CMS-Flow:Subgrid Turbulence Model

Subgrid Turbulence Model

In CMS-Flow eddy viscosity is calculated as ${\nu }_t=(1-{\theta }_m){\nu }_{tc}+{\theta }_m{\nu }_m$ where ${\theta }_m$ is weighting factor equal to ${\theta }_m=(H_s/h{)}^3$ in which $H_s$ is the significant wave height and ${\nu }_{tc}$ and ${\nu }_{tw}$ are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of Kraus and Larson (1991) ${\nu }_{t}w=\mathrm{\Lambda }{u}_{w}h$, where $\mathrm{\Lambda }$ is an empirical coefficient (default is 0.5), and $u_w$ is the wave bottom orbital velocity. The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress

     ${\nu }_{tc}={\nu }_{t0}+\sqrt{(c_0{u}_{*}h{)}^2+(l_h^2|S|{)}^2}$

where ${\nu }_{t0}$ is a base value approximately equal to the dynamic viscosity, and $c_0$ is an empirical coefficient and $l_h$ is the subgrid mixing length. The mixing length is calculated here as

     Failed to parse (syntax error): {\displaystyle l_h = \kappa min( \sqrt{\Delta x \Delta y}, c_{sm} 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