On the critical angle for ocean waves entering shore fast ice

A theoretical model is derived and presented for sea waves entering shore fast ice at other than normal incidence. The model assumes that the sea ice behaves as a thin elastic plate overlying a deep fluid foundation. Three ice-coupled waves are generated; a propagating wave, and two inhomogeneous plane waves which rapidly decay with penetration. At a certain angle of incidence, the critical angle, these ice-coupled waves coalesce into a wave travelling along the ice edge with an amplitude which varies into the ice cover as the sum of a constant term and an attenuated pattern of corrugations. At angles exceeding the critical angle, the constant term becomes evanescent but the general picture remains the same. A novel break-up mechanism is proposed, based on this modulation of amplitude with distance from the edge, for shore fast ice and ice floes which are large compared to the incident sea's wavelengths.