Grain-scale Modeling and Splash Parametrization for Aeolian Sand Transport

摘要

The collision of a spherical grain with a granular bed is commonlyparametrized by the splash function, which provides the velocity of therebounding grain and the velocity distribution and number of ejected grains.Starting from elementary geometric considerations and physical principles, likemomentum conservation and energy dissipation in inelastic pair collisions, wederive a rebound parametrization for the collision of a spherical grain with agranular bed. Combined with a recently proposed energy-splitting model [Ho${\it et\ al.}$, Phys. Rev. E 85, 052301 (2012)] that predicts how the impactenergy is distributed among the bed grains, this yields a coarse-grained butcomplete characterization of the splash as a function of the impact velocityand the impactor-bed grain-size ratio. The predicted mean values of the reboundangle, total and vertical restitution, ejection speed, and number of ejectedgrains are in excellent agreement with experimental literature data and withour own discrete-element computer simulations. We extract a set of analyticalasymptotic relations for shallow impact geometries, which can readily be usedin coarse-grained analytical modeling or computer simulations of geophysicalparticle-laden flows.