Several empirical formulas have been proposed to predict the near-bed conditions for sediment transport in steady channel flows; however, few are extendable to oscillatory flows. This study presents a method for evaluation of the reference concentration and the entrainment rate near the undisturbed bed under oscillatory sheet-flow conditions. A new expression of the erosion depth in terms of the Shields parameter is adopted in order to describe the conservation of sediment mass more accurately. Both the exponential law and the power law are used to represent the instantaneous sediment concentration profile. The newly obtained formulas explicitly express the reference concentration and the entrainment rate in terms of the near-bed flow conditions and the sediment properties. The maximum value of the reference concentration obtained has a similar trend as given by the classical formulas. However, the variation of the reference concentration within a period of the oscillatory flow shows better agreem...

A two-dimensional, two-phase flow model is applied to the study of sediment motion over vortex ripples under oscillatory flow conditions. The Reynolds-averaged continuity equations and momentum equations for both the fluid and sediment phases, which include the drag force, the added mass force, the lift force for interphase coupling, and the standard k–ε turbulence model as well as the Henze–Tchen particle turbulence model for closure, are numerically solved with a finite-volume method. The model is effective over the whole depth from the undisturbed sandy bed to the low concentration region above the ripples. Neither a reference concentration nor a pickup function is required over the ripple bed as in a conventional advection–diffusion model. There is also no need to identify the bed load and the suspended load. The study focuses on the effects of erodible ripples on the intrawave flow and sediment motion over the ripples. The computational results show reasonable agreement with the available laboratory data. It is demonstrated that the formation–ejection process of vortices and the trapping–lifting process of sediment over vortex ripples can be well described by the two-phase flow model. The numerical model can also accurately predict the vertical distribution of the mean sediment concentration.