Scattering of sound waves by a cylindrical vortex: a semi-analytical theory

Abstract

A semi-analytical theory for the scattering of plane sound waves by a compressible, non-homentropic, circular-cylindrical, single vortex is presented in this paper. As a special case, the scattering of sound by a cylindrical inhomogeneity (hot spot) is investigated. Contrary to the otherwise analogous quantum-mechanical scattering problem, there are singularities in the modified acoustic wave equation for radii xs ∈ (0, ∞) when the scattering by a vortex is considered. It will be shown how these singularities can be treated.This sound-scattering theory is applied to the problem of the interaction of weak plane shock waves with a strong cylindrical vortex. The calculated scattered sound signal has a rather complicated structure in which a cylindrical wave with an essentially quadrupolar directivity pattern is discernible. In the case of shock–hot-spot interaction a scattered sound signal with dipole-like amplitude is obtained. Both results qualitatively agree with experimental findings.