CMS-Flow:Bottom Friction: Difference between revisions
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In the situation without waves, the bottom shear stress is calculated based on the quadratic formula | In the situation without waves, the bottom shear stress is calculated based on the quadratic formula | ||
{{Equation| <math> \tau_m = \tau_c = \rho c_b |u_c| u_c </math> | | {{Equation| <math> \tau_m = \tau_c = \rho c_b |u_c| u_c </math> |1=1}} | ||
where <math> c_b </math> is the bottom friction coefficient, <math>u_c</math> is the depth-averaged current velocity. | where <math> c_b </math> is the bottom friction coefficient, <math>u_c</math> is the depth-averaged current velocity. | ||
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In this case the simplified expression for the combined wave and current mean shear stress is given by | In this case the simplified expression for the combined wave and current mean shear stress is given by | ||
<math> \tau_m = \rho c_b u_c \sqrt{ u_c^2 + c_w u_w^2 } </math> |2 | {{Equation| <math> \tau_m = \rho c_b u_c \sqrt{ u_c^2 + c_w u_w^2 } </math> |1=2}} | ||
where <math> u_w </math> is the wave bottom orbital velocity based on the significant wave height, and <math> c_w </math> is an empirical coefficient approximately equal to 0.5 (default). | where <math> u_w </math> is the wave bottom orbital velocity based on the significant wave height, and <math> c_w </math> is an empirical coefficient approximately equal to 0.5 (default). | ||
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For all of the other models, the mean shear stress is calculated as | For all of the other models, the mean shear stress is calculated as | ||
<math> \tau_m = \lambda_{wc} \tau_c </math> | | {{Equation| <math> \tau_m = \lambda_{wc} \tau_c </math> |1=3}} | ||
where <math> \lambda_{wc} </math> is the nonlinear wave enhancement factor which is parameterized in the generalized form (Soulsby, 1995) | where <math> \lambda_{wc} </math> is the nonlinear wave enhancement factor which is parameterized in the generalized form (Soulsby, 1995) | ||
<math> \lambda_{wc} = 1 + bX^p(1-X)^q </math> | | {{Equation| <math> \lambda_{wc} = 1 + bX^p(1-X)^q </math> |1=4}} | ||
where <math>b</math>, <math>p</math>, and <math>q</math> are coefficients that depend on the model selected and | where <math>b</math>, <math>p</math>, and <math>q</math> are coefficients that depend on the model selected and | ||
<math> X=\frac{\tau_w}{\tau_c + \tau_w} </math> | | {{Equation| <math> X=\frac{\tau_w}{\tau_c + \tau_w} </math> |1=5}} | ||
---- | ---- | ||
</big> | </big> | ||
[[CMS#Documentation_Portal | Documentation Portal]] | [[CMS#Documentation_Portal | Documentation Portal]] | ||
Revision as of 19:37, 25 May 2010
Bottom Friction
Flow without Waves
In the situation without waves, the bottom shear stress is calculated based on the quadratic formula
| 1 | ({{{2}}}) |
where is the bottom friction coefficient, is the depth-averaged current velocity.
Flow with Waves
There are five models available in CMS for calculating the combined wave and current mean shear stress:
- 1. Quadratic formula (named W09 in CMS)
- 2. Soulsby (1995) two coefficient data fit (named DATA2 in CMS)
- 3. Soulsby (1995) thirteen coefficient data fit (named DATA13 in CMS)
- 4. Fredsoe (1984) (named F84 in CMS)
- 5. Huynh-Thanh and Temperville (1991) (named HT91 in CMS)
In this case the simplified expression for the combined wave and current mean shear stress is given by
| 2 | ({{{2}}}) |
where is the wave bottom orbital velocity based on the significant wave height, and is an empirical coefficient approximately equal to 0.5 (default).
For all of the other models, the mean shear stress is calculated as
| 3 | ({{{2}}}) |
where is the nonlinear wave enhancement factor which is parameterized in the generalized form (Soulsby, 1995)
| 4 | ({{{2}}}) |
where , , and are coefficients that depend on the model selected and
| 5 | ({{{2}}}) |