Nonlinear Stage of the BenjaminFeir Instability: ThreeDimensional Coherent Structures and Rogue Waves
Abstract
A specific, genuinely threedimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deepwater wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly threedimensional 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.
 Publication:

Physical Review Letters
 Pub Date:
 July 2007
 DOI:
 10.1103/PhysRevLett.99.044502
 arXiv:
 arXiv:0704.3246
 Bibcode:
 2007PhRvL..99d4502R
 Keywords:

 47.15.km;
 47.11.j;
 47.27.De;
 47.35.Bb;
 Potential flows;
 Computational methods in fluid dynamics;
 Coherent structures;
 Gravity waves;
 Physics  Fluid Dynamics;
 Physics  Atmospheric and Oceanic Physics
 EPrint:
 11 pages, 7 figures, submitted to PRL