Forming of single and steep waves in uni-directioned wave trains and their properties

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Third order resonant interaction was shown to cause single and steep waves such as freak waves in uni-directional wave trains, by solving the hydrodynamic equations of irrotational flow for nonlinear waves with various spectra corresponding to swell from wind waves and by analyzing the observed wave data in sea area around Japan. The achievements are as follows :・Forced high-wave number modes exicited by the third order resonant and nonresonant interactions increase the occurrence probability of extremely high waves leading to freak waves. However, wave breaking reduces the nonlinear effects amplifying wave-height and fits the waveheight distribution to the Rayleigh distribution. As a result, Edgeworth-Rayleigh distribution was suggested as the waveheight distribution applicable to waves suffering the third order nonlinear interaction and breaking effects.・Analysis of wave data obtained off Yura fishery harbor facing the Japan sea made clear that giant freak waves of which waveheights exceed two times of H_<1/3> and further 10m are caused by nonlinear wave-wave interactions under strong but uniform winds in winter. Further, they showed that the occurrence probability is almost twice that predicted by the Reyleigh distribution.・Temporal and spatial surface profiles of the giant freak waves can be expressed approximately by using the space-time correlation function derived from the directional spectra.