Emergent rogue wave structures and statistics in spontaneous modulation instability

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.

doi:10.1038/srep10380

Cited by 111 publications

(119 citation statements)

References 33 publications

(45 reference statements)

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“…Heavy-tailed deviations from Gaussianity reported in previous experiments possibly arise from the stochastic generation of SFB that are localized in space and time, such as the PS. So far, this conjecture is supported by numerical simulations of the 1D-NLSE that have shown that some highamplitude coherent structures compatible with some breather solutions of the 1D-NLSE like the PS can spontaneously emerge from a stochastic background 25,28,36,38 .…”

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confidence: 78%

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

et al. 2017

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confidence: 78%

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

et al. 2017

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“…It was already shown that breather dynamics with pulsed excitation can be interpreted in terms of local breather states at different points on the pulse envelope [36,37]. Superregular breathers give an enlarged and generalized picture of the collision features with respect to recent numerical and experimental studies of breather structures and their interactions in optics or hydrodynamics [29][30][31]38].…”

Section: Introductionmentioning

confidence: 99%

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

et al. 2015

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Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the selfmodulation of the continuous "envelope waves" with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

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“…We point out that the unstable Peregrine envelope perturbation is now cloaked in the JONSWAP wave train, which reveals several in wave height similar wave modulations as the Peregrine-type wave packet. Note that MI in JONSWAP random sea states has been discussed in a general context for instance theoretically within the framework of the NLSE and the inverse scattering transform (IST) in [2,26], while numerically in [25,27] and experimentally in [28].…”

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confidence: 99%

Tracking Breather Dynamics in Irregular Sea State Conditions

Chabchoub

2016

Phys. Rev. Lett.

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Breather solutions of the nonlinear Schrödinger equation (NLSE) are known to be considered as backbone models for extreme events in the ocean as well as in Kerr media. These exact determinisitic rogue wave (RW) prototypes on a regular background describe a wide-range of modulation instability configurations. Alternatively, oceanic or electromagnetic wave fields can be of chaotic nature and it is known that RWs may develop in such conditions as well. We report an experimental study confirming that extreme localizations in an irregular oceanic JONSWAP wave field can be tracked back to originate from exact NLSE breather solutions, such as the Peregrine breather. Numerical NLSE as well as modified NLSE simulations are both in good agreement with laboratory experiments and highlight the significance of universal weakly nonlinear evolution equations in the emergence as well as prediction of extreme events in nonlinear dispersive media.Ocean extreme waves, also referred to as freak or rogue waves (RWs), are known to appear without warning and having disastrous impact, in consequence of the substantial large wave heights these can reach [1,2]. Studies on RWs attracted the scientific interest recently due to the interdisciplinary nature of the modulation instability (MI) of weakly nonlinear waves [3][4][5] as well as for the sake of accurate modeling and prediction of these mysterious extremes [6][7][8][9]. Indeed, exact solutions of the nonlinear Schrödinger equation (NLSE) provide backbone models that can be used to describe RWs, providing therefore deterministic numerical and laboratory prototypes to reveal novel insights of MI [10]. Within the vast range of pulsating NLSE solutions on finite background, there is one prominent candidate that is known to have similar physical properties as ocean RWs, namely, the doubly-localized Peregrine breather (PB) [11,12]. Despite the fact that it is theoretically assumed that the modulation period of the PB is infinite, laboratory observations confirmed that a finite number of waves in the background is sufficient to initiate its dynamics in nonlinear dispersive media [13][14][15]. These observations also proved that extreme localizations can be indeed discussed by means of the NLSE, despite violation of the theoretical assumption of the wave field to be or remain narrow-banded.Based on this latest progress, it is reasonable to study the dynamics of breathers, assuming irregularity of the underlying wave field in order to quantify limitations of the approach and to enlarge the scope of possible applications such as in oceanography. In fact, ocean waves' motion can be narrow-banded, such as in the case of swell. However, when winds, currents and wave breaking are at play, the wave field may experience strong irregularities, a state that limits applicability of the NLSE. Nevertheless, recent laboratory experiments showed the persistence of the PB in the presence of strong wind [16] and therefore its physical robustness to perturbations. To the best of our knowledge, the emergence o...

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Emergent rogue wave structures and statistics in spontaneous modulation instability

Cited by 111 publications

References 33 publications

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Tracking Breather Dynamics in Irregular Sea State Conditions

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