On the resonant hydroelastic behaviour of ice shelves

Rhythmic hydroelastic oscillations of ice shelves are a key mechanism believed to affect several phenomena observed in Polar Regions, such as the disintegration of ice shelves due to ocean wave impact or even the formation of localised distinctive atmospheric waves. The fundamental and lower hydroelastic modes of an ice-shelf/sub-ice-shelf cavity configuration can be studied by coupling shallow water theory and flexure dynamics of a slender, floating, cantilever beam. A crucial aspect of the analysis is the selection of appropriate boundary conditions at the grounding line of the ice shelf and at the freely floating end. The present study aims to determine appropriate and realistic homogeneous boundary conditions for eigenproblems of resonant ice-shelf vibrations. Through the formulation and solution of a wave impact Reflection-Transmission problem, frequencies that maximise specific norms of the ice-shelf response are identified. It is established that homogeneous conditions on the sub-ice-shelf cavity wave potential value, applied at the front of an ice-shelf, produce eigenfrequencies that in general match the norm maximisation frequencies. The methodology is employed for the prediction of characteristic periods of the Ross and Larsen C ice shelves.