Articles | Volume 23, issue 5
Research article
16 Sep 2016
Research article |  | 16 Sep 2016

Localized coherence of freak waves

Arnida L. Latifah and E. van Groesen

Abstract. This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated: dispersive focusing, normal sea condition, thunderstorm condition and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave.

Short summary
This paper showed the relevance of phase coherence by illustrations of signals with increasingly less restrictions on the phase function. Then the wavelet transform was used to determined the time–frequency spectrum of a time signal. We used the wavelet transform to identify critical group events of the influx signal and it is shown that the group event with the largest local energy signal is the most probable group to generate a freak wave. It gives a local mechanism of a freak wave appearance.