Parent Directory
| 
Revision Log
| 
Revision Graph
| 
Patch
--- manual/s_examples/baroclinic_gyre/fourlayer.tex 2010/08/27 13:25:31 1.27
+++ manual/s_examples/baroclinic_gyre/fourlayer.tex 2010/08/30 23:09:19 1.28
@@ -1,9 +1,9 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.27 2010/08/27 13:25:31 jmc Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.28 2010/08/30 23:09:19 jmc Exp $
% $Name: $
\section[Baroclinic Gyre MITgcm Example]{Four Layer Baroclinic Ocean Gyre In Spherical Coordinates}
-\label{www:tutorials}
-\label{sect:eg-fourlayer}
+%\label{www:tutorials}
+\label{sec:eg-fourlayer}
\begin{rawhtml}
<!-- CMIREDIR:eg-fourlayer: -->
\end{rawhtml}
@@ -29,7 +29,7 @@
in the verification directory under tutorial\_baroclinic\_gyre.
\subsection{Overview}
-\label{www:tutorials}
+%\label{www:tutorials}
This example experiment demonstrates using the MITgcm to simulate
a baroclinic, wind-forced, ocean gyre circulation. The experiment
@@ -47,7 +47,7 @@
according to latitude, $\varphi$
\begin{equation}
-\label{EQ:eg-fourlayer-fcori}
+\label{eq:eg-fourlayer-fcori}
f(\varphi) = 2 \Omega \sin( \varphi )
\end{equation}
@@ -57,7 +57,7 @@
The sinusoidal wind-stress variations are defined according to
\begin{equation}
-\label{EQ:taux}
+\label{eq:taux}
\tau_{\lambda}(\varphi) = \tau_{0}\sin(\pi \frac{\varphi}{L_{\varphi}})
\end{equation}
@@ -65,9 +65,9 @@
$\tau_0$ is set to $0.1N m^{-2}$.
\\
-Figure \ref{FIG:eg-fourlayer-simulation_config}
+Figure \ref{fig:eg-fourlayer-simulation_config}
summarizes the configuration simulated.
-In contrast to the example in section \ref{sect:eg-baro}, the
+In contrast to the example in section \ref{sec: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 orthogonal coordinate $(x,y,z)$. For this experiment description
@@ -86,14 +86,14 @@
linear
\begin{equation}
-\label{EQ:eg-fourlayer-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:eg-fourlayer-linear1_eos_pert}
+\label{eq:eg-fourlayer-linear1_eos_pert}
\rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
\end{equation}
@@ -122,13 +122,13 @@
imposed by setting the potential temperature, $\theta$, in each layer.
The vertical spacing, $\Delta z$, is constant and equal to $500$m.
}
-\label{FIG:eg-fourlayer-simulation_config}
+\label{fig:eg-fourlayer-simulation_config}
\end{figure}
\subsection{Equations solved}
-\label{www:tutorials}
+%\label{www:tutorials}
For this problem
-the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the
+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{marshall:97a} are
employed. The flow is three-dimensional with just temperature, $\theta$, as
an active tracer. The equation of state is linear.
@@ -137,12 +137,12 @@
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 experiment configuration (see section
-\ref{SEC:eg_fourl_code_config} ). This yields an active set of equations
+\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:eg-fourlayer-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}}
@@ -181,11 +181,11 @@
flow vector $\vec{u}$ on the sphere ($u=\dot{\lambda},v=\dot{\varphi}$).
The terms $H\widehat{u}$ and $H\widehat{v}$ are the components of the vertical
integral term given in equation \ref{eq:free-surface} and
-explained in more detail in section \ref{sect:pressure-method-linear-backward}.
+explained in more detail in section \ref{sec:pressure-method-linear-backward}.
However, for the problem presented here, the continuity relation (equation
\ref{eq:fourl_example_continuity}) differs from the general form given
-in section \ref{sect:pressure-method-linear-backward},
-equation \ref{eq:linear-free-surface=P-E+R}, because the source terms
+in section \ref{sec:pressure-method-linear-backward},
+equation \ref{eq:linear-free-surface=P-E}, because the source terms
${\cal P}-{\cal E}+{\cal R}$
are all $0$.
@@ -203,7 +203,7 @@
lateral and vertical boundary conditions for the $\nabla_{h}^{2}$
and $\frac{\partial^{2}}{\partial z^{2}}$ operators are specified
when the numerical simulation is run - see section
-\ref{SEC:eg_fourl_code_config}. For temperature
+\ref{sec:eg_fourl_code_config}. For temperature
the boundary condition is ``zero-flux''
e.g. $\frac{\partial \theta}{\partial \varphi}=
\frac{\partial \theta}{\partial \lambda}=\frac{\partial \theta}{\partial z}=0$.
@@ -211,7 +211,7 @@
\subsection{Discrete Numerical Configuration}
-\label{www:tutorials}
+%\label{www:tutorials}
The domain is discretised with
a uniform grid spacing in latitude and longitude
@@ -231,7 +231,7 @@
The procedure for generating a set of internal grid variables from a
spherical polar grid specification is discussed in section
-\ref{sect:spatial_discrete_horizontal_grid}.
+\ref{sec:spatial_discrete_horizontal_grid}.
\noindent\fbox{ \begin{minipage}{5.5in}
{\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em
@@ -252,32 +252,32 @@
-As described in \ref{sect:tracer_equations}, the time evolution of potential
+As described in \ref{sec: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{sect:tracer_equations_abII} is used to step forward the temperature
+\ref{sec: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{sect:flux-form_momentum_eqautions}.
+described in section \ref{sec:flux-form_momentum_equations}.
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
pressure is diagnosed explicitly by integrating density. The sea-surface
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{sect:finding_the_pressure_field}.
+\ref{sec:pressure-method-linear-backward} and
+\ref{sec:finding_the_pressure_field}.
\subsubsection{Numerical Stability Criteria}
-\label{www:tutorials}
+%\label{www:tutorials}
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:eg-fourlayer-munk_layer}
+\label{eq:eg-fourlayer-munk_layer}
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
\end{eqnarray}
@@ -293,7 +293,7 @@
parameter to the horizontal Laplacian friction
\begin{eqnarray}
-\label{EQ:eg-fourlayer-laplacian_stability}
+\label{eq:eg-fourlayer-laplacian_stability}
S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
\end{eqnarray}
@@ -305,7 +305,7 @@
$1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
\begin{eqnarray}
-\label{EQ:eg-fourlayer-laplacian_stability_z}
+\label{eq:eg-fourlayer-laplacian_stability_z}
S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
\end{eqnarray}
@@ -318,7 +318,7 @@
\noindent The numerical stability for inertial oscillations
\begin{eqnarray}
-\label{EQ:eg-fourlayer-inertial_stability}
+\label{eq:eg-fourlayer-inertial_stability}
S_{i} = f^{2} {\delta t}^2
\end{eqnarray}
@@ -331,7 +331,7 @@
speed of $ | \vec{u} | = 2 ms^{-1}$
\begin{eqnarray}
-\label{EQ:eg-fourlayer-cfl_stability}
+\label{eq:eg-fourlayer-cfl_stability}
C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
\end{eqnarray}
@@ -343,7 +343,7 @@
propagating at $2~{\rm m}~{\rm s}^{-1}$
\begin{eqnarray}
-\label{EQ:eg-fourlayer-igw_stability}
+\label{eq:eg-fourlayer-igw_stability}
S_{c} = \frac{c_{g} \delta t}{ \Delta x}
\end{eqnarray}
@@ -351,8 +351,8 @@
stability limit of 0.25.
\subsection{Code Configuration}
-\label{www:tutorials}
-\label{SEC:eg_fourl_code_config}
+%\label{www:tutorials}
+\label{sec:eg_fourl_code_config}
The model configuration for this experiment resides under the
directory {\it verification/tutorial\_barotropic\_gyre/}.
@@ -372,7 +372,7 @@
associated with this experiment.
\subsubsection{File {\it input/data}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file, reproduced completely below, specifies the main parameters
for the experiment. The parameters that are significant for this configuration
@@ -684,19 +684,19 @@
\begin{rawhtml}</PRE>\end{rawhtml}
\subsubsection{File {\it input/data.pkg}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it input/eedata}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it input/windx.sin\_y}}
-\label{www:tutorials}
+%\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 $Nm^{-2}$
@@ -709,7 +709,7 @@
input/windx.sin\_y} file.
\subsubsection{File {\it input/topog.box}}
-\label{www:tutorials}
+%\label{www:tutorials}
The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
@@ -721,7 +721,7 @@
code for creating the {\it input/topog.box} file.
\subsubsection{File {\it code/SIZE.h}}
-\label{www:tutorials}
+%\label{www:tutorials}
Two lines are customized in this file for the current experiment
@@ -748,20 +748,20 @@
\end{small}
\subsubsection{File {\it code/CPP\_OPTIONS.h}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
-\label{www:tutorials}
+%\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{Other Files }
-\label{www:tutorials}
+%\label{www:tutorials}
Other files relevant to this experiment are
\begin{itemize}
@@ -774,18 +774,18 @@
\end{itemize}
\subsection{Running The Example}
-\label{www:tutorials}
-\label{SEC:running_the_example}
+%\label{www:tutorials}
+%\label{sec:running_the_example}
\subsubsection{Code Download}
-\label{www:tutorials}
+%\label{www:tutorials}
In order to run the examples you must first download the code distribution.
Instructions for downloading the code can be found in section
-\ref{sect:obtainingCode}.
+\ref{sec:obtainingCode}.
\subsubsection{Experiment Location}
-\label{www:tutorials}
+%\label{www:tutorials}
This example experiments is located under the release sub-directory
@@ -793,7 +793,7 @@
{\it verification/exp2/ }
\subsubsection{Running the Experiment}
-\label{www:tutorials}
+%\label{www:tutorials}
To run the experiment
| ViewVC Help | |
| Powered by ViewVC 1.1.22 |