Solitary flexural–gravity waves in three dimensions

Abstract

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A369, 2942–2956 (doi:10.1098/rsta.2011.0104)). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.