Average flow generation by a pulsating flow near a curved interface

This paper is devoted to the study of curvature influence on the average flow generation near the fluid interface. The time averaging of a non-uniform pulsating flow often results in a nonzero average flow in the bulk. The well-known average flow occurs near a solid surface, the so-called Schlichting mechanism of the average flow generation. For flows with a free surface there is the other known mechanism of Longuet-Higgins, according to which the average flow is generated by surface waves traveling on a free surface. We found another mechanism for flow generation near a free surface. This mechanism is associated with the curvature of a free surface and does not depend on its deformations. In the present paper the influence of the curvature is studied for flow generation near the fluid interface. The investigation is carried out on an example of a liquid drop embedded in a viscous liquid. The effective boundary conditions for the tangential stress tensor and tangential velocity jumps are derived. It is shown that for comparable densities of fluids the generation mechanisms are similar to the mechanisms of Dore and Schlichting, which are determined near a flat interface. At a low density (and a low dynamic viscosity) inside the drop all of the above-mentioned mechanisms equally contribute to the average flow generation.