A thin plate approximation for ocean wave interactions with an ice shelf

TL;DR

This paper introduces a variational principle-based thin-plate approximation for modeling ocean wave interactions with ice shelves, incorporating water-ice coupling and extensional waves, significantly improving strain predictions in swell conditions.

Contribution

It develops a novel thin-plate approximation derived from a variational principle that includes water-ice coupling and extensional waves, enhancing modeling accuracy.

Findings

New approximation impacts strain predictions in swell regime

Inclusion of water-ice coupling alters wave interaction dynamics

Extensional waves significantly affect ice shelf response

Abstract

A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean draught. The variational principle is used to form a thin-plate approximation for the ice shelf, which includes water--ice coupling at the shelf front and extensional waves in the shelf, in contrast to the benchmark thin-plate approximation for ocean wave interactions with an ice shelf. The thin-plate approximation is combined with a single-mode approximation in the water, where the vertical motion is constrained to the eigenfunction that supports propagating waves. The new terms in the approximation are shown to have a major impact on predictions of ice shelf strains for wave periods in the swell regime.