Analysis of random nonlinear water waves: the Stokes–Woodward technique

Analysis of random nonlinear water waves: the Stokes–Woodward technique

A generalization of the Woodward's theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave–wave interaction in the case of water waves, can be inferred. Consi...

On Nonlinear Water Waves in a Channel

Nonlinear water waves.

This introduction to the issue provides a review of some recent developments in the study of water waves. The content and contributions of the papers that make up this Theme Issue are also discussed.

Nonlinear Fourier analysis of deep-water, random surface waves: theoretical formulation and experimental observations of rogue waves

Unidirectional deep-water waves are studied theoretically and experimentally. Theoretically we apply the theory of the nonlinear Schroedinger equation (NLS) using the inverse scattering transform, a kind of generalized, nonlinear Fourier analysis. We discover from the theoretical study that there are essentially four kinds of physical effects that can lead to extreme waves: (1) the superpositio...

Nonlinear Resonances of Water Waves

In the last fifteen years great progress has been made in the understanding of nonlinear resonance dynamics of water waves which is the main subject of discrete wave turbulence. Notions of scaleand angle-resonances have been introduced, new type of energy cascade due to nonlinear resonances in the gravity water waves has been discovered, conception of a resonance cluster has been much and succe...