Swell-induced flexural vibrations of a thickening ice shelf over a shoaling seabed

Abstract

A solution method is developed for a linear model of ice shelf flexural vibrations in response to ocean waves, in which the ice shelf thickness and seabed beneath the ice shelf vary over distance, and the ice shelf/sub–ice-shelf cavity are connected to the open ocean. The method combines a decomposition of the ice shelf displacement profile at a prescribed frequency of motion into mode shapes of free vibrations, a finite-element method for the cavity water motion and a non-local operator to connect to the open ocean. An investigation is conducted into the effects of ice shelf thickening, seabed shoaling and the grounding-line conditions on time-harmonic ice shelf vibrations, induced by regular incident waves in the swell regime. Furthermore, results are given for ice shelf vibrations in response to irregular incident waves by superposing time-harmonic responses, and ocean-to-ice-shelf transfer functions are derived. The findings add to evidence that ice shelves experience appreciable flexural vibrations in response to swell, and that ice shelf thickening and seabed shoaling can have a considerable influence on predictions of how ice shelves respond to ocean waves.