CMS-Flow:Subgrid Turbulence Model: Difference between revisions
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== Subgrid Turbulence Model == | == Subgrid Turbulence Model == | ||
In CMS-Flow eddy viscosity is calculated as the sum of the kinematic viscosity <math>\nu_{0}</math>, the current-related eddy viscosity | In CMS-Flow eddy viscosity is calculated as the sum of the kinematic viscosity <math>\nu_{0}</math>, the current-related eddy viscosity <math>\nu_c</math> and the wave-related eddy viscosity <math>\nu_w</math> | ||
<math> \nu_t = \nu_0 + \nu_c + \nu_w </math> | <math> \nu_t = \nu_0 + \nu_c + \nu_w </math> | ||
There are | There are three options for calculating the current-related eddy viscosity. The first is the Falconer (1980) equation given by | ||
<math> \nu_c = 0. | <math> \nu_c = 0.575c_b|U|h </math> | ||
where <math> | where <math>c_b</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 second option is | The second option is the parabolic model given by | ||
<math> \nu_c = c_0u_{*}h </math> | |||
where <math>c_0</math> is approximately equal to <math>\kappa/6</math> | |||
The third option for calculating <math>\nu_c</math> is the subgrid turbulence model given by | |||
<math> \nu_{c} = \sqrt{ (c_0 u_{*})^2 h + (c_1 \Delta |S|)^2} </math> | <math> \nu_{c} = \sqrt{ (c_0 u_{*})^2 h + (c_1 \Delta |S|)^2} </math> | ||
where <math>c_0</math> and <math>c_1</math> are empirical coefficients and <math>\Delta</math> is the average grid area. <math>c_0</math> is approximately equal to 0.0667 (default) but may vary from 0.01-0.2. <math>c_1</math> may vary from 0.1 to 0.5 and is set to a default value of 0.4. <math>|S|</math> is equal to | where <math>c_0</math> and <math>c_1</math> are empirical coefficients, and <math>\Delta</math> is the average grid area. <math>c_0</math> is approximately equal to 0.0667 (default) but may vary from 0.01-0.2. <math>c_1</math> may vary from 0.1 to 0.5 and is set to a default value of 0.4. <math>|S|</math> is equal to | ||
<math> |S| = \sqrt{ \biggl( 2\frac{ \partial U}{\partial x} \biggr) ^2 + 2\biggl( \frac{ \partial V}{\partial y} \biggr) ^2 + \biggl( \frac{ \partial U}{\partial y} + \frac{ \partial V}{\partial x} \biggr) ^2 } </math> | <math> |S| = \sqrt{ \biggl( 2\frac{ \partial U}{\partial x} \biggr) ^2 + 2\biggl( \frac{ \partial V}{\partial y} \biggr) ^2 + \biggl( \frac{ \partial U}{\partial y} + \frac{ \partial V}{\partial x} \biggr) ^2 } </math> | ||
Revision as of 18:54, 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 three options for calculating the current-related eddy viscosity. 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 the parabolic model given by
where is approximately equal to
The third option for calculating is the subgrid turbulence model given by
where and are empirical coefficients, and is the average grid area. is approximately equal to 0.0667 (default) but may vary from 0.01-0.2. may vary from 0.1 to 0.5 and is set to a default value of 0.4. 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.