CMS-Flow:Subgrid Turbulence Model

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Subgrid Turbulence Model

In CMS-Flow eddy viscosity is calculated as the sum of a base value , the current-related eddy viscosity and the wave-related eddy viscosity

       

Base Value Eddy Viscosity

The base value for the eddy viscosity is approximately equal to the kinematic eddy viscosity can be changed using the advanced card

     EDDY_VISCOSITY_CONSTANT           1.0e-6    ![m^2/sec], kinematic viscosity, ~1.0e-6

There are three options for calculating the current-related eddy viscosity.

Wave-Related Eddy Viscosity Component

The wave component of the eddy viscosity is calculated as

     

where is an empirical coefficient with a default value of 0.5 but may vary between 0.25 and 1.0. is the significant wave height and is bottom orbital velocity based on the significant wave height. may be changed using the advanced card

     EDDY_VISCOSITY_WAVE               0.5       ![-], wave coefficient

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

     

Current-Related Eddy Viscosity Component

There are three options for the current-related eddy viscosity: FALCONER, PARABOLIC, and SUBGRID. The default turbulence model is the subgrid model, but may be changed with the advanced card

     TURBULENCE_MODEL                  SUBGRID   !FALCONER | PARABOLIC | SUBGRID

1. Falconer Equation

The Falconer (1980) equation is the method is the default method used in the previous version of CMS, known as M2D. 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.

2. Parabolic Model

The second option is the parabolic model given by

     

where is approximately equal to and may be changed using the advanced card

     EDDY_VISCOSITY_BOTTOM             0.0667     ![-], bottom shear coefficient

2. Subgrid Turbulence Model

The third option for calculating is the subgrid turbulence model given by

     

where and are empirical coefficients related the turbulence produced by the bed and horizontal velocity gradients, 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 subgrid turbulence model parameters may be changed in the advanced cards as

     EDDY_VISCOSITY_BOTTOM             0.0667     ![-], bottom shear coefficient
     EDDY_VISCOSITY_HORIZONTAL         0.4       ![-], horizontal shear 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.


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