Freak Sea Waves and Group Structure

Abstract— Based on data from direct wave measurements conducted in the Black Sea, the statistical relationship between the parameters of freak waves and those characterizing the group structure is analyzed. The existence of statistical relationships between the abnormality index (AI), which characterize the probability of the occurrence of abnormally high waves, and the groupiness factor (GF), which characterizes the relative change in wave heights within a group, is shown. The correlation coefficient between GF and AI reaches 0.3. It is noted that although the process of the appearance of freak waves formation of the group structure are associated with the modulation instability of Stokes waves (Benjamin–Fair instability), no statistical relationship is observed between the parameters GF and AI and the Benjamin–Fair index (BFI). The correlation coefficient between the BFI and the excess kurtosis of surface elevations is 0.07, and between BFI and skewness is 0.37.