| 36 |
|
|
| 37 |
|
|
| 38 |
|
|
|
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} |
|
| 39 |
|
|
|
\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} |
|
| 40 |
|
|
| 41 |
\subsection{Equations Solved} |
\subsection{Equations Solved} |
| 42 |
\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. |
|
|
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 $\vec{u}$. |
|
|
\\ |
|
| 43 |
|
|
| 44 |
|
|
| 45 |
\subsection{Discrete Numerical Configuration} |
\subsection{Discrete Numerical Configuration} |
Parent Directory
| 
Revision Log
| 
Revision Graph
| 
Patch