On the scattering of sound by a rectilinear vortex

A re-examination is made of the two-dimensional interaction of a plane, tim e-harmonic sound wave with a rectilinear vortex of small core diameter at l ow Mach number. Sakov [1] and Ford and Smith [2] have independently resolve d the "infinite forward scatter" paradox encountered in earlier application s of the Born approximation to this problem. The first order scattered fiel d (Born approximation) has nulls in the forward and back scattering directi ons, but the interaction of the wave with non-acoustically compact componen ts of the vortex velocity field causes wavefront distortion, and the phase of the incident wave to undergo a significant variation across a parabolic domain whose axis extends along the direction of forward scatter from the v ortex core. The transmitted wave crests of the incident wave become concave and convex, respectively, on opposite sides of the axis of the parabola, a nd focusing and defocusing of wave energy produces corresponding increases and decreases in wave amplitude. Wave front curvature decreases with increa sing distance from the vortex core, with the result that the wave amplitude and phase are asymptotically equal to the respective values they would hav e attained in the absence of the vortex. The transverse acoustic dipole gen erated by translational motion of the vortex at the incident wave acoustic particle velocity, and the interaction of the incident wave with acoustical ly compact components of the vortex velocity field, are responsible for a s ystem of cylindrically spreading, scattered waves outside the parabolic dom ain. (C) 1999 Academic Press.