Nonlinear Schrödinger invariants and wave statistics

Third-order quasiresonant interactions among free waves and associated modulational instabilities can significantly affect the statistics of various surface features in narrowband waves. In particular, modulational instabilities tend to induce intermittent amplifications on the surface displacements, causing their statistics to deviate from the linear Gaussian and second-order models. Herein, we investigate the nature of such instabilities on the statistical and spectral characteristics of deep-water waves generated in a large wave basin. We analyze the spectral changes that occur as waves propagate along the basin, develop bounds on the spectrum bandwidth, and interpret various statistics based on third-order Gram–Charlier distributions.