Ideal-Fluid Flow through a Fixed Near-Wall Granular Layer in the Form of Semi-Infinite Step

We consider the problem on the flow of an ideal fluid along a flat surface with a fixed granular layer lying on it. The layer has the form of a semi-infinite step of finite thickness and consists of an infinite number of statistically uniformly distributed identical spherical granules. The problem is solved using a previously developed method of self-consistent field, which allows one to study the effects of hydrodynamic interaction of a large number of spherical particles in ideal-fluid flows, including in the presence of external boundaries, and to obtain averaged dynamic characteristics of such flows. An analytical function describing the averaged fluid velocity field both inside and outside the layer is obtained in the first approximation with respect to the volume fraction of the granules in the layer.