A new solution to the Fock-Leontovich-Pekeris problem. Under review

We study the classical problem of high frequency scattering of an incident plane wave by a smooth convex two-dimensional body. We present a new integral representation of the solution in a small neighbourhood of a point of ray tangency on the scatterer boundary from which penumbra (light-shadow boundary) effects originate. Our new representation allows matching of this inner field to the field away from the tangency point using the method of steepest descent. In particular we provide two ways of interpreting a diver-gent integral arising in the analysis of Tew et al. (Wave Motion 32, 2000), enabling the results of that paper to be used for quantitative calculations