General velocity formula of boundary layer above mobile sediment bed induced by asymmetric waves

Sediment movement in the wave boundary layer above a mobile sediment bed is complex. A velocity formula for the boundary layer is proposed for sheet flow induced by asymmetric waves above a mobile sediment bed. The formula consists of a free stream velocity and a defect function which contains a phase-lead, boundary layer thickness and mobile sediment bed. Phase-lag of sediment movement is considered in the formula for the mobile sediment bed. The formula needs six dependent variables about asymmetric wave and sediment characteristics. Asymmetry effects on parameters (orbital amplitude, roughness height, bed shear stress, and boundary layer thickness) are properly considered such that the formula can yield velocity differences among onshore, offshore, acceleration, and deceleration stages. The formula estimates the net boundary layer velocity resulting from the mobile sediment bed and asymmetric boundary layer thickness. In addition, a non-constant phase-lead also contributes to the net boundary layer velocity in asymmetric oscillatory sheet flow. Results of the formula are as good as that of a two-phase numerical model. Sheet flow transport induced by asymmetric waves, and the offshore net sediment transport rate with a large phase-lag under velocity-skewed waves, can be adequately estimated by the formula with a power sediment concentration function. •Velocity formula is proposed for wave boundary layer above mobile sediment bed•Phase-lag, phase-lead, boundary layer thickness and wave asymmetry are performed•The formula behaviors well enough as that of a two-phase model•Net sediment transport rate is reasonably predicted from onshore to offshore