Abstract
Scattering of sound incident upon an arbitrary vorticity field is investigated, and general formula of the scattered wave is presented. Under the condition of weakly unsteady field, the scattering amplitude is expressed as a function f (n, n0, ω) dependent on unit vectors n0 and n in the incident and scattered directions respectively, and also on the vorticity distribution ω through its Fourier component of the wave number k0 (n-n0), k0 being the incident wave number. The amplitude satisfies the reciprocity relation f (n, n0, ω) =f (-n0, -n, -ω), which can be deduced from the energy conservation and linearity of the scattering process and the time reversal invariance of the basic equations. Explicit expressions of the amplitude are given for the two vortex systems known as Hill's spherical vortex and a vortex ring of thin vortex core.
General amplitude formula in two dimensional problem is also derived and applied to several cases (a vortex filament, a vortex pair, vortex arrays, etc.), some of which are compared with known formulae. Comments are given about relationship to the associated fields of the scattering problem.
