Observation of Nonlinear Effects in Ocean Surface Wave Frequency Spectra

Abstract

Nonlinearity and directionality of an evolving open-ocean surface wave field are investigated under increasing wind forcing. In addition to the frequency wave elevation spectrum, the frequency wave slope spectrum, the bicoherence of the wave elevation time series, and the peak wavenumber at a given frequency estimated by the maximum likelihood method are examined. As the wave field matures, an increasing portion of the high-frequency components of the wave elevation spectrum becomes phase correlated with the dominant wave component. This observation clearly suggests that the contribution to the frequency spectrum from the higher harmonics generated by steep dominant waves becomes increasingly important relative to the contribution from free waves that propagate at their own phase speed predicted by the dispersion relation. The observation therefore invalidates the common assumption that an ocean surface wave spectrum is a superposition of linear surface wave components of different frequencies. In addition, close examination of the frequency slope spectra and the peak wavenumber estimates suggests that the observed phase-coupled modes are generated by short-crested two-dimensional dominant wave patterns rather than by long-crested dominant waves.