Random walks across the sea: the origin of rogue waves?

TL;DR

This paper proposes that linear interference of a finite number of waves can explain rogue ocean waves, with a threshold number of interfering waves determining the likelihood of extreme events, aiding in forecasting.

Contribution

It introduces a model showing linear interference of limited waves can account for rogue waves and suggests nonlinear analysis for estimating wave interference in sea states.

Findings

Linear interference explains heavy tails in wave height distribution.

Threshold of about ten interfering waves determines rogue wave likelihood.

Model enables potential forecasting of extreme ocean waves.

Abstract

Ocean rogue waves are large and suddenly appearing surface gravity waves, which may cause severe damage to ships and other maritime structures. Despite years of research, the exact origin of rogue waves is still disputed. Linear interference of waves with random phase has often been cited as one possible explanation, but apparently does not satisfactorily explain the probability of extreme events in the ocean. Other explanations therefore suggested a decisive role of a nonlinearity in the system. Here we show that linear interference of a finite and variable number of waves may very well explain the heavy tail in the wave height distribution. Our model can explain all prototypical ocean rogue waves reported so far, including the "three sisters" as well as rogue holes. We further suggest nonlinear time series analysis for estimation of the characteristic number of interfering waves for a given sea state. If ocean dynamics is ruled by interference of less than ten waves, rogue waves cannot appear as a matter of principle. In contrast, for larger numbers, their appearance is much more likely than predicted by parameterless models or longterm observation. The pronounced threshold behavior of our model enables effective forecasting of extreme ocean waves.