Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves

Details Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves

2007-04-24

arxiv.org/abs/0704.3246v1

Phys. Rev. Lett. 99, 044502 (2007).

Physics

Fluid Dynamics

11 pages, 7 figures, submitted to PRL

Scientific paper

10.1103/PhysRevLett.99.044502

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly three-dimensional potential flows of an ideal fluid with a free surface in terms of conformal variables. Spontaneous formation of zigzag patterns for wave amplitude is observed in a nonlinear stage of the instability. If initial wave steepness is sufficiently high ($ka>0.06$), these coherent structures produce rogue waves. The most tall waves appear in ``turns'' of the zigzags. For $ka<0.06$, the structures decay typically without formation of steep waves.

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