arXiv subjects

Félicien Bonnefoy

Publications and source records attributed to Félicien Bonnefoy.

8 recordsLinked to original sources

arXiv2026

Diffraction of deep-water solitons

Solitons are localized nonlinear wave packets that propagate without spreading because nonlinearity balances dispersion. Their robustness is well understood in effectively one-dimensional systems, but introducing additional spatial dimensions is generally expected to destabilize them or destroy their coherent character. Here we experimentally investigate how deep-water gravity-wave solitons behave when a controlled transverse degree of freedom is introduced through diffraction. Using a large-scale water-wave facility, we generate solitonic wave packets whose transverse structure is imposed across a segmented wavemaker through either a sharp slit or a smooth Gaussian apodization. The resulting two-dimensional wave fields are measured with high spatial resolution. Diffraction reshapes the transverse profile of the wave packet while its longitudinal dynamics retain the characteristic features of a soliton. Nonlinear spectral analysis confirms that the solitonic content is preserved along the direction of propagation, whereas the transverse evolution follows the linear Fresnel laws of diffraction. These observations reveal an unexpected coexistence of nonlinear soliton dynamics and classical wave diffraction.

nlin.PS↗

arXiv2023

Interaction of soliton gases in deep-water surface gravity waves

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. We report hydrodynamic experiments in which we investigate the interaction between two "beams" or "jets" of soliton gases having nearly identical amplitudes but opposite velocities of the same magnitude. The space-time evolution of the two interacting soliton gas jets is recorded in a 140-m long water tank where the dynamics is described at leading order by the focusing one-dimensional nonlinear Schrodinger equation. Varying the relative initial velocity of the two species of soliton gas, we change their interaction strength and we measure the macroscopic soliton gas density and velocity changes due to the interaction. Our experimental results are found to be in good quantitative agreement with predictions of the spectral kinetic theory of soliton gas despite the presence of perturbative higher-order effects that break the integrability of the wave dynamics.

nlin.PS↗

arXiv2022

Statistics of rogue waves in isotropic wave fields

We investigate the statistics of rogue waves occurring in the inverse cascade of surface gravity wave turbulence. In such statistically homogeneous, stationary and isotropic wave fields, low-frequency waves are generated by nonlinear interactions rather than directly forced by a wave maker. This provides a laboratory realization of arguably the simplest nonlinear sea state, in which long-time acquisitions are performed and compared with theoretical models. The analysis of thousands of rogue waves reveals that some of their properties crucially depend on four-wave resonant interactions, large crests being for instance more likely than predicted by second-order models.

physics.flu-dyn↗

arXiv2020

Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. Despite significant theoretical developments and observational evidence of ubiquity of soliton gases in fluids and optical media their controlled experimental realization has been missing. We report the first controlled synthesis of a dense soliton gas in deep-water surface gravity waves using the tools of nonlinear spectral theory (inverse scattering transform (IST)) for the one-dional focusing nonlinear Schrödinger equation. The soliton gas is experimentally generated in a one-dimensional water tank where we demonstrate that we can control and measure the density of states, i. e. the probability density function parametrizing the soliton gas in the IST spectral phase space. Nonlinear spectral analysis of the generated hydrodynamic soliton gas reveals that the density of states slowly changes under the influence of perturbative higher-order effects that break the integrability of the wave dynamics.

nlin.PS↗

arXiv2020

From modulational instability to focusing dam breaks in water waves

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wavepacket towards the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semi-classical limit of the 1D focusing nonlinear Schrodinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semi-classical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

nlin.PS↗

arXiv2019

CN-Stream: Open-source library for nonlinear regular waves using stream function theory

CN-Stream is a library for the computation of nonlinear regular ocean waves. The library is developed in order to be easily integrated with wave generation models in CFD solvers. It is based on the stream function theory and provides significant improvements regarding the applicability of the method for waves close to breaking (in deep or shallow water) compared to the classical implementation of Rienecker and Fenton [26]. The complete description of the wave field is available, including the free-surface evolution and the wave kinematics in the fluid domain. It is released as open-source, developed and distributed under the terms of GPL v3.

physics.flu-dyn↗

arXiv2018

Coexistence of solitons and extreme events in deep water surface waves

We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave background. Such a coexistence is expected by the integrable turbulence theory for the nonlinear Schr{ö}dinger equation (NLSE), and we report the first experimental observation in the context of hydrodynamic waves. We characterize the formation, the properties and the dynamics of these nonlinear coherent structures (solitons and extreme events) within the incoherent wave background. The extreme events result from the strong steepening of wave train fronts, and their emergence occurs after roughly one nonlinear length scale of propagation (estimated from NLSE). Solitons arise when nonlinearity and dispersion are weak, and of the same order of magnitude as expected from NLSE. We characterize the statistical properties of this state. The number of solitons and extreme events is found to increase all along the propagation, the wave-field distribution has a heavy tail, and the surface elevation spectrum is found to scale as a frequency power-law with an exponent --4.5 $\pm$ 0.5. Most of these observations are compatible with the integrable turbulence theory for NLSE although some deviations (e.g. power-law spectrum, asymmetrical extreme events) result from effects proper to hydrodynamic waves.

nlin.PS↗

arXiv2015

Role of the basin boundary conditions in gravity wave turbulence

Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. Quasi-one dimensional field of nonlinear waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4, which is the value predicted by the weak turbulence theory. The physical mechanisms involved are probably different according to the boundary condition used, but cannot be easily discriminated with only temporal measurements. We have also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with a recent theoretical value.

physics.flu-dyn↗