CMS-Flow:Subgrid Turbulence Model: Difference between revisions

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       <math> \nu_{c} = \sqrt{ (c_0 u_* h)^2 + (c_{sm}^2 \Delta x \Delta y |S| )^2 } </math>
       <math> \nu_{c} = \sqrt{ (c_0 u_* h)^2 + (c_{sm}^2 \Delta x \Delta y |S| )^2 } </math>


where <math>c_0</math> is an empirical coefficient approximately equal to 1/6, <math>c_{sm}</math> is an empirical coefficient between 0.25-0.5, <math>\Delta x</math> and math>\Delta y</math> are the grid dimensions in the x and y directions and <math>|S|</math>     Normal  0        false  false  false                            MicrosoftInternetExplorer4          is equal to
where <math>c_0</math> is an empirical coefficient approximately equal to 1/6, <math>c_{sm}</math> is an empirical coefficient between 0.25-0.5, <math>\Delta x</math> and <math>\Delta y</math> are the grid dimensions in the x and y directions and <math>|S|</math> is equal to  


       <math> |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>
       <math> |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>

Revision as of 23:36, 2 November 2009

Eddy Viscosity

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, is an empirical coefficient between 0.25-0.5, and are the grid dimensions in the x and y directions and is equal to

     

The wave component of the eddy viscosity is calculated as

     

where is an empirical coefficient, is the water density, and is the total wave dissipation.



CMS-Flow