Freak Waves: a Possible Explanation

Abstract

A possible explanation is proposed for the occurrence of freak waves, which are defined as waves with larger heights than expected based on the Rayleigh distribution. The suggested cause is due to nonlinearities of superposition of waves which are not accounted for in the Rayleigh distribution. When two waves combine, if their fundamental components add linearly, it can be shown that the combined wave height increases by more than the sum of the fundamental components. The argument does not address the correctness of linear addition of the fundamental components nor does it include energy closure. An example is presented illustrating the concept.