Abstract:
The quantification of vertical sediment exchange intensity through vertical sediment flux is crucial in coastal engineering. Vertical sediment is necessary as near-bed sediment boundary condition to describe suspended load transport. Therefore, the prediction of suspended load transport critically depends on the precision of vertical sediment flux. The classical formula is unsuitable for graded sediment and the oscillatory sheet flow because it does not consider the gradation effect of graded sediment and dynamics characteristics caused by waves. This paper presents an instantaneous vertical sediment flux formula for graded sediment under wave-driven sheet flow. The vertical sediment flux formula is derived from the mass conservation-based concentration profile formula of graded sediment using size faction approach, including the vertical sediment net flux, downward settling flux, and upward suspension flux. The features of wave-driven sheet flow, such as sediment phase lag, acceleration effect and asymmetric boundary layer development are taken into account. The inhibition effect of high concentration for settling velocity by (1-C)n is incorporated into the downward settling flux formula. The total vertical sediment net flux is the conduct of the sediment concentration, relative position and the variation rate of sediment amount and the upward suspension flux is related to the free stream velocity and acceleration. The graded sediment characteristics are considered by a hiding-exposure factor and the settling velocity of different fractions. Firstly, the vertical sediment flux date from Aberdeen Oscillatory Flow Tunnel is used to validate the prediction of formula. Results show that the formula can well reproduce the instantaneous vertical sediment flux under the velocity-skewed and sine wave and the accuracy of prediction by the proposed formula is better than the classical formula. There are non-zero upward suspension fluxes and downward settling fluxes near flow reversal due to the sediment phase lag. In addition, the total vertical sediment net flux is positive (negative) during the flow acceleration (deceleration) and will reach zero near the flow reversal (zero velocity) or flow peak (zero acceleration). The hiding-exposure effect indicates the interaction among different fractions, which reduces the fine fractional and increases the coarse fractional vertical sediment flux. The difference between the coarse and fine fraction become larger than exclude hiding-exposure effect. It is different from the fractional reference concentration and shows the anti-equal mobility state. The settling velocity hindered by high sediment concentration at reference height. The downward settling flux for fine fraction shows anti-phase phenomenon at the reference height due to larger settling velocity hinder factor (n=4.58), which is also opposite to the reference concentration and the others fractional downward settling flux. The proposed instantaneous vertical sediment flux formula is suitable for use as near-bed boundary condition in numerical model under wave-driven sheet flow and further enhances the understanding about sheet flow graded sediment transport, which holds significant potential for application prospect in coastal engineering.