Instantaneous sediment transport formula for sheet flow beneath asymmetric wave and current

An instantaneous formula is obtained for the sheet flow transport beneath the wave and the current by a product integration of the concentration and velocity profiles over the mobile seabed. The formula involves: (1) The product of the erosion depth and the free stream velocity, which can be reduced to the Shields parameter of power 3/2 in accordance with the classical formulae. (2) The ratio of the wave boundary layer thickness to the erosion depth. The formula incorporates the effects of the acceleration and the phase lag on the erosion depth, the asymmetric wave boundary layer and the wave-current interaction. The validation of the formula is made by the data obtained from the oscillatory tunnels covering a wide range of wave-current and sediment conditions. The instantaneous sediment transport rate is compared with the power function of the velocity with different exponents. The formula consists of a wave force part and a current force part and their relative importance depends on the wave shapes. The present formula gives very good results for the net sediment transport as compared to several existing steady and unsteady formulae. The net sediment transport rates are affected by not only the acceleration, the phase lag and the wave-current interaction, but also the asymmetric boundary layer development.