Mathematical Studies of Wave Propagation in Sea-ice: Sea-ice Dynamics

During the winter months the sea around the coast of Antarctica freezes and form a vast area of ice covered region. The ice sheets found in this area are large and apparently featureless. Therefore a large-scale sea ice sheet has been modeled as a thin elastic plate for small deflection. Partial differential equations are derived to describe vertical deflection of a thin elastic plate coupled with incompressible fluid. The Fourier transform is used to derive the vertical deflection of the ice sheet. A fundamental solution can be expressed by infinite summations of fractional functions at complex roots of the dispersion equation. The Fundamental solution is reduced to a sum of special functions at three roots of a fifth order polynomial when the water depth is infinite. The reflection and transmission of wave energy between two semi-infinite ice sheets joined by a straight-line transition is considered. Analytical formulas for the modal expansion of the waves in the ice sheet are derived using the Wiener-Hopf technique. This monograph should be a good introduction for post-graduate students to the linear hydro-elasticity.