Article,
Narrow-band nonlinear sea waves
J. Geophys. Res., 85 (C3): 1548--1552 (Mar 20, 1980)
DOI: 10.1029/jc085ic03p01548
Abstract
Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.
