Bottom Friction

Bottom Friction

The mean (short-wave averaged) bed shear stress, $\tau _{bi}$, is calculated as

$\tau _{bi}=\lambda _{wc}\tau _{ci}$ (2-8)

where

$\lambda _{wc}=$ nonlinear bottom friction enhancement factor $\left(\lambda _{wc}\geq 1\right)$ [-]

$\tau _{c}=$ current-related bed shear stress vector [Pa]

The current bed shear stress is given by

$\tau _{ci}=\rho c_{b}UU_{i}$ (2-9)

where

$\rho =$ water density (~1025 kg/m³)

c_b = bed friction coefficient [-]

$U=$ current magnitude = ${\sqrt {U_{i}^{2}+U_{j}^{2}}}$ [m/s]

The bottom roughness is specified with either a Manning's roughness coefficient $\eta$ , Nikuradse roughness height k_s , or bed friction coefficient c_b . It is important to note that the roughness value is held constant throughout the simulation and is not changed according to bed composition and bedforms. This is a common engineering approach which can be justified by the lack of data to initialize the bed composition, and the large error in estimating the bed composition evolution and bedforms. In addition using a constant bottom roughness simplifies the model calibration. In future versions of CMS, it option to automatically estimate the bed roughness from the bed composition and bedforms will be added.

The bed friction coefficient c_b is related to the Manning’s roughness coefficient $\eta$ by (Graf and Altinakar 1998)

<math>c_b = \left(\frac{\kappa}{ln\left(\frac{{z}_0}{h} + 1\right)} \right)