Self-modulation of oceanic waves on an ice-covered surface

We study the self-modulation of flexural-gravity waves on a water surface covered by a compressed ice sheet. For weakly nonlinear long perturbations of the potential flow, we derive the nonlinear Schrödinger equation and investigate the conditions when a quasi-sinusoidal wave becomes unstable with respect to the amplitude modulation. The domains of instability are presented in the planes of parameters depending on the values of the local water depth, and the coefficients of ice rigidity/elasticity and of longitudinal stress. We show that under some conditions the occurrence of the modulational instability of oceanic waves under ice looks feasible and present estimates for the real oceanic conditions. Depending on the conditions, bright envelope solitons or dark solitons can emerge on the surface.

A.S. acknowledges the support from Laboratory of Dynamical Systems and Applications NRU HSE (the Ministry of Science and Higher Education of the Russian Federation Grant No. 075-15-2019-1931) and by the Russian Foundation for Basic Research (Grant No. 21-55-15008). Y.S. acknowledges the funding provided by the grant No. FSWE-2020-0007 through the State task program in the sphere of scientific activity of the Ministry of Science and Higher Education of the Russian Federation.