CMS-Flow:Bottom Friction: Difference between revisions

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In the CMS, the mean (shot-wave averaged) bottom shear stress is calculated based on the general quadratic formula
In the CMS, the mean (shot-wave averaged) bottom shear stress is calculated based on the general quadratic formula
  {{Equation| <math> \tau_m = \lambda_{wc} m_b \rho c_b |u_c| u_c </math> |2=1}}
  {{Equation| <math> \tau_m = \lambda_{wc} m_b \rho c_b |U| U </math> |2=1}}
where <math> \lambda_{wc} </math> is the nonlinear wave enhancement factor, <math>m_b</math> is a bed slope friction coefficient, <math> c_b </math> is the bottom friction coefficient,  and <math>u</math> is the depth-averaged current velocity.
where <math> \lambda_{wc} </math> is the nonlinear wave enhancement factor, <math>m_b</math> is a bed slope friction coefficient, <math> c_b </math> is the bottom friction coefficient,  and <math>u</math> is the depth-averaged current velocity.


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For the quadratic formula, the wave enhancement factor is simply  
For the quadratic formula, the wave enhancement factor is simply  
       {{Equation| <math> \lambda_{wc} = \frac{\sqrt{ u_c^2 + c_w u_w^2 }}{u_c^2} </math>  |2=7}}
       {{Equation| <math> \lambda_{wc} = \frac{\sqrt{ U^2 + c_w U_w^2 }}{U} </math>  |2=7}}
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). Therefore, the quadratic formula reduces to <math> \tau_m = m_b \rho c_b u_c \sqrt{ u_c^2 + c_w u_w^2 } </math>.  
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). Therefore, the quadratic formula reduces to <math> \tau_m = m_b \rho c_b u_c \sqrt{ u_c^2 + c_w u_w^2 } </math>.  
For all other models, the nonlinear wave enhancement factor <math> \lambda_{wc} </math> is parameterized using the the generalized form proposed by Soulsby (1995)
For all other models, the nonlinear wave enhancement factor <math> \lambda_{wc} </math> is parameterized using the the generalized form proposed by Soulsby (1995)

Revision as of 15:21, 1 February 2011

The bottom roughness is specified in CMS with either a Manning's n coefficient, roughness height (Nikradse bed roughness), or bed friction coefficient. It is important to note that the roughness value is held constant throughout the simulation and is not changed according to bed composition and bed forms. It is also independent of the bed roughness calculation used for various sediment transport formula, since different formulas use different methods for computing the bed shear stresses.

In the CMS, the mean (shot-wave averaged) bottom shear stress is calculated based on the general quadratic formula

  (1)

where is the nonlinear wave enhancement factor, is a bed slope friction coefficient, is the bottom friction coefficient, and is the depth-averaged current velocity.

The bed slope friction coefficient is equal to

  (2)

The bed friction coefficient is related to the Manning's coefficient by

  (3)

where is the gravitational constant, and is the water depth.

Similarly, the bed friction coefficient is related to the roughness height by

  (4)

In the case of currents only the he nonlinear wave enhancement factor equal and .

In the presence of waves, \lambda_{wc} is calculated based on one of five models:

  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)

For the quadratic formula, the wave enhancement factor is simply

  (7)

where is the wave bottom orbital velocity based on the significant wave height, and is an empirical coefficient approximately equal to 0.5 (default). Therefore, the quadratic formula reduces to . For all other models, the nonlinear wave enhancement factor is parameterized using the the generalized form proposed by Soulsby (1995)

  (7)

where , , and are coefficients that depend on the model selected and

  (8)

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