Studies in reverberation. II. Scattering of sound by a cylindrical vortex embedded in a fluid at rest

A solution is obtained for the scattering of a plane sound wave incident normally on a fluid cylinder rotating uniformly in a fluid at rest. In the long wave approximation the amplitude of the scattered wave is proportional to the peripheral velocity of the cylinder. There is no reflection in the forward and backward directions (theta = pi, theta = 0) due to normal incidence to the direction of the flow, and similarly, scattering in the directions theta = (pi/2) and theta = (3pi/2) also vanishes due to cancellation by counterflow. The scattering pattern is thus in the butterfly form.