Observations of the wind-wave spectrum and steep wave statistics in open ocean waters

The experimental data from the Southern Ocean Waves Experiment (SOWEX) and the Duck, North Carolina experiment (DNC) is used to investigate validity of the Hara-Belcher equilibrium spectrum for wind-waves under open ocean conditions. Wavenumber spectral calculations admit saturation spectra which when scaled by $k\times u2*g$ reveal that the spectra fall within the bounds of the Hara-Belcher model. These spectral calculations are also consistent with the Phillips model of the equilibrium spectrum of wind-waves leaving the discrimination between the two models as unclear.; As an initial step in the direction of understanding the nonlinear phenomenon of wave breaking, a steep wave statistic Λ_T (k) is calculated from surface wave height data. Estimates of the steep wave statistic at different wave slope thresholds from the SOWEX Experiment and DNC experiment show that all seas have approximately the same total length of crests at low wave slope thresholds regardless of wind forcing. The steep wave statistic versus wave slope threshold has a normal distribution with a decay rate that is larger for the low wind cases than the high wind cases. Normalization of Λ_T ( k) by the cut of the saturation spectrum in the wind direction, namely B(k, &thetas;_w), did not successfully collapse the results. Thus the relationship of the wavenumber spectrum to the steep wave statistic is not one to one. Crest length statistics show that waves of small crest length and/or long wavelengths appear more often on the ocean surface while directionality studies show that majority of wave crests are in perpendicular to the wind. In addition, the distribution of steep wave troughs indicates that the wave fields, to first order, possess the same amount of steep wave crests and troughs. However, the high wind case of June 10th from the SOWEX experiment has more high wave slope crests than troughs above wave slope threshold 0.17.