Asymptotic solutions for the two‐dimensional diffracted field

Abstract

AbstractA simple formula is derived to estimate the asymptotic field diffracted by an infinitely long cylindrical object with an arbitrary cross section when an arbitrary cylindrical wave with directivity is incident. In the analysis, the problem of diffraction of a cylindrical wave by an infinitely long slit is formulated by means of the Kobayashi‐Nomura method, and an asymptotic series solution is derived with respect to the distances between the source and the scatterer and between the scatterer and the observation point. The solution is given in the form of a diffraction pattern function for the plane wave incidence and its derivative. The method is applicable to any diffraction (or scattering) problems of the object for which the pattern function is known. The result is applied to the problems of diffraction by a half‐plane and a wedge and of scattering by a circular cylinder, and practical representations are derived. For the half‐plane problem, the results are compared with those derived by other methods and complete agreement is confirmed. Numerical calculations for the slit diffraction problem and scatterings from the cylinder result in accurate results even when the distance between the object and the source is extremely small, as long as the second or the third term is taken into consideration. The method is believed to be an effective one.