CMS-Flow:Bottom Friction

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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

  τm=λwcmbρcb|uc|uc (1)

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

The bed slope friction coefficient mb is equal to

  mb=1+(zbx)2+(zby)2 (2)

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

  cb=gn2h1/3 (3)

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

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

  cb=(κln(30ks/h)+1)2 (4)
In the case of currents only the he nonlinear wave enhancement factor equal and τm=τc=mbρcb|uc|uc. In the presence of waves, \lambda_{wc} is parametrized using either a simplified quadratic formula 
     
  λwc=uc2+cwuw2uc2 (7)

The second option is general parametrization of Soulsby (1995)

  λwc=1+bXp(1X)q (7)

where b, p, and q are coefficients that depend on the model selected and

  X=τwτc+τw (8)


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 quadratic formula the combined wave and current mean shear stress is given by

  τm=mbρcbucuc2+cwuw2 (5)

where uw is the wave bottom orbital velocity based on the significant wave height, and cw is an empirical coefficient approximately equal to 0.5 (default).

For all of the other models, the mean shear stress is calculated as

  τm=λwcτc (6)

where λwc is the nonlinear wave enhancement factor which is parameterized in the generalized form (Soulsby, 1995)

  λwc=1+bXp(1X)q (7)

where b, p, and q are coefficients that depend on the model selected and

  X=τwτc+τw (8)

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