Scalar Wave Diffraction by Tangent Rays

R H Tew, S J Chapman, J R King, J R Ockendon, B J Smith & I Zafarullah

Modern asymptotic methods are used to provide as complete as possible a description of the scattering of a high-frequency time-harmonic acoustic plane wave by a two-dimensional convex obstacle. The cases of infinite and finite scatterers are considered separately, and descriptions of the diffracted fields and the transition solutions valid across shadow boundaries are presented.

For a finite scatterer, expressions are given for the directivity function (or angular variation) of the scattered field in the very far field encompassing all angular directions; in particular this results in the prediction of a narrow range of angles for which the directivity is an order of magnitude lower than in general.