--- manual/s_examples/barotropic_gyre/baro.tex 2001/11/13 18:19:18 1.5 +++ manual/s_examples/barotropic_gyre/baro.tex 2008/01/15 17:05:12 1.15 @@ -1,9 +1,6 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.5 2001/11/13 18:19:18 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.15 2008/01/15 17:05:12 jmc Exp $ % $Name: $ -\section{Example: Barotropic Ocean Gyre In Cartesian Coordinates} -\label{sec:eg-baro} - \bodytext{bgcolor="#FFFFFFFF"} %\begin{center} @@ -16,23 +13,20 @@ %{\large May 2001} %\end{center} -This is the first in a series of sections describing -example MITgcm numerical experiments. The example experiments -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 -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} +\begin{rawhtml} + +\end{rawhtml} +\begin{center} +(in directory: {\it verification/tutorial\_barotropic\_gyre/}) +\end{center} 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 similar +a Barotropic, wind-forced, ocean gyre circulation. The files for this +experiment can be found in the verification directory tutorial\_barotropic\_gyre. +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}. @@ -45,19 +39,19 @@ 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} @@ -65,24 +59,30 @@ $\tau_0$ is set to $0.1N m^{-2}$. \\ \\ -Figure \ref{FIG:simulation_config} +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} +%% \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{ + \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{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{Marshall97a} is +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 @@ -92,7 +92,7 @@ configuration as follows \begin{eqnarray} -\label{EQ:model_equations} +\label{EQ:eg-baro-model_equations} \frac{Du}{Dt} - fv + g\frac{\partial \eta}{\partial x} - A_{h}\nabla_{h}^2u @@ -115,6 +115,7 @@ \subsection{Discrete Numerical Configuration} +\label{www:tutorials} The domain is discretised with a uniform grid spacing in the horizontal set to @@ -123,12 +124,13 @@ 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: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} @@ -144,7 +146,7 @@ \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} @@ -156,7 +158,7 @@ \cite{adcroft:95} \begin{eqnarray} -\label{EQ:inertial_stability} +\label{EQ:eg-baro-inertial_stability} S_{i} = f^{2} {\delta t}^2 \end{eqnarray} @@ -168,7 +170,7 @@ 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} @@ -176,10 +178,12 @@ 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 +directory {\it verification/tutorial\_barotropic\_gyre/}. +The experiment files \begin{itemize} \item {\it input/data} \item {\it input/data.pkg} @@ -195,6 +199,7 @@ 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 @@ -306,16 +311,19 @@ \end{small} \subsubsection{File {\it input/data.pkg}} +\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} This file uses standard default values and does not contain 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 $Nm^{-2}$. @@ -326,6 +334,7 @@ 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 ($x,y$) @@ -337,6 +346,7 @@ 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 @@ -359,12 +369,14 @@ \end{small} \subsubsection{File {\it code/CPP\_OPTIONS.h}} +\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} This file uses standard default values and does not contain customizations for this experiment.