CMS-Flow:Subgrid Turbulence Model

Eddy Viscosity

In CMS-Flow eddy viscosity is calculated as the sum of the kinematic viscosity ${\nu }_{t0}$, the current-related eddy viscosity ${\nu }_c$ and the wave-related eddy viscosity ${\nu }_w$

     ${\nu }_t={\nu }_{t0}+{\nu }_c+{\nu }_w$

There are two options to calculate ${\nu }_c$. The first is the Falconer (1980) equation given by

     ${\nu }_c=0.575C_b|U|h$

where $C_b$ is the bottom friction coefficient, $U$ is the depth-averaged current velocity, and $h$ is the total water depth.

The second option is a subgrid turbulence model given by

     ${\nu }_c=\sqrt{(c_0{u}_{*}h{)}^2+(c_{sm}^2\mathrm{\Delta }x\mathrm{\Delta }y|S|{)}^2}$

where $c_0$ is an empirical coefficient approximately equal to 1/6, $c_{sm}$ is an empirical coefficient between 0.25-0.5, $\mathrm{\Delta }x$ and math>\Delta y</math> are the grid dimensions in the x and y directions and $|S|$ Normal 0 false false false MicrosoftInternetExplorer4 is equal to

     Failed to parse (syntax error): {\displaystyle  |S| = \sqrt{2(\frac{ \partial u}{\partial x})^2 + 2(\frac{ \partial v}{\partial y})^2 +(\frac{\partial u}{\partial y} + \partial v}{\partial x})^2} }

The wave component of the eddy viscosity is calculated as

     ${\nu }_w=k(D/\rho {)}^{1/3}$

where $k$ is an empirical coefficient, $\rho$ is the water density, and $D$ is the total wave dissipation.

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CMS-Flow