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) Failed to parse (unknown function "\del"): {\displaystyle \nu_tw = \del 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

     $\nu _{tc}=\nu _{t0}+sqrt{(c_{0}u_{*}h)^{2}+(l_{h}^{2}abs{S})^{2}}$

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 (unknown function "\del"): {\displaystyle l_h = \kappa min(sqrt{\del x \del y}, c_{sm} h) } where $c_{sm}$ is an empirical coefficient (Smagorinsky coefficient).