--- manual/s_examples/rotating_tank/tank.tex 2004/07/26 21:25:34 1.8 +++ manual/s_examples/rotating_tank/tank.tex 2004/07/27 13:40:09 1.9 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.8 2004/07/26 21:25:34 afe Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.9 2004/07/27 13:40:09 afe Exp $ % $Name: $ \bodytext{bgcolor="#FFFFFFFF"} @@ -51,59 +51,6 @@ 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} -\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:eg-baro-munk_layer} -M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} -\end{eqnarray} - -\noindent of $\approx 100$km. This is greater than the model -resolution $\Delta x$, ensuring that the frictional boundary -layer is well resolved. -\\ - -\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:95} - - - -\begin{eqnarray} -\label{EQ:eg-baro-laplacian_stability} -S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} -\end{eqnarray} - -\noindent evaluates to 0.012, which is well below the 0.3 upper limit -for stability. -\\ - -\noindent The numerical stability for inertial oscillations -\cite{adcroft:95} - -\begin{eqnarray} -\label{EQ:eg-baro-inertial_stability} -S_{i} = f^{2} {\delta t}^2 -\end{eqnarray} - -\noindent evaluates to $0.0144$, which is well below the $0.5$ upper -limit for stability. -\\ - -\noindent The advective CFL \cite{adcroft:95} for an extreme maximum -horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ - -\begin{eqnarray} -\label{EQ:eg-baro-cfl_stability} -S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} -\end{eqnarray} - -\noindent evaluates to 0.12. This is approaching the stability limit -of 0.5 and limits $\delta t$ to $1200s$. \subsection{Code Configuration} \label{www:tutorials}