A new view of nonlinear water waves: The Hilbert spectrum

We survey the newly developed Hilbert spectral analysis method and its appl ications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inade quacy of presently available methods in nonlinear and nonstationary data an alysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically me aningful interpretations of the underlying dynamic processes.