Sound interaction with moving vortices

Abstract

This report is devoted to the nonlinear acoustic pressure of sound waves propagating in the vicinity of a rather general class of localized flows induced by the motion of spherically symmetric structures of the type of vortices in the liquid, say, biological, atmosphere, or ocean inhomogeneous environment. As a result expressions for cyclic and mean forces exerted on a vortex are derived. Conventional general expression for transport cross section derived in nonlinear theory of interaction of sound with rigid particles is proven to be incorrect for the vortex-sound interaction case. The absence of mean force is demonstrated for specific case of Hills vortex both in the traveling and standing sound wave fields. It is underlined, however, that the force could be observable if the distribution of mean sound energy in the incident sound field in the frames of vortex dimensions could be characterized by a nonzero spatial gradient. Instead of the previously used expression for mean radiation force exerted on a moving inhomogeneity valid for a solid particle based on its transport cross section, the correct generalized expression for force exerted on vortex structure is derived.