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  • Open Access

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

A. Chabchoub1,*, N. Hoffmann1, M. Onorato2,3, and N. Akhmediev4

  • 1Mechanics and Ocean Engineering, Hamburg University of Technology Eißendorfer Straße 42, 21073 Hamburg, Germany
  • 2Dipartimento di Fisica, Università degli Studi di Torino, Torino 10125, Italy
  • 3Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, Torino 10125, Italy
  • 4Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia

  • *amin.chabchoub@tuhh.de
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Phys. Rev. X 2, 011015 – Published 29 March, 2012

DOI: https://doi.org/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.

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Oceanic rogue waves are relatively large surface waves that appear spontaneously far at sea. They can suddenly develop from very calm and apparently safe sea states, cause serious damage to ships or offshore structures, and then disappear without a trace. Where these apparent anomalies come from is still a puzzle for scientists. A simple theoretical model for describing the evolution of these waves is a nonlinear Schrödinger equation. This equation, due to its nonlinearity, has a set of hierarchically ordered solutions known as rational breathers, or evolving solitons growing out of, and amplifying, a small localized wave perturbation. Recently, we created the lowest order rational breather, also known as the Peregrine soliton, in a laboratory-scale water tank. One open question was then: Could higher-order strongly amplifying breathers, or super rogue waves, be generated also in such a water tank? In this paper, we combine an experiment with the theory to show that the answer is an affirmative “yes.”

To generate these solutions in an open water tank, we start with a carrier wave that is a wave-tank analogue of the stable small ocean waves. The mathematical initial conditions describing small localized perturbations for the generation of the higher-order breathers are simulated exactly with a computer controlled paddle and stage-wise experiments are carefully designed to remove artifacts or get around the constraints imposed by the limited size of the tank. Indeed, large localized waves with an amplification factor of 5—super rogue waves in this laboratory setting—grow out of the small perturbation in the manner predicted by the equation.

We believe that our work not only suggests an easily accessible platform for exploring extreme water-wave dynamics, but may also stimulate similar experimental studies on high-order breather solutions in other fields such as optics, plasma physics, and superfluidity where nonlinear dynamics rules.

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Phys. Rev. X 2, 011015– Published 29 March, 2012
  • Received 17 January 2012
Article part of CHORUS
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This 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.

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