CMS-Flow:Subgrid Turbulence Model: Difference between revisions
No edit summary |
|||
| Line 14: | Line 14: | ||
There are three options for calculating the current-related eddy viscosity. | There are three options for calculating the current-related eddy viscosity. | ||
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> | |||
'''Current-Related Eddy Viscosity''' | '''Current-Related Eddy Viscosity''' | ||
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 Falconer (1980) equation is the method is the default method used in the previous version of CMS, known as M2D. | ||
| Line 26: | Line 41: | ||
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. | 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. | ||
''2. Parabolic Model'' | |||
The second option is the parabolic model given by | The second option is the parabolic model given by | ||
| Line 36: | Line 51: | ||
EDDY_VISCOSITY_BOTTOM 0.015 ![-], bottom shear coefficient, ~0.1667 | EDDY_VISCOSITY_BOTTOM 0.015 ![-], bottom shear coefficient, ~0.1667 | ||
''2. Subgrid Turbulence Model'' | |||
The third option for calculating <math>\nu_c</math> is the subgrid turbulence model given by | The third option for calculating <math>\nu_c</math> is the subgrid turbulence model given by | ||
| Line 46: | Line 61: | ||
<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> | ||
The turbulence model parameters may be changed in the advanced cards as | The turbulence model parameters may be changed in the advanced cards as | ||
Revision as of 19:05, 5 May 2010
Subgrid Turbulence Model
In CMS-Flow eddy viscosity is calculated as the sum of a base value Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_{0}} , the current-related eddy viscosity Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_c} and the wave-related eddy viscosity Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_w}
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_t = \nu_0 + \nu_c + \nu_w }
Base 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.
The wave component of the eddy viscosity is calculated as
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_w = \Lambda u_w H_s }
where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Lambda} is an empirical coefficient approximately equal to 0.5, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle H_s } is the significant wave height and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle u_w} is bottom orbital velocity based on the significant wave height. Outside of the surf zone the bottom orbital velocity is calculated as
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle u_w = \frac{ \pi H_s}{T_p \sinh(kh) } }
where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle H_s} is the significant wave height, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle T_p} is the peak wave period, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle k=2\pi/L} is the wave number. Inside the surf zone, the turbulence due to wave breaking is considered by increasing the bottom orbital velocity as
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle u_w = \frac{ H_s}{2h}\sqrt{gh} }
Current-Related Eddy Viscosity
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
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_c = 0.575c_b|U|h }
where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_b} is the bottom friction coefficient, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle U} is the depth-averaged current velocity, and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle h} is the total water depth.
2. Parabolic Model
The second option is the parabolic model given by
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_c = c_0u_{*}h }
where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_0} is approximately equal to Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \kappa/6} and may be changed using the advanced card
EDDY_VISCOSITY_BOTTOM 0.015 ![-], bottom shear coefficient, ~0.1667
2. Subgrid Turbulence Model
The third option for calculating Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_c} is the subgrid turbulence model given by
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \nu_{c} = \sqrt{ (c_0 u_{*})^2 h + (c_1 \Delta |S|)^2} }
where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_0} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_1} are empirical coefficients, and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Delta} is the average grid area. Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_0} is approximately equal to 0.0667 (default) but may vary from 0.01-0.2. Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle c_1} may vary from 0.1 to 0.5 and is set to a default value of 0.4. Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle |S|} is equal to
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle |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 } }
The turbulence model parameters may be changed in the advanced cards as
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.