Freak Wave Formation from Phase Coherence

This paper describes freak waves by a (pseudo-)maximal wave proposed in [1]. The freak wave is a consequence of a group event that is present in a time signal at some position and contains successive high amplitudes with different frequencies. The linear theory predicts the position and time of the maximal amplitude wave quite well by minimizing the variance of the total wave phase of the given initial signal. The formation of the freak wave is shown to be mainly triggered by the local interaction of waves evolving from the group event that already contained large local energy. In the evolution, the phases become more coherent and the local energy is focussed to develop a larger amplitude. We investigate two laboratory experimental signals, a dispersive focussing wave with harmonic background and a scaled New Year wave. Both signals generate a freak wave at the predicted position and time and the freak wave can be described by a pseudo-maximal wave with specific parameters.