CMS-Flow:Subgrid Turbulence Model

Subgrid Turbulence Model

In CMS-Flow eddy viscosity is calculated as the sum of the kinematic viscosity $\nu _{0}$, the current-related eddy viscosity $\nu _{c}$ and the wave-related eddy viscosity $\nu _{w}$

     $\nu _{t}=\nu _{0}+\nu _{c}+\nu _{w}$  

The wave contribution is included using the equation of Kraus and Larson (1991)

     $\nu _{w}=\Lambda u_{w}h$

where $\Lambda$ is an empirical coefficient (default is 0.5), and $u_{w}$ is the wave bottom orbital velocity and $h$ is the water depth.

The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress

     $\nu _{c}=\nu _{0}+{\sqrt {(c_{0}u_{*}h)^{2}+(c_{1}\Delta |S|)^{2}}}$

where $\nu _{0}$ is a base value approximately equal to the kinematic viscosity, $c_{0}$ is an empirical coefficient, $c_{sm}$ is an empirical coefficient (Smagorinsky coefficient), $\Delta$ is the local cell area, and $|S|$ is equal to

     $|S|={\sqrt {{\biggl (}{\frac {\partial U}{\partial x}}{\biggr )}^{2}+{\biggl (}{\frac {\partial V}{\partial y}}{\biggr )}^{2}+{\frac {1}{2}}{\biggl (}{\frac {\partial U}{\partial y}}+{\frac {\partial V}{\partial x}}{\biggr )}^{2}}}$

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References

LARSON, M.; HANSON, H., and KRAUS, N. C., 2003. Numerical modeling of beach topography change. Advances in Coastal Modeling, V.C. Lakhan (eds.), Elsevier Oceanography Series, 67, Amsterdam, The Netherlands, 337-365.

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CMS-Flow