Freak Waves Generated by Modulation Instability Under Different Initial Conditions

摘要

Modulation Instability, also called B-F Instability, is widely recognized as the key reason of nonlinear Freak Wave generation. However, the majority of current researches concentrated only on the Most Unstable Condition (MUC for short). In this paper, systematic study covering various occurrence conditions of Modulation Instability has been investigated to discuss the wave train evolution characteristics corresponding to different initial sideband conditions. The results show that under non-MUC, though sidebands grow more slowly and generation of Freak Wave takes longer time, the maximum wave amplitudes tend to increase linearly as the initial ratio of relative spectrum width to wave steepness decreasing. It indicates that compared with the MUC, wave trains corresponding to narrower initial spectrum could produce stronger Freak Waves, also the evolution and characteristic parameters of which demonstrate stronger nonlinearity under non-MUC.