Wave friction factor as related to the Shields parameter for steady currents

Abstract

The wave friction factor f w is an important dimensionless parameter used to estimate wave-induced bed shear stress which, together with current-induced bed shear stress, controls sediment transport in the marine and lacustrine environment. However, f w is either overestimated or underestimated by existing equations. The matter is complicated by the fact that different equations must be used for hydrodynamically smooth or rough flows, but the limit between these two boundary conditions is still poorly defined. Some equations also require estimated values for the Nikuradse roughness length and the wave boundary layer thickness, neither of which can be derived accurately. It is, therefore, not surprising that f w values as calculated by existing equations differ by as much as a factor of 3. In the present paper, f w is related to the Shields parameter β for unidirectional currents, which not only facilitates the direct comparison and summation of bed shear stresses, but also yields a more accurate equation valid for grains of different density in any fluid irrespective of the boundary condition.