A simple model of unsteady sheet-flow sediment transport

Abstract

A simple, quasi-steady, one-dimensional, vertical (1DV) model of unsteady sheet flow is presented. The central aim is to provide greater realism in the near-bed, high-concentration layer, than is possible using models based on the classical reference-concentration approach. This is achieved by tracking erosion and deposition at the bottom of the mobile sediment layer in relation to the amount of sediment present in the sheet-flow and suspension layers. The model relies on empirical assumptions for the time-varying sheet-flow layer thickness ( δ) and time-varying equivalent bed roughness ( k s). The formulations adopted yield realistic instantaneous vertical profiles of velocity and sediment concentration from the stationary bed, through the high-concentration sheet-flow layer up into the outer suspension layer. The suspension layer itself is modelled using a standard k– ε turbulence-closure scheme, together with the sediment continuity equation. Matching conditions are applied at the interface between the sheet-flow and suspension layers. Preliminary results presented here include initial validation comparisons with the data set of Horikawa et al. [Horikawa, K., Watanabe, A., Katori, S., 1982. Sediment transport under sheet flow conditions. Proceedings of the 18th International Conference on Coastal Engineering, Cape Town. ASCE, Reston VA, USA, 1335–1352.]. Further comparisons with the experiments of Dohmen-Janssen et al. [J. Geophys. Res. 106 (2001) 27103] cover a wide range of wave–current conditions and sand grain sizes. The results are satisfactory with respect to the measured velocity and concentration profiles, apart from cases involving fine sand for which the effects of flow unsteadiness are not accounted for in the formulation. In addition, the new model provides satisfactory predictions of sand transport rates.