Drift of elastic floating ice sheets by waves and current: Multiple sheets

Abstract

A nonlinear theoretical model for deformations, oscillations, and drift motions of multiple elastic ice sheets in shallow waters due to combined nonlinear waves and uniform current is presented. The model is based on the Green–Naghdi theory for the fluid motion and the thin plate theory for the deformation of the ice sheets. In principle, there are N number of the floating sheets with arbitrary lengths, drafts, and rigidities, which may be located at arbitrary distances from each other. Nonlinear waves of solitary and cnoidal types are considered, and there are no restrictions on the wave properties (wave height or wave period). The sheets, located at different positions, are shown to drift with different speeds, but surge in most of the wave conditions with equal amplitudes. It is shown systematically that wavelength and spacing between the sheets are the critical parameters determining the drift response of a set of freely floating ice sheets. When wavelength is equal to the distance between the centers of the sheets, they bend and drift in resonance, causing the largest wave reflection. The ambient current is found to affect the drift motion of the sheets nonlinearly. This work complements the part I paper of the same title, where drift motion of a single ice sheet was investigated.