Wave diffraction by a small elevation of the bottom of an ocean with an ice-cover

Abstract

Diffraction of water waves by a small cylindrical elevation of the bottom of a laterally unbounded ocean covered by an ice sheet is investigated by the perturbation analysis. The ice sheet is modelled as a thin elastic plate. The reflection and transmission coefficients are evaluated up to the first order in terms of integrals involving the shape function representing the bottom elevation. Three particular forms of the shape function are considered for which explicit expressions for these coefficients are obtained. For the particular case of a patch of sinusoidal undulations at the bottom, the reflection coefficient up to first order is found to be an oscillatory function of the ratio of the wavelength of the bottom undulations and that of the incident wave train. When this ratio approaches 0.5, the reflection coefficient becomes a multiple of the number of undulations and high reflection of the incident wave energy occurs if this number is large. Reflection coefficient is depicted graphically to visualize the effect of the presence of ice-cover and the number of undulations.