Nonlinearity of abnormal waves by the Hilbert–Huang Transform method

• The nonlinearity of full-scale abnormal wave data is studied by the HHT method.
• The variation of local frequency within one wave is intra-wave frequency modulation.
• The vertical asymmetry is studied in relation to the intra-wave frequency modulation.
• Measure of intra-wave frequency modulation is proposed using instantaneous frequency.
• Larger intra-wave frequency modulation is associated with higher vertical asymmetry.

The nonlinearity of full-scale abnormal wave data is studied by the Hilbert–Huang Transform method. The vertical asymmetry of abnormal waves is examined in relation to the level of the intra-wave frequency modulation of different Intrinsic Mode Functions. The Draupner New Year wave data time series is used as an example of a vertically asymmetric abnormal wave, while record 37 from the hurricane Camille dataset is chosen as an example of a vertically symmetric abnormal wave. A measure of intra-wave frequency modulation is proposed based on the instantaneous frequency variations within one single wave. The study of the variation of local frequency in the vicinity of abnormal waves demonstrates that a larger intra-wave frequency modulation is associated with a higher asymmetry of the wave profile.