Higher‐order spectral analysis of nonlinear ocean surface gravity waves

Abstract

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 2ƒp about twice the primary power spectral peak frequency ƒp. However, the interpretation of the bispectrum at sum frequencies of approximately 3ƒp 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 3ƒp. In 8 m depth the tertiary bottom‐pressure field is dominated by interactions between three colinearly propagating wind‐wave components with frequencies close to ƒp. 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 ƒp and obliquely propagating higher‐frequency wind waves. The phases of the higher‐order spectra are consistent with weakly nonlinear wave theory (Hasselmann, 1962).