--- manual/s_examples/rotating_tank/tank.tex 2004/07/26 21:09:47 1.7 +++ manual/s_examples/rotating_tank/tank.tex 2004/07/26 21:25:34 1.8 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.7 2004/07/26 21:09:47 afe Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.8 2004/07/26 21:25:34 afe Exp $ % $Name: $ \bodytext{bgcolor="#FFFFFFFF"} @@ -36,94 +36,10 @@ -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 -to the problems described analytically by Stommel in 1966 -\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}. - -In this experiment the model -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 -the coriolis parameter $f$ is defined according to a mid-latitude beta-plane -equation - -\begin{equation} -\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 $\beta = 10^{-11}s^{-1}m^{-1}$. -\\ -\\ - The sinusoidal wind-stress variations are defined according to - -\begin{equation} -\label{EQ:eg-baro-taux} -\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) -\end{equation} -\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and -$\tau_0$ is set to $0.1N m^{-2}$. -\\ -\\ -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} -\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: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{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 experiment configuration (see section -\ref{SEC:code_config} ), yielding an active set of equations solved in this -configuration as follows - -\begin{eqnarray} -\label{EQ:eg-baro-model_equations} -\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 -& = & -0 -\\ -\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u} -&=& -0 -\end{eqnarray} - -\noindent where $u$ and $v$ and the $x$ and $y$ components of the -flow vector $\vec{u}$. -\\ \subsection{Discrete Numerical Configuration}