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


       <math> \tau_m = \tau_c = \rho c_b |U| U </math>
       <math> \tau_m = \tau_c = \rho c_b |u_c| u_c </math>


where <math> c_b </math> is the bottom friction coefficient, <math> U</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.


'''Flow with Waves'''
'''Flow with Waves'''
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       <math> \tau_m = \lambda_{wc} \tau_c  </math>
       <math> \tau_m = \lambda_{wc} \tau_c  </math>


where <math> lambda_{wc} </math> is the nonlinear wave enhancement factor which varies depending on the model selected. There are five models available in CMS.
where <math> lambda_{wc} </math> is the nonlinear wave enhancement factor which varies depending on the model selected. There are five models available in CMS:
1. Simplified quadratic formula
2. Soulsby (1995) Data2 Method
3. Soulsby (1995) Data13 Method
4. Fredsoe (1984) Model
5. Huynh-Thanh and Temperville (1991) Model


''1. Simplified Quadradric Formula''
In this case the simplified expression for the combined wave and current mean shear stress is given by


in this case the enhancement factor is equal to
      <math> \tau_m = \rho c_b \sqrt{ u_c^2 + c_w u_w^2 } u_c  </math>


       <math>\lambda_{wc} = \frac{\sqrt{ u_c^2 + c_w u_w^2 } } {u_c} </math>
For all of the other models, the general parameterization of Soulsby (1995) is used to calculate <math> \lambda_{wc}
</math>.
 
       <math> \lambda_{wc} = 1 + bX^p(1-X)^q, with X=\frac{\tau_w}{tau_c + tau_w} </math>

Revision as of 19:35, 5 May 2010

Bottom Friction

Flow without Waves

In the situation without waves, the bottom shear stress is calculated based on the quadratic formula

     

where is the bottom friction coefficient, is the depth-averaged current velocity.

Flow with Waves

In the case with waves, the bottom friction is calculated with the generalized formula

     

where is the nonlinear wave enhancement factor which varies depending on the model selected. There are five models available in CMS: 1. Simplified quadratic formula 2. Soulsby (1995) Data2 Method 3. Soulsby (1995) Data13 Method 4. Fredsoe (1984) Model 5. Huynh-Thanh and Temperville (1991) Model

In this case the simplified expression for the combined wave and current mean shear stress is given by

     

For all of the other models, the general parameterization of Soulsby (1995) is used to calculate .