Creeping waves and resonances in transient scattering by smooth convex objects

Abstract

Scattering by smooth convex objects, excited by a transient field with broad spectral content, has been analyzed either by ray formulations, which are useful at observation times descriptive of the early arrivals, or by the complex resonances of the singularity expansion method (SEM), which are most appropriate at intermediate and late observation times. Within the framework of SEM, efforts have recently been made to show that in a grouping of the resonances along "layers," rather than along the conventional "arcs" based on an angular harmonic field representation, the higher order resonances behave collectively like a wave traveling circumferentially around the object. This observation has provided the stimulus for the present investigation in which the relation between the wavefront arrivals (creeping waves) and the SEM resonances is placed on a rigorous basis. Using a perfectly conducting circular cylinder as a canonical model, this is done by direct application of the theory of characteristic Green's functions to construct alternative field solutions, and by collective summation of groups of wavefront arrivals or groups of resonances. The connection between creeping waves and resonances thus having been established, hybrid formulations are developed which combine the creeping waves and the SEM resonances within a single rigorous framework so as to maximize the utility of each over the entire range of observation times. These results are then generalized to smooth cylindrical objects with noncircular convex shape.