates using the MITgcm to simulate
 a baroclinic, wind-forced, ocean gyre circulation. The experiment 
-is a numerical rendition of the gyre circulation problem simliar
+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}.
 \\
@@ -43,7 +43,7 @@
 according to latitude, $\varphi$
 
 \begin{equation}
-\label{EQ:fcori}
+\label{EQ:eg-fourlayer-fcori}
 f(\varphi) = 2 \Omega \sin( \varphi )
 \end{equation}
  
@@ -61,13 +61,13 @@
 $\tau_0$ is set to $0.1N m^{-2}$. 
 \\
 
-Figure \ref{FIG:simulation_config}
-summarises the configuration simulated.
-In contrast to the example in section \ref{sec:eg-baro}, the 
+Figure \ref{FIG:eg-fourlayer-simulation_config}
+summarizes the configuration simulated.
+In contrast to the example in section \ref{sect:eg-baro}, the 
 current experiment simulates a spherical polar domain. As indicated
 by the axes in the lower left of the figure the model code works internally
-in a locally orthoganal coordinate $(x,y,z)$. For this experiment description 
-the local orthogonal model coordinate $(x,y,z)$ is synonomous 
+in a locally orthogonal coordinate $(x,y,z)$. For this experiment description 
+the local orthogonal model coordinate $(x,y,z)$ is synonymous 
 with the coordinates $(\lambda,\varphi,r)$ shown in figure
 \ref{fig:spherical-polar-coord}
 \\
@@ -82,14 +82,14 @@
 linear
 
 \begin{equation}
-\label{EQ:linear1_eos}
+\label{EQ:eg-fourlayer-linear1_eos}
 \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
 \end{equation}
 
 \noindent which is implemented in the model as a density anomaly equation
 
 \begin{equation}
-\label{EQ:linear1_eos_pert}
+\label{EQ:eg-fourlayer-linear1_eos_pert}
 \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
 \end{equation}
 
@@ -114,26 +114,26 @@
 imposed by setting the potential temperature, $\theta$, in each layer.
 The vertical spacing, $\Delta z$, is constant and equal to $500$m.
 }
-\label{FIG:simulation_config}
+\label{FIG:eg-fourlayer-simulation_config}
 \end{figure}
 
 \subsection{Equations solved}
 For this problem
-the implicit free surface, {\bf HPE} (see section \ref{sec:hydrostatic_and_quasi-hydrostatic_forms}) form of the 
-equations described in Marshall et. al \cite{Marshall97a} are
+the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the 
+equations described in Marshall et. al \cite{marshall:97a} are
 employed. The flow is three-dimensional with just temperature, $\theta$, as 
 an active tracer.  The equation of state is linear.
-A horizontal laplacian operator $\nabla_{h}^2$ provides viscous
+A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
 dissipation and provides a diffusive sub-grid scale closure for the 
 temperature equation. A wind-stress momentum forcing 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
+are explicitly switched off for this experiment configuration (see section
 \ref{SEC:eg_fourl_code_config} ). This yields an active set of equations
 solved in this configuration, written in spherical polar coordinates as 
 follows
 
 \begin{eqnarray}
-\label{EQ:model_equations}
+\label{EQ:eg-fourlayer-model_equations}
 \frac{Du}{Dt} - fv + 
   \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} - 
   A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}} 
@@ -210,7 +210,7 @@
 Vertically the 
 model is configured with four layers with constant depth, 
 $\Delta z$, of $500$~m. The internal, locally orthogonal, model coordinate 
-variables $x$ and $y$ are initialised from the values of
+variables $x$ and $y$ are initialized from the values of
 $\lambda$, $\varphi$, $\Delta \lambda$ and $\Delta \varphi$ in
 radians according to
 
@@ -221,7 +221,7 @@
 
 The procedure for generating a set of internal grid variables from a
 spherical polar grid specification is discussed in section 
-\ref{sec:spatial_discrete_horizontal_grid}.
+\ref{sect:spatial_discrete_horizontal_grid}.
 
 \noindent\fbox{ \begin{minipage}{5.5in}
 {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em
@@ -242,15 +242,15 @@
 
 
 
-As described in \ref{sec:tracer_equations}, the time evolution of potential 
+As described in \ref{sect:tracer_equations}, the time evolution of potential 
 temperature, 
 $\theta$, (equation \ref{eq:eg_fourl_theta})
 is evaluated prognostically. The centered second-order scheme with
 Adams-Bashforth time stepping described in section 
-\ref{sec:tracer_equations_abII} is used to step forward the temperature 
+\ref{sect:tracer_equations_abII} is used to step forward the temperature 
 equation. Prognostic terms in
 the momentum equations are solved using flux form as
-described in section \ref{sec:flux-form_momentum_eqautions}.
+described in section \ref{sect:flux-form_momentum_eqautions}.
 The pressure forces that drive the fluid motions, (
 $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface 
 elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the 
@@ -258,15 +258,15 @@
 height, $\eta$, is diagnosed using an implicit scheme. The pressure
 field solution method is described in sections
 \ref{sect:pressure-method-linear-backward} and 
-\ref{sec:finding_the_pressure_field}.
+\ref{sect:finding_the_pressure_field}.
 
 \subsubsection{Numerical Stability Criteria}
 
-The laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
+The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
 This value is chosen to yield a Munk layer width,
 
 \begin{eqnarray}
-\label{EQ:munk_layer}
+\label{EQ:eg-fourlayer-munk_layer}
 M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
 \end{eqnarray}
 
@@ -279,10 +279,10 @@
 
 \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
+parameter to the horizontal Laplacian friction
 
 \begin{eqnarray}
-\label{EQ:laplacian_stability}
+\label{EQ:eg-fourlayer-laplacian_stability}
 S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
 \end{eqnarray}
 
@@ -294,7 +294,7 @@
 $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
 
 \begin{eqnarray}
-\label{EQ:laplacian_stability_z}
+\label{EQ:eg-fourlayer-laplacian_stability_z}
 S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
 \end{eqnarray}
 
@@ -307,7 +307,7 @@
 \noindent The numerical stability for inertial oscillations
 
 \begin{eqnarray}
-\label{EQ:inertial_stability}
+\label{EQ:eg-fourlayer-inertial_stability}
 S_{i} = f^{2} {\delta t}^2
 \end{eqnarray}
 
@@ -320,7 +320,7 @@
 speed of $ | \vec{u} | = 2 ms^{-1}$
 
 \begin{eqnarray}
-\label{EQ:cfl_stability}
+\label{EQ:eg-fourlayer-cfl_stability}
 C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
 \end{eqnarray}
 
@@ -329,10 +329,10 @@
 \\
 
 \noindent The stability parameter for internal gravity waves
-propogating at $2~{\rm m}~{\rm s}^{-1}$ 
+propagating at $2~{\rm m}~{\rm s}^{-1}$ 
 
 \begin{eqnarray}
-\label{EQ:igw_stability}
+\label{EQ:eg-fourlayer-igw_stability}
 S_{c} = \frac{c_{g} \delta t}{ \Delta x}
 \end{eqnarray}
 
@@ -355,7 +355,7 @@
 \item {\it code/SIZE.h}. 
 \end{itemize}
 contain the code customisations and parameter settings for this 
-experiements. Below we describe the customisations
+experiments. Below we describe the customisations
 to these files associated with this experiment.
 
 \subsubsection{File {\it input/data}}
@@ -372,7 +372,7 @@
 the initial and reference values of potential temperature at each model
 level in units of $^{\circ}$C.
 The entries are ordered from surface to depth. For each
-depth level the inital and reference profiles will be uniform in
+depth level the initial and reference profiles will be uniform in
 $x$ and $y$. The values specified here are read into the
 variable 
 {\bf
@@ -418,7 +418,7 @@
 
 \item Line 6, 
 \begin{verbatim} viscAz=1.E-2, \end{verbatim} 
-this line sets the vertical laplacian dissipation coefficient to
+this line sets the vertical Laplacian dissipation coefficient to
 $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
 for this operator are specified later. 
 The variable 
@@ -438,7 +438,7 @@
 \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}
 viscAr
 \begin{rawhtml} </A>\end{rawhtml}
-}. At each time step, the viscous term contribution to the momentum eqautions
+}. At each time step, the viscous term contribution to the momentum equations
 is calculated in routine
 {\it S/R CALC\_DIFFUSIVITY}.
 
@@ -697,8 +697,8 @@
 \end{verbatim}
 This line requests that the simulation be performed in a 
 spherical polar coordinate system. It affects the interpretation of
-grid inoput parameters, for exampl {\bf delX} and {\bf delY} and
-causes the grid generation routines to initialise an internal grid based
+grid input parameters, for example {\bf delX} and {\bf delY} and
+causes the grid generation routines to initialize an internal grid based
 on spherical polar geometry.
 The variable
 {\bf
@@ -733,7 +733,7 @@
 This line sets the southern boundary of the modeled
 domain to $0^{\circ}$ latitude. This value affects both the
 generation of the locally orthogonal grid that the model
-uses internally and affects the initialisation of the coriolis force.
+uses internally and affects the initialization of the coriolis force.
 Note - it is not required to set
 a longitude boundary, since the absolute longitude does
 not alter the kernel equation discretisation.
@@ -960,7 +960,7 @@
 The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) 
 map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the
 default for MITgcm).
-Although $\tau_{x}$ is only a function of latituted, $y$,
+Although $\tau_{x}$ is only a function of latitude, $y$,
 in this experiment
 this file must still define a complete two-dimensional map in order
 to be compatible with the standard code for loading forcing fields 
@@ -1061,7 +1061,7 @@
 % pwd
 \end{verbatim}
 
- You shold see a response on the screen ending in
+ You should see a response on the screen ending in
 
 {\it verification/exp2/input }
 
