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) $\nu _{t}w=\Lambda u_{w}h$, 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

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