  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.
