Abstract
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 (), these coherent structures produce rogue waves. The most tall waves appear in turns of the zigzags. For , the structures decay typically without formation of steep waves.
- Received 6 February 2007
DOI:https://doi.org/10.1103/PhysRevLett.99.044502
©2007 American Physical Society