HIGHER-ORDER SPECTRAL-ANALYSIS OF NONLINEAR OCEAN SURFACE GRAVITY-WAVES

Bispectral and trispectral analyses are used to detect secondary and tertiary wave components resulting from nonlinear interactions among large-amplitude ocean surface gravity waves in 8- and 13-m water depths. Bispectra of bottom-pressure measurements indicate forced secondary waves at frequencies 2f(p) about twice the primary power spectral peak frequency f(p). However, the interpretation of the bispectrum at sum frequencies of approximately 3f(p) is ambiguous because contributions of both secondary and tertiary forced waves may be significant. Trispectral analysis confirms the presence of tertiary waves with frequency approximately 3f(p) In 8 m depth the tertiary bottom-pressure field is dominated by interactions between three colinearly propagating wind-wave components with frequencies close to f(p). In 13 m depth these relatively short-wavelength forced waves are strongly attenuated at the seafloor and the tertiary wave field is driven by interactions between the dominant waves at f(p) and obliquely propagating higher-frequency wind waves. The phases of the higher-order spectra are consistent with weakly nonlinear wave theory (Hasselmann, 1962).