Inertia effects of a localized force distribution near a wall in a slow shear flow

Abstract

From recorded observations in oscillatory flows over a bed sparsely covered with sand, it has been suggested that the initial stage of ripple formation involves hydrodynamic interaction at a distance among particles which are far apart. This mechanism appears to be common to both a thick layer of sand bed and a monolayer of beads on a smooth plane. In view of these facts it is helpful to study first a simpler problem that is of relevance in laminar flows. Specifically, the case where the typical particle radius is much smaller than the spacing, which is in turn much smaller than the thickness of Stokes boundary layer, is considered. With a view to examining the far field, a quasisteady Oseen approximation is invoked, and the boundary-layer flow is replaced by a linear shear and the particle by a localized force distribution. The results are used to infer the tendency of interaction between two particles.