Observation of Nonlinear Steep Waves
Nonlinearity and directionality of evolving open-ocean wave fields are investigated using wave height records from a triangular wave gauge array. 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 estimates at a given frequency are examined. The results suggest that as the wave field matures, the contribution to the frequency spectrum from the directional higher bound harmonics generated by short-crested steep dominant waves becomes increasingly important relative to the contribution from free waves. Next, a wavelet analysis methodology is used to estimate the statistics of steep waves. The method is applied to open ocean spatial wave height data. Results show that high wave slope crests appear over a wide range of wavenumbers, with a large amount being much shorter than the dominant wave. At low wave slope thresholds, all wave fields have roughly the same amount of wave crests regardless of wind forcing. The steep wave statistic decays exponentially with the square of the wave slope threshold, with a decay rate that is larger for the low wind cases than the high wind cases. Comparison of the steep wave statistic with past measurements of the breaking wave statistic suggests a breaking wave slope threshold of about 0.12. Although the steep wave statistic roughly increases with the cube of the wind speed as the breaking wave statistic does, other factors besides the wind speed also affect the level of the steep wave statistic. Comparison of the steep wave statistic to the saturation spectrum reveals a reasonable correlation at high wave slope thresholds. The crest directionality statistic shows that most of the steep wave crests are normal to the direction of the mean wind. This is inconsistent with the Fourier wavenumber spectrum that shows a broad bimodal directional spreading at high wavenumbers. The crest length statistics demonstrate that the wave field is dominated by short-crested waves with small crest length/wavelength ratios.