Narrow‐band nonlinear sea waves

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.