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.