Envelope solitary waves and dark solitons at a water--ice interface

A. T. Il'ichev

Informatics and Automation, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 163-177

Résumé

The article is devoted to the study of some self-focusing and defocusing features of monochromatic waves in basins with horizontal bottom under an ice cover. The form and propagation of waves in such basins are described by the full 2D Euler equations. The ice cover is modeled by an elastic Kirchhoff–Love plate and is assumed to be of considerable thickness so that the inertia of the plate is taken into account in the formulation of the model. The Euler equations involve the additional pressure from the plate that is freely floating at the surface of the fluid. Obviously, the self-focusing is closely connected with the existence of so-called envelope solitary waves, for which the envelope speed (group speed) is equal to the speed of filling (phase speed). In the case of defocusing, solitary envelope waves are replaced by so-called dark solitons. The indicated families of solitary waves are parametrized by the wave propagation speed and bifurcate from the quiescent state. The dependence of the existence of envelope solitary waves and dark solitons on the basin's depth is investigated.