CMS-Flow:Subgrid Turbulence Model

Subgrid Turbulence Model

The 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 $del$ is an empirical coefficient (set to 0.5 here), and $u_w$ is the wave bottom orbital velocity. The current-related eddy viscosity is calculated using a subgrid turbulence in which the turbulent eddy viscosity is a function of the flow gradients and the grid size model of the form

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

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 $l_h=\kappa min(\sqrt{\delta x\delta y},c_{sm}h)$ where $c_{sm}$ is an empirical coefficient (Smagorinsky coefficient).