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

     $\nu _{c}={\sqrt {(c_{0}u_{*}h)^{2}+(c_{sm}^{2}\Delta x\Delta y|S|)^{2}}}$

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

     $|S|={\sqrt {2{\biggl (}{\frac {\partial U}{\partial x}}{\biggr )}^{2}+2{\biggl (}{\frac {\partial V}{\partial y}}{\biggr )}^{2}+{\biggl (}{\frac {\partial U}{\partial y}}+{\frac {\partial V}{\partial x}}{\biggr )}^{2}}}$

The wave component of the eddy viscosity is calculated as

     $\nu _{w}=k(D/\rho )^{1/3}H_{s}$

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

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CMS-Flow