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 (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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 (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle l_h = \kappa min(sqrt{\del x \del y}, c_{sm} h) } where $c_{sm}$ is an empirical coefficient (Smagorinsky coefficient).