Statistics of rogue waves in isotropic wave fields

Michel, Guillaume; Bonnefoy, Félicien; Ducrozet, Guillaume; Falcon, Éric

doi:10.1017/jfm.2022.436

Cited by 5 publications

(3 citation statements)

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“…Finally, our experimental system, currently limited to cases of linear and nonlinear continuous waves, thus offers a convenient platform to tackle the question of Anderson localization of nonlinear structures (as nonlinearity can be controlled here), such as solitons 41 , 42 , 57 , nonlinear pulses 43 , 44 , 46 , 47 , and the possible existence of solitons within the band gap 58 , 59 . To what extent our work could be linked to the occurrence of extreme waves induced by variable bathymetry is also of primary importance in oceanography 60 – 62 .…”

Section: Discussionmentioning

confidence: 99%

Effects of nonlinearity on Anderson localization of surface gravity waves

Ricard,

Novkoski,

Falcon

2024

Nat Commun

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Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves (optics, microwaves, and acoustics), but whether wave localization is enhanced or weakened for nonlinear waves is a long-standing debate. Here, we show that the nonlinearity strengthens the localization of surface-gravity waves propagating in a canal with a random bottom. We also show experimentally how the localization length depends on the nonlinearity, which has never been reported previously with any type of wave. To do so, we use a full space-and-time-resolved wavefield measurement as well as numerical simulations. The effects of the disorder level and the system’s finite size on localization are also reported. We also highlight the first experimental evidence of the macroscopic analog of Bloch’s dispersion relation of linear hydrodynamic surface waves over periodic bathymetry.

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Section: Discussionmentioning

confidence: 99%

Effects of nonlinearity on Anderson localization of surface gravity waves

Ricard,

Novkoski,

Falcon

2024

Nat Commun

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“…To evaluate the integrations with respect to q, we shall exponentiate the Diracδ in the definition of the cross section (23) and use the inverse Fourier transform of Π in (57). The resulting expression is…”

Section: Derivation Of the Hamiltonian In The Diffusive Limitmentioning

confidence: 99%

“…In relation with geophysical applications, several experiments with fundamental scopes in wave kinetic theory have been recently devised. For instance this led to the very first observation of the regime of inertial wave turbulence in a rotating flow [21], the identification of regimes of weakly and strongly nonlinear internal wave turbulence in an experiment of stratified turbulence [22], experiments on statistical properties of water waves in a large basin [23], the validation of the inverse cascade phenomenon [24], and extension of the range of scales for observing pure gravity wave turbulence in the laboratory [25] using reduced gravity experiments.…”

Section: Introductionmentioning

confidence: 99%

Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium

Onuki,

Guioth,

Bouchet

2023

Preprint

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The wave kinetic equation predicts the averaged temporal evolution of a continuous spectral density of waves either randomly interacting or scattered by the fine structure of a medium. In a wide range of systems, the wave kinetic equation is derived from a fundamental equation of wave motion, which is symmetric through time-reversal. By contrast, the corresponding wave kinetic equations is time-irreversible: its solutions monotonically increase an entropy-like quantity. A similar paradox appears whenever one make a mesoscopic description of the evolution of a very large number of microscopic degrees of freedom, the paradigmatic example being the kinetic theory of dilute gas molecules leading to the Boltzmann equation. Since Boltzmann, it has been understood that a probabilistic understanding solves the apparent paradox. More recently, it has been understood that the kinetic description itself, at a mesoscopic level, should not break time reversal symmetry [1]. The time reversal symmetry remains a fundamental property of the mesoscopic stochastic process: without external forcing the path probabilities obey a detailed balance relation with respect to an equilibrium quasipotential. The proper theoretical or mathematical tool to derive fully this mesoscopic time reversal stochastic process is large deviation theory: a This publication is part of a special issue in homage of the memory of Krzysztof Gawȩdzki. The subject of this work is large deviation theory applied to wave turbulence. Large deviation theory applied to complex dynamics and turbulent flows was one of the subjects for which Krzysztof Gawȩdzki made a number of important contributions during the last few years, see for instance [3][4][5][6][7][8]. He taught many of us, including Freddy Bouchet, many aspects of large deviation theory. We wrote a common paper on the subject of large deviation theory and non-equilibrium quasipotentials for stochastic particles with mean field interactions [8]. Given his scientific qualities, and his deep sense of friendship, it is great pleasure for us to pay homage to Krzysztof Gawȩdzki through this modest contribution.

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