Instability and Nonlinear Evolution of Narrow-Band Directional Ocean Waves

TL;DR

This paper uses numerical simulations to study the instability and nonlinear evolution of narrow-band directional ocean waves, revealing how spectral broadening stabilizes the system and relates to extreme wave events.

Contribution

It demonstrates the nonlinear saturation of modulational instability through spectral broadening, aligning with experimental observations and extending understanding to other physics fields.

Findings

Narrower directional spectra increase the likelihood of extreme waves.

Spectral broadening stabilizes the water-wave system.

Simulation results agree with large-scale wave-basin experiments.

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.