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A variational principle is proposed to derive the governing equations for theproblem of ocean wave interactions with a floating ice shelf, where the iceshelf is modelled by the full linear equations of elasticity and has anArchimedean draught. The variational principle is used to form a thin-plateapproximation for the ice shelf, which includes water--ice coupling at theshelf front and extensional waves in the shelf, in contrast to the benchmarkthin-plate approximation for ocean wave interactions with an ice shelf. Thethin-plate approximation is combined with a single-mode approximation in thewater, where the vertical motion is constrained to the eigenfunction thatsupports propagating waves. The new terms in the approximation are shown tohave a major impact on predictions of ice shelf strains for wave periods in theswell regime.

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