Two-phase continuum theory for windblown sand

We outline the derivation of a two-phase continuum theory for grains, jumping above a bed of sand, while accelerated by a turbulent shearing flow, colliding with the bed, rebounding, and, perhaps, generating other grains. Relations between the shear and normal stresses and vertical derivatives of components of the average particle velocity are determined by averaging the dynamical equations for the particle trajectories. This provides the closure for the system of differential equations that govern the behavior of the wind and particles above the bed. Boundary conditions are obtained by averaging the results of experiments on rebound and ejection of particles from a particle bed. We solve the resulting system of equations subject to the derived boundary conditions for steady, uniform flows over both particle and rigid beds, and obtain unsteady, uniform solutions and steady, nonuniform solutions that provide information regarding saturation times and lengths, respectively.