Near-Bed Sediment Condition in Oscillatory Sheet Flows

Abstract

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 agreement with the measured data than the classical formulas. In addition, the newly obtained formulas are found to have an evident advantage over the classical ones because they can reasonably interpret the sediment concentration as the flow reverses. The new formulas on the total vertical flux of sediment are also shown to reasonably agree with the measured data. It is demonstrated that the entrainment functions obtained under steady flow conditions, particularly those over a starved bed, are not directly applicable to oscillatory sheet-flow occasions.