Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves

A Chabchoub,N Akhmediev,N Hoffmann,M Onorato

doi:10.1103/physrevx.2.011015

Abstract

Super rogue waves with an amplitude of up to 5 times the background value are observed in a water-wave tank for the first time. Nonlinear focusing of the local wave amplitude occurs according to the higher-order breather solution of the nonlinear wave equation. The present result shows that rogue waves can also develop from very calm and apparently safe sea states. We expect the result to have a significant impact on studies of extreme ocean waves and to initiate related studies in other disciplines concerned with waves in nonlinear dispersive media, such as optics, plasma physics, and superfluidity.Received 17 January 2012DOI:https://doi.org/10.1103/PhysRevX.2.011015This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

Highlights

The nature of rogue waves (RWs) has been discussed in the literature for more than a decade [1,2,3,4]
The nonlinear theory predicts that, in addition to the unique fundamental Peregrine soliton, there is an infinite hierarchy of higherorder breather solutions with a progressively increasing amplitude [18,19] that are localized both in space and time
The large amplification of the peak amplitude above the background wave height by a factor of 5 suggests the existence of a new class of waves to be called ‘‘super rogue waves.’’ The second-order RW solution observed in the present study can be considered the first representative of this class

Summary

INTRODUCTION

The nature of rogue waves (RWs) has been discussed in the literature for more than a decade [1,2,3,4]. The nonlinear theory predicts that, in addition to the unique fundamental Peregrine soliton, there is an infinite hierarchy of higherorder breather solutions with a progressively increasing amplitude [18,19] that are localized both in space and time. The study of these solutions is crucial in explaining the even higher amplitude waves that can be observed. These observations may have far reaching consequences in our efforts to understand the waves that are, by far, still being characterized as ‘‘mysterious.’’

MATHEMATICS AND EXPERIMENT

OBSERVATIONS OF THE HIGHER-ORDER ROGUE WAVE

SUMMARY