CMS-Flow:Subgrid Turbulence Model: Difference between revisions
| Line 4: | Line 4: | ||
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}^2 \Delta x \Delta y |S| )^2 } </math> | <math> \nu_{tc} = \nu_{t0} + \sqrt{ (c_0 u_* h)^2 + (c_{sm}^2 \Delta x \Delta y |S| )^2 } + k(D/\rho)^{1/3}</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>c_{sm}</math> is an empirical coefficient (Smagorinsky coefficient). | 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>c_{sm}</math> is an empirical coefficient (Smagorinsky coefficient). | ||
Revision as of 21:38, 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 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.