Far-field analysis of the Malyuzhinets solution for plane and surface waves diffraction by an impedance wedge

Abstract

The basic problem of determining the far-field scattered from the edge of a wedge of exterior angle 2 Φ with arbitrary impedance conditions on either face is considered. An accurate solution in the form of a Sommerfeld integral obtained by Malyuzhinets is evaluated for kr≫1. A fairly complete discussion of the far-field response is provided, including uniform and non-uniform asymptotic approximations. The far-field is split into edge-diffracted, surface, and geometrical optics waves, including multiply reflected components. The edge-diffracted field is defined by the diffraction coefficient, which we show has a simple factorisation: D= u 0( φ) u 0( φ 0) F Φ ( φ, φ 0), where φ and φ 0 are the source and observation directions, u 0( φ) is the value of the wave function at the edge for a plane wave of unit amplitude incident from the direction φ, and F Φ ( φ, φ 0) involves only trigonometric functions. We demonstrate that the monostatic tip diffraction from a wedge of arbitrary angle can be made to vanish by appropriate choice of the surface impedance. The unique value of impedance is always real, and an explicit formula is given for its evaluation. New results are presented for the reflection and transmission of surface waves on an impedance wedge, including simple approximations for an internal wedge with small Φ. Finally, a complete uniform description of the far-field is given in the format of the Uniform Asymptotic Theory of Diffraction.