Scalar wave diffraction by tangent rays

Modern asymptotic methods are used to provide as complete as possible a des cription of the scattering of a high-frequency time-harmonic acoustic plane wave by a two-dimensional convex obstacle. The cases of infinite and finit e scatterers are considered separately, and descriptions of the diffracted fields and the transition solutions valid across shadow boundaries are pres ented. For a finite scatterer, expressions are given for the directivity fu nction (or angular variation) of the scattered field in the very far-field encompassing all angular directions; in particular this results in the pred iction of a narrow range of angles for which the directivity is an order of magnitude lower than in general. (C) 2000 Elsevier Science B.V. All rights reserved.