Instability and Nonlinear Evolution of Narrow-Band Directional Ocean Waves

Abstract

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the modulational instability for long-crested wave-trains, which agrees well with recent large-scale experiments in wave-basins, where it was found that narrower directional spectra leads to self-focusing of ocean waves and an enhanced probability of extreme events. We find that the modulational instability is nonlinearly saturated by a broadening of the wave-spectrum, which leads to the stabilization of the water-wave system. Applications of our results to other fields of physics, such as nonlinear optics and plasma physics are discussed.

4 pages, 4 figures. To appear in Physical Review Letters

References in corpus (4)

• Capillary rogue waves
• Non-Gaussian statistics and extreme waves in a nonlinear optical cavity
• Freak waves in the linear regime: A microwave study
• Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves

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