CMS-Flow:Eddy Viscosity
In CMS-Flow eddy viscosity is calculated as the sum of a base value math\nu_{0}/math, the current-related eddy viscosity math\nu_c/math and the wave-related eddy viscosity math\nu_w/math
| {{{1}}} | (1) |
The base value for the eddy viscosity is approximately equal to the kinematic eddy viscosity can be changed using the advanced cards (Click [here] for further details).
Current-Related Eddy Viscosity Component
There are four options for the current-related eddy viscosity: FALCONER, PARABOLIC, SUBGRID, and MIXING-LENGTH. The default turbulence model is the subgrid model, but may be changed with the advanced card TURBULENCE_MODEL.
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
| U | (4) |
where mathc_b/math is the bottom friction coefficient, mathU/math is the depth-averaged current velocity, and mathh/math is the total water depth.
Parabolic Model
The second option is the parabolic model given by
| {{{1}}} | (5) |
where mathc_0/math is approximately equal to math\kappa/6/math.
Subgrid Turbulence Model
The third option for calculating math\nu_c/math is the subgrid turbulence model given by
| \bar{S} | (6) |
where mathc_0/math and mathc_1/math are empirical coefficients related the turbulence produced by the bed and horizontal velocity gradients, and math\Delta/math is the average grid area. mathc_0/math is approximately equal to 0.0667 (default) but may vary from 0.01-0.2. mathc_{1}/math is equal to approximately the square of the Smagorinsky coefficient and may vary from 0.1 to 0.5 (default is 0.4). math|\bar{S}|/math is equal to
| math | (\bar{S}) |
= \sqrt{
2\biggl( \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 |2=7}}
and
| {{{1}}} | (8) |
The subgrid turbulence model parameters may be changed in the advanced cards EDDY_VISCOSITY_BOTTOM, and EDDY_VISCOSITY_HORIZONTAL.
Mixing Length Model
Wave-Related Eddy Viscosity
The wave component of the eddy viscosity is calculated as
| {{{1}}} | (2) |
where math\Lambda/math is an empirical coefficient with a default value of 0.5 but may vary between 0.25 and 1.0. math H_s /math is the significant wave height and mathu_w/math is bottom orbital velocity based on the significant wave height. math\Lambda/math may be changed using the advanced card EDDY_VISCOSITY_WAVE.
Outside of the surf zone the bottom orbital velocity is calculated as
| {{{1}}} | (2) |
where mathH_s/math is the significant wave height, mathT_p/math is the peak wave period, mathk=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
| {{{1}}} | (3) |
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.