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On the basis of advanced concentration and velocity profiles above a mobile seabed, an instantaneous analytical model is derived for sediment transport in asymmetric oscillatory flow. The applied concentration profile is obtained from the classical exponential law based on mass conservation, and asymmetric velocity profile is developed following the turbulent boundary layer theory and the asymmetric wave theory. The proposed model includes two parts: the basic part that consists of erosion depth and free stream velocity, and can be simplified to the total Shields parameter power 3/2 in accordance with the classical empirical models, and the extra vital part that consists of phase-lead, boundary layer thickness and erosion depth. The effects of suspended sediment, phase-lag and asymmetric boundary layer development are considered particularly in the model. The observed instantaneous transport rate proportional to different velocity exponents due to phase-lag is unified and summarised by the proposed model. Both instantaneous and half period empirical formulas are compared with the developed model, using extensive data on a wide range of flow and sediment conditions. The synchronous variation in instantaneous transport rate with free stream velocity and its decrement caused by increased sediment size are predicted correctly. Net transport rates, especially offshore transport rates with large phase-lag under velocity skewed flows, which existing instantaneous type formulas failed to predict, are predicted correctly in both direction and magnitude by the proposed model. Net sediment transport rates are affected not only by suspended sediment and phase-lag, but also by the boundary layer difference between onshore and offshore.

Instantaneous sediment transport model for asymmetric oscillatory sheet flow