--- manual/s_examples/barotropic_gyre/baro.tex 2001/11/13 20:13:54 1.7 +++ manual/s_examples/barotropic_gyre/baro.tex 2002/02/28 19:32:19 1.8 @@ -1,9 +1,6 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.7 2001/11/13 20:13:54 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.8 2002/02/28 19:32:19 cnh Exp $ % $Name: $ -\section{Example: Barotropic Ocean Gyre In Cartesian Coordinates} -\label{sect:eg-baro} - \bodytext{bgcolor="#FFFFFFFF"} %\begin{center} @@ -16,7 +13,7 @@ %{\large May 2001} %\end{center} -This is the first in a series of sections describing +This is the first in a series of tutorials describing example MITgcm numerical experiments. The example experiments include both straightforward examples of idealized geophysical fluid simulations and more involved cases encompassing @@ -28,7 +25,9 @@ the experimental configuration and detailed information on how to configure the MITgcm code and input files for each experiment. -\subsection{Experiment Overview} +\section{Barotropic Ocean Gyre In Cartesian Coordinates} +\label{sect:eg-baro} + This example experiment demonstrates using the MITgcm to simulate a Barotropic, wind-forced, ocean gyre circulation. The experiment @@ -45,19 +44,19 @@ 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} @@ -65,7 +64,7 @@ $\tau_0$ is set to $0.1N m^{-2}$. \\ \\ -Figure \ref{FIG:simulation_config} +Figure \ref{FIG:eg-baro-simulation_config} summarizes the configuration simulated. \begin{figure} @@ -77,7 +76,7 @@ \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} @@ -92,7 +91,7 @@ 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 @@ -128,7 +127,7 @@ 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 +143,7 @@ \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 +155,7 @@ \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 +167,7 @@ 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} @@ -176,7 +175,7 @@ of 0.5 and limits $\delta t$ to $1200s$. \subsection{Code Configuration} -\label{SEC:code_config} +\label{SEC:eg-baro-code_config} The model configuration for this experiment resides under the directory {\it verification/exp0/}. The experiment files