--- manual/s_examples/barotropic_gyre/baro.tex 2010/08/27 13:25:31 1.19 +++ manual/s_examples/barotropic_gyre/baro.tex 2010/08/30 23:09:19 1.20 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.19 2010/08/27 13:25:31 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.20 2010/08/30 23:09:19 jmc Exp $ % $Name: $ \bodytext{bgcolor="#FFFFFFFF"} @@ -14,8 +14,8 @@ %\end{center} \section[Barotropic Gyre MITgcm Example]{Barotropic Ocean Gyre In Cartesian Coordinates} -\label{www:tutorials} -\label{sect:eg-baro} +%\label{www:tutorials} +\label{sec:eg-baro} \begin{rawhtml} \end{rawhtml} @@ -39,19 +39,19 @@ equation \begin{equation} -\label{EQ:eg-baro-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:eg-baro-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:eg-baro-taux} +\label{eq:eg-baro-taux} \tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) \end{equation} @@ -59,7 +59,7 @@ $\tau_0$ is set to $0.1N m^{-2}$. \\ \\ -Figure \ref{FIG:eg-baro-simulation_config} +Figure \ref{fig:eg-baro-simulation_config} summarizes the configuration simulated. %% === eh3 === @@ -76,11 +76,11 @@ \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:eg-baro-simulation_config} +\label{fig:eg-baro-simulation_config} \end{figure} \subsection{Equations Solved} -\label{www:tutorials} +%\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. @@ -88,11 +88,11 @@ 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 experiment configuration (see section -\ref{SEC:code_config} ), yielding an active set of equations solved in this -configuration as follows +\ref{sec:eg-baro-code_config} ), yielding an active set of equations solved +in this configuration as follows \begin{eqnarray} -\label{EQ:eg-baro-model_equations} +\label{eq:eg-baro-model_equations} \frac{Du}{Dt} - fv + g\frac{\partial \eta}{\partial x} - A_{h}\nabla_{h}^2u @@ -115,7 +115,7 @@ \subsection{Discrete Numerical Configuration} -\label{www:tutorials} +%\label{www:tutorials} The domain is discretised with a uniform grid spacing in the horizontal set to @@ -124,13 +124,13 @@ model is configured with a single layer with depth, $\Delta z$, of $5000$~m. \subsubsection{Numerical Stability Criteria} -\label{www:tutorials} +%\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:95}, \begin{eqnarray} -\label{EQ:eg-baro-munk_layer} +\label{eq:eg-baro-munk_layer} M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} \end{eqnarray} @@ -146,7 +146,7 @@ \begin{eqnarray} -\label{EQ:eg-baro-laplacian_stability} +\label{eq:eg-baro-laplacian_stability} S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} \end{eqnarray} @@ -158,7 +158,7 @@ \cite{adcroft:95} \begin{eqnarray} -\label{EQ:eg-baro-inertial_stability} +\label{eq:eg-baro-inertial_stability} S_{i} = f^{2} {\delta t}^2 \end{eqnarray} @@ -170,7 +170,7 @@ horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ \begin{eqnarray} -\label{EQ:eg-baro-cfl_stability} +\label{eq:eg-baro-cfl_stability} S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} \end{eqnarray} @@ -178,8 +178,8 @@ of 0.5 and limits $\delta t$ to $1200s$. \subsection{Code Configuration} -\label{www:tutorials} -\label{SEC:eg-baro-code_config} +%\label{www:tutorials} +\label{sec:eg-baro-code_config} The model configuration for this experiment resides under the directory {\it verification/tutorial\_barotropic\_gyre/}. @@ -199,7 +199,7 @@ to these files 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 @@ -311,19 +311,19 @@ \end{small} \subsubsection{File {\it input/data.pkg}} -\label{www:tutorials} +%\label{www:tutorials} This file uses standard default values and does not contain customizations for this experiment. \subsubsection{File {\it input/eedata}} -\label{www:tutorials} +%\label{www:tutorials} This file uses standard default values and does not contain customizations 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 $Nm^{-2}$. @@ -334,7 +334,7 @@ code for creating the {\it 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 ($x,y$) @@ -346,7 +346,7 @@ 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 @@ -369,14 +369,14 @@ \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 customizations 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 customizations for this experiment.