CMS-Flow:Subgrid Turbulence Model

Subgrid Turbulence Model

In CMS-Flow eddy viscosity is calculated as

     $\nu _{t}=(1-\theta _{m})\nu _{c}+\theta _{m}\nu _{w}$  

where $\theta _{m}$ is weighting factor equal to $\theta _{m}=(H_{s}/h)^{3}$ in which $H_{s}$ is the significant wave height and $\nu _{c}$ and $\nu _{w}$ are the current- and wave-related eddy viscosity components respectively. 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

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

where $\nu _{0}$ is a base value approximately equal to the kinematic viscosity, $c_{0}$ is an empirical coefficient, $l_{h}$ is the subgrid mixing length, 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 mixing length is calculated here as

     $l_{h}=c_{sm}{\textrm {min}}({\sqrt {\Delta x\Delta y}},h)$ 

where $c_{sm}$ is an empirical coefficient (Smagorinsky coefficient).

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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