Freak Waves in Unidirectional Wave Trains and Their Properties

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Abstract
This study aims to make clear the cause and occurrence condition of two-dimensional (2-D) freak waves by solving the hydrodynamic equations of 2-D irrotational flow for nonlinear waves with various spectra corresponding to swell from wind waves and describing the long-time evolution. As a result, it is shown that the third order resonant interaction causes the 2-D freak waves of which surface profiles are very similar with those observed in nature and multiplies the occurrence probability with the decreasing of the spectral bandwith in deep water. Conversely, the feature of the freak waves — single and outstanding wave height — gets prominent with the broadening of the spectral bandwith.

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