Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet

TL;DR

This paper investigates the nonlinear modulation and instability of flexural-gravity waves on ice-covered water surfaces, deriving a nonlinear Schrödinger equation and analyzing the conditions for modulational instability.

Contribution

It derives the nonlinear Schrödinger equation for flexural-gravity waves on ice-covered water and explores the instability conditions under various physical parameters.

Findings

Modulational instability can develop from shorter wave groups than in deep-water gravity waves.

Instability can occur at shallower depths than the classical kh=1.363 threshold.

The shape of instability domains varies with physical parameters.

Abstract

We study the nonlinear modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet of given thickness and density in a basin of a constant depth. For weakly nonlinear perturbations, we derive the nonlinear Schr\"odinger equation and investigate the conditions when a quasi-sinusoidal wave becomes unstable with respect to amplitude modulation. The domains of instability are presented in the planes of governing physical parameters; the shapes of the domains exhibit fairly complicated patterns. It is shown that under certain conditions the modulational instability can develop from shorter groups and for fewer wave periods than in the situation of deep-water gravity waves on a free water surface. The modulational instability can occur at the conditions shallower than that known for the free water surface kh = 1.363, where k is the wavenumber and h is the water depth. Estimates of parameters of modulated waves are given for the typical physical conditions of an ice-covered sea.