Modeling spatial nonequilibrium saltation under turbulent water flow at low Shields stress

In this study, we extend the mechanistic equilibrium saltation model of Ashida and Michiue (1972) for nearly horizontal sand beds to the case of spatial nonequilibrium sand transport, which allows us to calculate sand transport rates over varying mildly-sloped topographies. Our model incorporates a generalized description of the reduction of the Shields stress within the saltation layer due to momentum transfer from the fluid to the grains. We show that the stronger the reduction of the Shields stress the weaker is the influence of the saltation step length on the spatial transition from a nonequilibrium to an equilibrium state. We validate our model with different experimental data sets and show that it can reasonably explain the recently measured dependency of the minimal length of barchan dunes on the shear velocity (Franklin and Charru, 2011).