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Numerical investigation of the instability and nonlinear evolution of narrow-band directional ocean waves

Eliasson, Bengt and Shukla, Padma (2010) Numerical investigation of the instability and nonlinear evolution of narrow-band directional ocean waves. Physical Review Letters, 105 (1). ISSN 0031-9007

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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 lead 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.