Oblique wave scattering by undulations on the bed of an ice-covered ocean

THE PROBLEM of oblique wave scattering by cylindrical undulations on the bed of an ice-covered ocean is investigated by using a simplified perturbation analysis. The first-order potential function satisfies a boundary value problem (BVP) which is solved by employing the Green integral theorem after constructing an appropriate Green function. Analytical expressions for the first-order reflection and transmission coefficients are then obtained from the solution of this BVP, in terms of the integrals involving the shape function describing undulations. Three particular forms of the shape function are considered for which the reflection and transmission coefficients up to the first-order are obtained exactly.