CMS-Flow:Bottom Friction

Bottom Friction

Flow without Waves

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

     $\tau _{m}=\tau _{c}=\rho c_{b}|u_{c}|u_{c}$

where $c_{b}$ is the bottom friction coefficient, $u_{c}$ 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. Simplified quadratic formula (named W09 in CMS)

2. Soulsby (1995) Data2 (named DATA2 in CMS)

3. Soulsby (1995) Data13 (named DATA13 in CMS)

4. Fredsoe (1984) (names 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

     $\tau _{m}=\rho c_{b}u_{c}{\sqrt {u_{c}^{2}+c_{w}u_{w}^{2}}}$

where $u_{w}$ is the wave bottom orbital velocity based on the significant wave height, and $c_{w}$ is an empirical coefficient approximately equal to 0.5 (default).

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

     $\tau _{m}=\lambda _{wc}\tau _{c}$

where $\lambda _{wc}$ is the nonlinear wave enhancement factor which is parameterized in the generalized form (Soulsby, 1995)

     $\lambda _{wc}=1+bX^{p}(1-X)^{q}$

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

     $X={\frac {\tau _{w}}{\tau _{c}+\tau _{w}}}$

The default method for calculating the mean shear stress is the simplified quadratic formula, but the user may change this by using the advanced card

    WAVE-CURRENT_MEAN_STRESS       W09  !W09 | DATA2 | DATA13 | F84 | HT91