Higher-order statistics and extreme waves

Abstract

A sparse second-order time-domain Volterra model is used to decompose a random (sea) wave train into its first- and second-order components. Extreme waves are shown to result from short-term phase locking of the first- and second-order components. The feasibility of using a wavelet-based bicoherence "spectrum" to detect the strong, but short lived, phase coupling is investigated. The results are encouraging and suggest the wavelet-based bicoherence is a topic worth considering further.