CMS-Flow:Subgrid Turbulence Model

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Subgrid Turbulence Model

The eddy viscosity is calculated as where is weighting factor equal to in which is the significant wave height and and are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of KRAUS and LARSON (1991) , where is an empirical coefficient (set to 0.5 here), and 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 is a base value approximately equal to the dynamic viscosity, and is an empirical coefficient and is the subgrid mixing length. The mixing length is calculated here as where is an empirical coefficient (Smagorinsky coefficient).