| 203 |
of enstrophy-dissipation and the resulting eddy viscosity are |
of enstrophy-dissipation and the resulting eddy viscosity are |
| 204 |
\begin{eqnarray} |
\begin{eqnarray} |
| 205 |
L_\eta(A_{hLeith})\propto\pi A_{hLeith}^{1/2}\eta^{-1/6}=\pi A_{hLeith}^{1/3}|\nabla \av \omega_3|^{-1/3}\\ |
L_\eta(A_{hLeith})\propto\pi A_{hLeith}^{1/2}\eta^{-1/6}=\pi A_{hLeith}^{1/3}|\nabla \av \omega_3|^{-1/3}\\ |
| 206 |
A_{hLeith}={\sf viscC2Leith}|\nabla \av \omega_3|L^3\\ |
A_{hLeith}=\left(\frac{{\sf viscC2Leith}}{\pi}\right)^3L^3|\nabla \av \omega_3|\\ |
| 207 |
|\nabla\omega_3|\equiv\sqrt{\left[\pd{x}{\ }\left(\pd{x}{\av \tv}-\pd{y}{\av \tu}\right)\right]^2+\left[\pd{y}{\ }\left(\pd{x}{\av \tv}-\pd{y}{\av \tu}\right)\right]^2} |
|\nabla\omega_3|\equiv\sqrt{\left[\pd{x}{\ }\left(\pd{x}{\av \tv}-\pd{y}{\av \tu}\right)\right]^2+\left[\pd{y}{\ }\left(\pd{x}{\av \tv}-\pd{y}{\av \tu}\right)\right]^2} |
| 208 |
\end{eqnarray} |
\end{eqnarray} |
|
NOTE:: may be useful to redefine viscC2Leith for consistency with Smag... |
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|
\begin{eqnarray} |
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A_{hLeith}=\left(\frac{{\sf viscC2Leith}}{\pi}\right)^3L^3|\nabla \av \omega_3| |
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\end{eqnarray} |
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| 209 |
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| 210 |
\subsubsection{Modified Leith Viscosity} |
\subsubsection{Modified Leith Viscosity} |
| 211 |
The argument above for the Leith viscosity parameterization uses |
The argument above for the Leith viscosity parameterization uses |
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