Instability and Nonlinear Evolution of Narrow-Band Directional Ocean Waves

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.