Ocean waves and ice sheets

A complete analytical study is presented of the reflection and transmission of surface gravity waves incident on ice-covered ocean. The ice cover is i dealized as a plate of elastic material for which flexural motions are desc ribed by the Timoshenko-Mindlin equation. A suitable non-dimensionalization extracts parameters useful for the characterization of ocean-wave and ice- sheet interactions, and for scaled laboratory studies. The scattering probl em is simplified using Fourier transforms and the Wiener-Hopf technique; th e solution is eventually written down in terms of some easily evaluated qua dratures. An important feature of this solution is that the physical condit ions at the edge of the ice sheet are explicitly built into the analysis, a nd power-flow theorems provide verification of the results. Asymptotic resu lts for large and small values of the non-dimensional parameters are extrac ted and approximations are given for general parameter values.