--- manual/s_examples/barotropic_gyre/baro.tex 2001/09/27 00:58:17 1.2 +++ manual/s_examples/barotropic_gyre/baro.tex 2001/11/13 20:13:54 1.7 @@ -1,7 +1,8 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.2 2001/09/27 00:58:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/barotropic_gyre/baro.tex,v 1.7 2001/11/13 20:13:54 adcroft Exp $ % $Name: $ \section{Example: Barotropic Ocean Gyre In Cartesian Coordinates} +\label{sect:eg-baro} \bodytext{bgcolor="#FFFFFFFF"} @@ -15,16 +16,14 @@ %{\large May 2001} %\end{center} -\subsection{Introduction} - -This document is the first in a series of documents describing +This is the first in a series of sections describing example MITgcm numerical experiments. The example experiments -include both straightforward examples of idealised geophysical +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 -experiements are presented, as well as experiments employing -cartesian, spherical-polar and cube-sphere coordinate systems. +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. @@ -32,8 +31,8 @@ \subsection{Experiment Overview} 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 simliar +a Barotropic, wind-forced, ocean gyre circulation. 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}. @@ -41,7 +40,7 @@ is configured to represent a rectangular enclosed box of fluid, $1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally -in the ``north-south'' direction. Topologically the grid is cartesian and +in the ``north-south'' direction. Topologically the grid is Cartesian and the coriolis parameter $f$ is defined according to a mid-latitude beta-plane equation @@ -67,7 +66,7 @@ \\ \\ Figure \ref{FIG:simulation_config} -summarises the configuration simulated. +summarizes the configuration simulated. \begin{figure} \begin{center} @@ -81,33 +80,27 @@ \label{FIG:simulation_config} \end{figure} -\subsection{Discrete Numerical Configuration} - - The model is configured in hydrostatic form. The domain is discretised with -a uniform grid spacing in the horizontal set to - $\Delta x=\Delta y=20$~km, so -that there are sixty grid cells in the $x$ and $y$ directions. Vertically the -model is configured with a single layer with depth, $\Delta z$, of $5000$~m. -The implicit free surface form of the -pressure equation described in Marshall et. al \cite{Marshall97a} is -employed. -A horizontal laplacian operator $\nabla_{h}^2$ provides viscous +\subsection{Equations Solved} +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. +A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous 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 experiement configuration (see section -\ref{SEC:code_config} ), yielding an active set of equations solved in this -configuration as follows +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 \begin{eqnarray} \label{EQ:model_equations} -\frac{Du}{Dt} - fv + - g\frac{\partial \eta}{\partial x} - - A_{h}\nabla_{h}^2u +\frac{Du}{Dt} - fv + + g\frac{\partial \eta}{\partial x} - + A_{h}\nabla_{h}^2u & = & \frac{\tau_{x}}{\rho_{0}\Delta z} \\ \frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} - - A_{h}\nabla_{h}^2v + A_{h}\nabla_{h}^2v & = & 0 \\ @@ -117,13 +110,22 @@ \end{eqnarray} \noindent where $u$ and $v$ and the $x$ and $y$ components of the -flow vector $\vec{u}$. +flow vector $\vec{u}$. \\ + +\subsection{Discrete Numerical Configuration} + + The domain is discretised with +a uniform grid spacing in the horizontal set to + $\Delta x=\Delta y=20$~km, so +that there are sixty grid cells in the $x$ and $y$ directions. Vertically the +model is configured with a single layer with depth, $\Delta z$, of $5000$~m. + \subsubsection{Numerical Stability Criteria} -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_thesis}, +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} @@ -137,7 +139,7 @@ \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 \cite{Adcroft_thesis} +parameter to the horizontal Laplacian friction \cite{adcroft:95} @@ -151,7 +153,7 @@ \\ \noindent The numerical stability for inertial oscillations -\cite{Adcroft_thesis} +\cite{adcroft:95} \begin{eqnarray} \label{EQ:inertial_stability} @@ -162,7 +164,7 @@ limit for stability. \\ -\noindent The advective CFL \cite{Adcroft_thesis} for an extreme maximum +\noindent The advective CFL \cite{adcroft:95} for an extreme maximum horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ \begin{eqnarray} @@ -188,8 +190,8 @@ \item {\it code/CPP\_OPTIONS.h}, \item {\it code/SIZE.h}. \end{itemize} -contain the code customisations and parameter settings for this -experiements. Below we describe the customisations +contain the code customizations and parameter settings for this +experiments. Below we describe the customizations to these files associated with this experiment. \subsubsection{File {\it input/data}} @@ -201,7 +203,7 @@ \begin{itemize} \item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets -the laplacian friction coefficient to $400 m^2s^{-1}$ +the Laplacian friction coefficient to $400 m^2s^{-1}$ \item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets $\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ @@ -219,7 +221,7 @@ startTime=0, \end{verbatim} this line indicates that the experiment should start from $t=0$ -and implicitly supresses searching for checkpoint files associated +and implicitly suppresses searching for checkpoint files associated with restarting an numerical integration from a previously saved state. \item Line 29, @@ -241,7 +243,7 @@ usingCartesianGrid=.TRUE., \end{verbatim} This line requests that the simulation be performed in a -cartesian coordinate system. +Cartesian coordinate system. \item Line 41, \begin{verbatim} @@ -306,12 +308,12 @@ \subsubsection{File {\it input/data.pkg}} This file uses standard default values and does not contain -customisations for this experiment. +customizations for this experiment. \subsubsection{File {\it input/eedata}} This file uses standard default values and does not contain -customisations for this experiment. +customizations for this experiment. \subsubsection{File {\it input/windx.sin\_y}} @@ -359,11 +361,11 @@ \subsubsection{File {\it code/CPP\_OPTIONS.h}} This file uses standard default values and does not contain -customisations for this experiment. +customizations for this experiment. \subsubsection{File {\it code/CPP\_EEOPTIONS.h}} This file uses standard default values and does not contain -customisations for this experiment. +customizations for this experiment.