"Breathing" rogue wave observed in numerical experiment

Abstract

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show the spontaneous formation of a single extreme wave on the deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.

6 pages, 12 figures

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• Predictability of the Appearance of Anomalous Waves at Sufficiently Small Benjamin-Feir Indices
• Anomalous wave as a result of the collision of two wave groups on sea surface
• Canonical variables for steep planar water waves over nonuniform bed
• On the modulation instability development in optical fiber systems
• 3D effects in the dynamics of oceanic rogue waves: A numerical study