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that there are sixty grid cells in the $x$ and $y$ directions. Vertically the |
that there are sixty grid cells in the $x$ and $y$ directions. Vertically the |
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model is configured with a single layer with depth, $\Delta z$, of $5000$~m. |
model is configured with a single layer with depth, $\Delta z$, of $5000$~m. |
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\subsubsection{Numerical Stability Criteria} |
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\label{www:tutorials} |
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The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$. |
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This value is chosen to yield a Munk layer width \cite{adcroft:95}, |
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\begin{eqnarray} |
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\label{EQ:eg-baro-munk_layer} |
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M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
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\end{eqnarray} |
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\noindent of $\approx 100$km. This is greater than the model |
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resolution $\Delta x$, ensuring that the frictional boundary |
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layer is well resolved. |
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\\ |
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\noindent The model is stepped forward with a |
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time step $\delta t=1200$secs. With this time step the stability |
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parameter to the horizontal Laplacian friction \cite{adcroft:95} |
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\begin{eqnarray} |
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\label{EQ:eg-baro-laplacian_stability} |
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S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} |
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\end{eqnarray} |
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\noindent evaluates to 0.012, which is well below the 0.3 upper limit |
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for stability. |
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\\ |
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\noindent The numerical stability for inertial oscillations |
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\cite{adcroft:95} |
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\begin{eqnarray} |
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\label{EQ:eg-baro-inertial_stability} |
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S_{i} = f^{2} {\delta t}^2 |
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\end{eqnarray} |
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\noindent evaluates to $0.0144$, which is well below the $0.5$ upper |
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limit for stability. |
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\\ |
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\noindent The advective CFL \cite{adcroft:95} for an extreme maximum |
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horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ |
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\begin{eqnarray} |
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\label{EQ:eg-baro-cfl_stability} |
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S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} |
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\end{eqnarray} |
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\noindent evaluates to 0.12. This is approaching the stability limit |
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of 0.5 and limits $\delta t$ to $1200s$. |
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| 54 |
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| 55 |
\subsection{Code Configuration} |
\subsection{Code Configuration} |
| 56 |
\label{www:tutorials} |
\label{www:tutorials} |
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