Explicit approximation for velocity and sediment flux above mobile sediment bed beneath current and asymmetric wave

Abstract

An explicit approximation is proposed for velocity distribution and sediment flux above mobile sediment bed beneath current and asymmetric wave. The predicted velocity is decomposed into an oscillatory part and a current part such that the interaction between current and asymmetric wave can be performed directly. The oscillatory part consists of a free stream velocity and a defect function which includes phase lead, mobile sediment bed level and wave boundary layer thickness. The oscillatory part is influenced by the current due to the changes of both mobile sediment bed level and wave boundary layer thickness. The current part is influenced by a wave eddy viscosity in the wave boundary layer and by an apparent wave roughness of the combined wave-current flow outside the wave boundary layer. Eight free variables are required for the approximation, and iterative bottom shear stress and roughness height are applied for the wave boundary layer thickness and mobile sediment bed level. The mobile sediment bed level takes account of the effects of phase lag (phase shift and residual), acceleration and flow asymmetry. Therefore, the mobile bed effect, instantaneous velocity, net velocity and sediment flux in the wave boundary layer can be reasonably presented by the explicit approximation beneath current and asymmetric wave.