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

${\tau }_m={\tau }_c=\rho c_b|u_c|u_c$

(1)

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. 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 expression for the combined wave and current mean shear stress is given by

${\tau }_m=\rho c_b{u}_c\sqrt{u_c^2+c_w{u}_w^2}$

(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

${\tau }_m={\lambda }_{wc}{\tau }_c$

(3)

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

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

(4)

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

$X=\frac{{\tau }_w}{{\tau }_c+{\tau }_w}$

(5)

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