Net sheet-flow sediment transport rate: Additivity of wave propagation and nonlinear waveshape effects

Net wave-induced sheet-flow sediment transport rate, Qnet, can be produced by two co-existing effects: nonlinear waveshape and wave propagation, which alter the intra-wave boundary layer flow and sediment concentration. A intriguing question is whether the two effects can be simply added (the additivity hypothesis). This paper addresses this question based on simulations of a one-phase numerical model for sheet-flow sediment transport and examinations of the governing equations for boundary layer flow and sediment concentration. The additivity for the mean velocity (or streaming) is first demonstrated under typical field conditions. The main reason is that the two driving forces, i.e., momentum transfer produced by wave propagation and intra-wave asymmetry of flow turbulence produced by nonlinear waveshape, do not affect each other. The net sediment flux is separated into wave-and current-related components. Since the mean concentration profile is determined by the first-order process, the 'current'-related flux produced by the two effects, following the mean velocity, can be superimposed. After examining the leading Fourier components, the wave-related flux is also found to follow the additivity hypothesis. The findings are confirmed by numerical experiments. The implication of this work is that a practical formula for Qnet can be designed with two separate components for nonlinear-waveshape and wave-propagation effects.