Scattering of acoustic waves by a circular disc in the interface between two fluids

Abstract

The scattering of acoustic waves by a sound-hard circular disc situated in the planar interface between two different fluids is considered. The incident wave is taken as a plane wave and a Hankel transform representation of the scattered field is used. After some manipulations using the boundary conditions, this leads to an integral equation over the disc for the potential jump across the disc. This jump is expanded in a series of Legendre functions which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre functions. The far fields are calculated and the implications of energy conservation are explored and used as a numerical check. A few numerical computations showing the disc-scattered far-field amplitude and the total scattered energy are given and are shown to compare favorably with the expectations from simple ray theory at higher frequencies.