Uniform asymptotic behaviour of the field produced by plane wave reflection at a convex cylinder. I

Abstract

THE problem of plane wave diffraction at an ideally reflecting cylinder is discussed. A parabolic equation method is used to find asymptotic expressions for the wave field, valid in the illuminated region right up to the shadow boundary. The matching of this asymptotic field with the asymptotic field in the shadow region is examined. A uniform asymptotic expression for the two-dimensional Green's function for a convex ideally reflecting cylinder was obtained and investigated in [1, 2]. In the present paper the problem of plane wave diffraction at a convex cylinder is investigated, and simpler asymptotic expressions are obtained. In part I, which is essentially heuristic, a parabolic equation method is used to find the asymptotic behaviour of the field in the illuminated region, which holds right up to the shadow boundary, and its matching with the asymptotic field in the shadow region is investigated. (It may be noted that the term “uniform asymptotic behaviour” is used in a different sense in [3, 4]; the expressions of [3, 4] do not hold close to the shadow boundary.) The asymptotic values obtained for the current in the illuminated side of the cylinder are compared with numerical values obtained by exact solution of the circular cylinder case. Part II of the paper will be devoted to a strict mathematical proof of the asymptotic expressions obtained.