CMS-Flow:Subgrid Turbulence Model: Difference between revisions
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<math> \nu_t = \nu_0 + \nu_c + \nu_w </math> | <math> \nu_t = \nu_0 + \nu_c + \nu_w </math> | ||
The | There are two options to calculate <math>\nu_c</math>. The first is the Falconer (1980) equation given by | ||
<math> \ | <math> \nu_c = 0.575C_f|U|h </math> | ||
where | where <math>C_f</math> is the bottom friction coefficient, <math>U</math> is the depth-averaged current velocity, and <math>h</math> is the total water depth. | ||
The | The second option is a subgrid turbulence model given by | ||
<math> \nu_{c} = | <math> \nu_{c} = c_b u_{*} h + c_h \Delta A |S| </math> | ||
where | where <math>c_b</math> is an empirical coefficient approximately equal to 1/6 (default), <math>c_h</math> is an empirical coefficient between 0.1-0.5 (default is 0.4), <math>\Delta A = \Delta x \Delta y</math> is the local grid cell area, and <math>|S|</math> is equal to | ||
<math> |S| = \sqrt{ \biggl( \frac{ \partial U}{\partial x} \biggr) ^2 + \biggl( \frac{ \partial V}{\partial y} \biggr) ^2 + \frac{1}{2} \biggl( \frac{ \partial U}{\partial y} + \frac{ \partial V}{\partial x} \biggr) ^2 } </math> | <math> |S| = \sqrt{ \biggl( \frac{ \partial U}{\partial x} \biggr) ^2 + \biggl( \frac{ \partial V}{\partial y} \biggr) ^2 + \frac{1}{2} \biggl( \frac{ \partial U}{\partial y} + \frac{ \partial V}{\partial x} \biggr) ^2 } </math> | ||
The wave component of the eddy viscosity is calculated as | |||
<math> \nu_w = \Lambda u_w H_s </math> | |||
where <math>\Lambda</math> is an empirical coefficient approximately equal to 0.5, <math> H_s </math> is the significant wave height and <math>u_w</math> is bottom orbital velocity based on the significant wave height. Outside of the surf zone the bottom orbital velocity is calculated as | |||
<math> u_w = \frac{ \pi H_s}{T_p \sinh(kh) } </math> | |||
where <math>H_s</math> is the significant wave height, <math>T_p</math> is the peak wave period, <math>k=2\pi/L</math> is the wave number. Inside the surf zone, the turbulence due to wave breaking is considered by increasing the bottom orbital velocity as | |||
<math> u_w = \frac{ H_s}{2h}\sqrt{gh} </math> | |||
The default turbulence model is the subgrid model, but may be changed with the advanced card | |||
TURBULENCE_MODEL SUBGRID !FALCONER | PARABOLIC | SUBGRID | SUBGRID-WU | |||
The turbulence model parameters may be changed in the advanced cards as | |||
EDDY_VISCOSITY_CONSTANT 1.0e-6 ![m^2/sec], kinematic viscosity, ~1.0e-6 | |||
EDDY_VISCOSITY_BOTTOM 0.015 ![-], bottom shear coefficient, ~0.1667 | |||
EDDY_VISCOSITY_HORIZONTAL 0.2 ![-], smagorinsky coefficient, ~0.1-0.5 | |||
EDDY_VISCOSITY_WAVE 0.5 ![-], wave coefficient, ~0.25-0.5 | |||
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Revision as of 18:43, 5 May 2010
Subgrid Turbulence Model
In CMS-Flow eddy viscosity is calculated as the sum of the kinematic viscosity , the current-related eddy viscosity and the wave-related eddy viscosity
There are two options to calculate . The first is the Falconer (1980) equation given by
where is the bottom friction coefficient, is the depth-averaged current velocity, and is the total water depth.
The second option is a subgrid turbulence model given by
where is an empirical coefficient approximately equal to 1/6 (default), is an empirical coefficient between 0.1-0.5 (default is 0.4), is the local grid cell area, and is equal to
The wave component of the eddy viscosity is calculated as
where is an empirical coefficient approximately equal to 0.5, is the significant wave height and is bottom orbital velocity based on the significant wave height. Outside of the surf zone the bottom orbital velocity is calculated as
where is the significant wave height, is the peak wave period, is the wave number. Inside the surf zone, the turbulence due to wave breaking is considered by increasing the bottom orbital velocity as
The default turbulence model is the subgrid model, but may be changed with the advanced card
TURBULENCE_MODEL SUBGRID !FALCONER | PARABOLIC | SUBGRID | SUBGRID-WU
The turbulence model parameters may be changed in the advanced cards as
EDDY_VISCOSITY_CONSTANT 1.0e-6 ![m^2/sec], kinematic viscosity, ~1.0e-6
EDDY_VISCOSITY_BOTTOM 0.015 ![-], bottom shear coefficient, ~0.1667
EDDY_VISCOSITY_HORIZONTAL 0.2 ![-], smagorinsky coefficient, ~0.1-0.5
EDDY_VISCOSITY_WAVE 0.5 ![-], wave coefficient, ~0.25-0.5
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.