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We study the nonlinear modulation property of flexural-gravity waves on awater surface covered by a compressed ice sheet of given thickness and densityin a basin of a constant depth. For weakly nonlinear perturbations, we derivethe nonlinear Schr\"odinger equation and investigate the conditions when aquasi-sinusoidal wave becomes unstable with respect to amplitude modulation.The domains of instability are presented in the planes of governing physicalparameters; the shapes of the domains exhibit fairly complicated patterns. Itis shown that under certain conditions the modulational instability can developfrom shorter groups and for fewer wave periods than in the situation ofdeep-water gravity waves on a free water surface. The modulational instabilitycan occur at the conditions shallower than that known for the free watersurface 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 physicalconditions of an ice-covered sea.

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