The problem of viscous fluid flow along a flat solid surface with a stationary granular layer in the form of an infinite rectangular barrier is considered. The granular layer consists of an infinite number of identical spherical granules statistically uniformly distributed in the layer. The problem is solved based on the previously developed self-consistent field method, which allows studying the effects of hydrodynamic interaction of a large number of spherical particles in viscous fluid flows, including in the presence of external boundaries, and obtaining averaged dynamic characteristics of such flows. The solution to the problem, describing the averaged field of fluid velocity both outside and inside the granular layer, is obtained in the final analytical form in the first approximation by the volume fraction of granules in the layer. As a result, a characteristic feature of the fluid flow in the form of a large-scale stationary vortex is obtained, inside which the entire layer is located.
O. B Gus’kov (Wed,) studied this question.