Motion of particles in the field of nonlinear wave packets in a liquid layer under an ice cover

A. T. Il'ichev   ; A. S. Savin   ; A. Yu. Shashkov

Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 586-600

Résumé

We consider a liquid layer of a finite depth described by Euler's equations. The ice cover is geometrically modeled by a nonlinear elastic Kirchhoff–Love plate. We determine the trajectories of liquid particles under an ice cover in the field of a nonlinear surface traveling wave rapidly decaying at infinity, namely, a solitary wave packet (a monochromatic wave under the envelope, with the wave velocity equal to the envelope velocity) of a small but finite amplitude. Our analysis is based on the use of explicit asymptotic expressions for solutions describing the wave structures at the water–ice interface of a solitary wave packet type, as well as asymptotic solutions for the velocity field generated by these waves in the depth of the liquid.

Détail

Keywords: ice cover, solitary wave packet, central manifold, trajectories of liquid particles.
Mots-clés : bifurcation

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