CMS-Flow:Subgrid Turbulence Model: Difference between revisions

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In CMS-Flow eddy viscosity is calculated as <math> \nu_t = (1-\theta_m)\nu_{tc} + \theta_m \nu_m </math>  where <math>\theta_m</math>  is weighting factor equal to <math>\theta_m = (H_s/h)^3 </math>  in which <math>H_s</math>  is the significant wave height and <math>\nu_{tc}</math>  and <math>\nu_{tw}</math>  are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of Kraus and Larson (1991)  <math> \nu_tw = \Lambda u_w h </math>, where  <math>\Lambda</math> is an empirical coefficient (default is 0.5), and  <math>u_w</math> is the wave bottom orbital velocity. The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress
In CMS-Flow eddy viscosity is calculated as <math> \nu_t = (1-\theta_m)\nu_{tc} + \theta_m \nu_m </math>  where <math>\theta_m</math>  is weighting factor equal to <math>\theta_m = (H_s/h)^3 </math>  in which <math>H_s</math>  is the significant wave height and <math>\nu_{tc}</math>  and <math>\nu_{tw}</math>  are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of Kraus and Larson (1991)  <math> \nu_tw = \Lambda u_w h </math>, where  <math>\Lambda</math> is an empirical coefficient (default is 0.5), and  <math>u_w</math> is the wave bottom orbital velocity. The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress


       <math> \nu_{tc} = \nu_{t0} + \sqrt{ (c_0 u_* h)^2 + (c_{sm} \Delta x \Delta y  |S| )^2 } </math>
       <math> \nu_{tc} = \nu_{t0} + \sqrt{ (c_0 u_* h)^2 + (\sqrt{c_{sm} \Delta x \Delta y} |S| )^2 } </math>


where  <math>\nu_{t0}</math> is a base value approximately equal to the dynamic viscosity, and <math>c_0</math>  is an empirical coefficient and  <math>l_h</math> is the subgrid mixing length. The mixing length is calculated here as   
where  <math>\nu_{t0}</math> is a base value approximately equal to the dynamic viscosity, and <math>c_0</math>  is an empirical coefficient and  <math>l_h</math> is the subgrid mixing length. The mixing length is calculated here as   

Revision as of 20:34, 2 November 2009

Subgrid Turbulence Model

In CMS-Flow 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 (default is 0.5), and is the wave bottom orbital velocity. The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress

     

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).


References

LARSON, M.; HANSON, H., and KRAUS, N. C., 2003. Numerical modeling of beach topography change. Advances in Coastal Modeling, V.C. Lakhan (eds.), Elsevier Oceanography Series, 67, Amsterdam, The Netherlands, 337-365.


CMS-Flow