Modelling hydroelastic flexure of arbitrarily shaped ice shelves forced by long ocean waves

Abstract

Flexure of Antarctic ice shelves under excitation from long ocean waves induces mechanical ice-shelf stresses that amplify fractures and, hence, contribute to calving events. Here, a solution method is developed for a hydroelastic mathematical model of wave-induced ice-shelf flexure, based on the conventional theory of a Kirchoff–Love plate floating on shallow water under linearised conditions, but allowing wave forcing of ice shelves with variations in both horizontal dimensions, and where the ice shelves are of arbitrary shape, including non-uniform thickness. The method uses finite elements specifically designed for the high-order hydroelastic system, and a Dirichlet-to-Neumann map to bound the computational domain in the open ocean. Following verification, the method is used to conduct novel studies on how the ice-shelf deflection is affected by the ice-shelf shape, the incident wave direction and the proportion of the shelf that is grounded. The efficiency of the method allows the studies to be conducted over a broad frequency range, such that resonant responses are identified. The method is also used to model the response of the Drygalski Ice Tongue to long-wave forcing.