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

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

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

where $lambda_{wc}$ is the nonlinear wave enhancement factor which varies depending on the model selected. There are five models available in CMS: 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

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

For all of the other models, the general parameterization of Soulsby (1995) is used to calculate $\lambda _{wc}$.

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

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

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

The default model is the simplified quadratic formula, but the user may change the model by using the advanced card

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