Incipient motion of sediment in wave and combined wave-current boundary layers

Based on the theory of wave boundary layers and the Shields curve, the criterion curve is developed for the incipient motion of sediment in a wave boundary layer in this study. Two factors (X and Y) are proposed to characterize the turbulent structure of wave-current boundary layers, and an empirical relationship between Y and X is established. Furthermore, a criterion curve is derived for the incipient motion of sediment in combined wave-current boundary layers. This is done through the consideration of individual criterion curves for waves only and currents only. Results show that the criterion curve for waves is consistent with the Shields curve for the laminar flow regime and for the rough turbulent flow regime, while for the laminar-rough turbulent flow transition regime, it follows a broken line distribution, which is the extension of the two flow regimes. The proposed two factors X and Y could reasonably describe the relative relation of waves and currents and the non-linear effect of wave-current interaction. The criterion curve for combined waves and currents transits between individual criterion curves for waves only and currents only, depending on the values of X and corresponding Y. The proposed criterion curve for combined waves and currents agrees well with the measured data and could be used for different hydrodynamic conditions (i.e., waves, currents, or their combined actions) and different particle sizes (i.e., from coarse to fine).