Long time evolution of modulated wave trains

Freak waves, a typical nonlinear wave disaster, pose a serious threat to human life and property safety. Therefore, the study of Freak waves is crucial for marine disaster prevention. The study employs the High-Order Spectral method to investigate the generation and characteristics of Freak waves and the evolution of wave field parameters in the long time evolution process of modulated wave trains. It reveals that the appearance of Freak waves is accompanied by the aggregation and separation of wave groups. The evolution of freak degree y, kurtosis mu 4, skewness mu 3, wave steepness and spectral bandwidth B all exhibit distinct stage characteristics. In the stage of modulation instability, only one type and a constant number of wave groups exist, with wave field parameters exhibiting periodic recurrence. In contrast, various types and numbers of wave groups emerge in the stage of wave group interaction. And the occurrence probability of Freak waves increases, the fluctuation range of y also significantly expands, waves become more irregular. mu 4, mu 3, local wave steepness eloc and B all increase significantly. Meanwhile, excessive nonlinearity leads to frequent wave breaking and a decline in mean wave steepness em.