Evolution of a Random Directional Wave and Freak Wave Occurrence

The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05<epsilon<0.11, with directional spreading up to 368 and frequency bandwidth 0.2<delta k/k<0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave-wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin-Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell-wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave-wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.