Focusing of nonlinear wave groups in deep water
C. Kharif, E. Pelinovsky1) +, T. Talipova+, A. Slunyaev+
Institut de Recherche sur les Phenomenes Hors Equilibre, Parc Scientifique et Technologique de Luminy
13288 Marseille, Cedex 9, France
+Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics
603600 Nizhny Novgorod, Russia
PACS: 47.35.+i, 92.10.Hm, 92.60.Dj
Abstract
The freak wave phenomenon in the ocean is explained by the nonlinear dynamics
of phase modulated wave trains. It is shown that the preliminary
quadratic phase modulation of wave packets leads to the significant
amplification of the "usual" modulation (Benjamin-Feir) instability. Physically, the
phase modulation of water waves may be due to a variable wind in storm areas.
The well-known breather solutions of the cubic Schrodinger equation appear on
the final stage of the nonlinear dynamics of the wave packets, when the
phase modulation becomes more uniform.