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. A 369, 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’.
Highlights
In this paper, we consider an incompressible and inviscid fluid covered by an ice sheet
A renewed interest in waves generated by moving loads on top of floating ice sheets has been sparked in the last 40 years by a series of experiments in cold regions (e.g. [2,3,4,5,6]), where ice roads and runways are used during the winter
These are computed in three dimensions for water of finite or infinite depth, using the nonlinear model formulated in Plotnikov & Toland [11] for the ice sheet
Summary
We consider an incompressible and inviscid fluid covered by an ice sheet. Most of the analytical and numerical studies of nonlinear flexural–gravity waves (or hydroelastic waves) concentrate on two-dimensional problems. Fully localized three-dimensional solitary waves have been computed in a quintic Hamiltonian model derived from the full nonlinear Euler equations [38]. The focus of this work is on waves generated by moving pressures and on fully localized solitary flexural–gravity waves These are computed in three dimensions for water of finite or infinite depth, using the nonlinear model formulated in Plotnikov & Toland [11] for the ice sheet. Waves generated by a moving load on a nonlinear fluid–linear elastic plate configuration have been computed using a boundary integral method [44] and solitary waves have been found [45]. The paper ends with conclusions and discussions of the results
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