Wave groupiness analysis of the process of 2D freak wave generation in random wave trains

• The evolution of wave groups in the process of freak wave generation was analyzed.
• Wave groupiness was described in terms of two new groupiness parameters.
• The relationship between groupiness parameters and the kurtosis was also given.

In this investigation of the groupiness properties of unstable random wave trains, the evolution of wave groups in the process of freak wave generation and their scale-averaged wavelet power W(t) are analyzed. Wave groupiness is described in terms of two new groupiness parameters, group height GFW and group length GLW, which are defined based on the wavelet transform. The relationship between GFW, GLW and the kurtosis of the wave surface are also given. Detailed analyses show that wave groups play an important role in the process of freak wave generation. The group height parameter GFW reflects the wave train instability well. More unstable wave trains (i.e., those with a larger Benjamin–Feir index) are reflected in larger values of GFW, which gradually increases with wave evolution during wave propagation; however, GLW is not obviously related to wave instability but is associated with the bandwidth of the frequency spectrum. The ratio of GFW to GLW is strongly related to kurtosis, implying that it is a good indicator of freak wave generation.