Grain transport mechanics in shallow overland flow

A physical model based on continuum multiphase flow is described to represent saltating transport of grains in shallow overland flows. The two-phase continuum flow of water and sediment considers coupled StVenant-type equations. The interactive cumulative effect of grains is incorporated by a dispersive stress term. The mean fluid thrust on the particle in the saltation layer of grains is expressed in terms of a slip velocity. The continuum model leads to the unexpected, but an interesting result is that particle velocity increases with the solid concentration. This increase predicts monotonic behaviour leading to overestimates of particle velocity at higher sediment concentration. To improve the predictions, grain dynamic equations, which incorporate bed collision, are analysed. The analysis leads to an improved model for predicting saltation height. Incorporation of the results in the continuum model yields a velocity-concentration relationship that is consistent with experimental observations for increasing concentration. Laboratory flume experiments explore the evaluation of various parameters from the measured particle velocities by photonic probes.