Hilbert spectra of nonlinear ocean waves

The Hilbert-Huang transform (HHT) analysis interprets wave nonlinearity in terms of frequency modulation instead of harmonic generation. The resulting spectrum contains much higher spectral energy at low frequency and sharper drop off at high frequency in comparison with the spectra derived from Fourier-based analysis methods. The high energy level in the low-frequency components of the Hilbert spectrum seems to be consistent with the rich group structure apparent in typical ocean-wave records. For wind-generated waves, the spectral level of the Fourier spectrum is about two orders of magnitude smaller than that of the Hilbert spectrum at the first subharmonic of the peak frequency. The mean frequency of the Fourier spectrm is 20% higher than that of the Hilbert spectrum. Furthermore, the frequency of the wave groups is also more likely to be properly identified in the Hilbert spectrum than in the Fourier spectrum. The implications for ocean engineering and air-sea interaction are discussed.