arXiv subjects

Eric Falcon

Publications and source records attributed to Eric Falcon.

At least 19 recordsLinked to original sources

arXiv2026

Experimental evidence of Kelvin wave turbulence along a vortex core

Wave turbulence is a regime of interacting nonlinear waves occurring in most physical systems. Kelvin waves are helical distortions that propagate along vortex filaments and are believed to play a central role in quantum turbulence up to atmospheric vortices. Yet, Kelvin wave turbulence has remained inaccessible to direct experimental observation. Here, we report the first direct experimental observation of Kelvin-wave turbulence along a single vortex filament in a classical fluid under controlled conditions. Using high-resolution spatiotemporal measurements, we resolve Kelvin-wave dynamics over a broad range of scales and obtain wave-amplitude spectra consistent with the predicted weak-turbulence cascade. We identify six-wave resonant interactions as the mechanism driving this energy transfer, providing direct experimental support for a long-standing prediction of weak-turbulence theory. These results establish an experimental platform for investigating energy transport along vortex filaments, with broader implications for both classical and quantum turbulent systems.

physics.flu-dyn↗

arXiv2026

Free-surface deformations induced by three-dimensional turbulence

We report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, we perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (-2.5), suggesting the advection of turbulent structures at the free surface. We develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (-7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold.

physics.flu-dyn↗

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↗

arXiv2026

Finite-system size effects in gravity-capillary wave turbulence

We experimentally investigate the effects of finite-system size on the dynamics of weakly nonlinear random gravity-capillary surface waves. Experiments are conducted in rectangular tanks with varying aspect ratios, in which the fluid surface is perturbed locally and erratically by small, partially submerged magnets. Driven by an oscillating vertical electromagnetic field, these magnets generate a statistically homogeneous and isotropic random wave field. This setup enables us to probe finite-size effects without the dominant influence of global forcing present in horizontally oscillated tanks. Spatiotemporal measurements of the wave field reveal multiple branches in the wave-energy spectrum along the unconfined direction, corresponding to sloshing modes in the confined direction. We show that the spectral properties of these modes can be tuned by varying either the wave steepness or the confinement. Signatures of discrete wave turbulence in the confined direction and mesoscopic continuous wave turbulence in the unconfined direction are observed. As the confinement is gradually relaxed, we further demonstrate a smooth transition from discrete to continuous wave turbulence, consistent with the nonlinear-to-discreteness timescale ratio. Using high-order correlation analysis, we also show that finite-size effects alter wave dynamics by depleting two-dimensional three-wave resonant interactions along the confined direction.

physics.flu-dyn↗

arXiv2026

Collapse of statistical equilibrium in large-scale hydroelastic turbulent waves

At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence, and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among large-scale modes, in line with the Rayleigh-Jeans spectrum. Key open questions now pertain to either the emergence, decay, collapse, or other nonstationary evolutions from this state. Here, we experimentally investigate the free decay of large-scale hydroelastic turbulent waves, initially in a regime of statistical equilibrium. Using space- and time-resolved measurements, we show that the total energy of these large-scale tensional waves decays as a power law in time. We derive an energy decay law from the theoretical initial equilibrium spectrum and the linear viscous damping, as no net energy flux is carried. Our prediction then shows a good agreement with experimental data over nearly two decades in time, for various initial effective temperatures of the statistical equilibrium state. We further identify the dissipation mechanism and confirm it experimentally. Our approach could be applied to other decaying turbulence systems, with the large scales initially in statistical equilibrium.

physics.flu-dyn↗

arXiv2025

Thermodynamics and Statistical Equilibrium of Large-Scale Hydroelastic Wave Turbulence

Understanding how statistical equilibrium can occur in out-of-equilibrium systems is of paramount interest, as it would enable the use of statistical mechanics tools to these systems. Here, we report the first experimental evidence of statistical equilibrium of the large scales of hydroelastic turbulent waves driven by small-scale random forcing. The wave field statistics at scales larger than the forcing scale, resolved in space and time, align well with the predictions of Rayleigh-Jeans equilibrium spectra over more than a decade. We measure zero net energy flux in this regime, as expected. We also determine the effective temperature, entropy, and heat capacity of this nonequilibrium system, demonstrating that classical thermodynamic concepts apply to describe large scales in statistical equilibrium of turbulent systems.

physics.flu-dyn↗

arXiv2024

Soliton Dynamics over a Disordered Topography

We report on the dynamics of a soliton propagating on the surface of a fluid in a 4-m-long canal with a random or periodic bottom topography. Using a full space-and-time resolved wavefield measurement, we evidence, for the first time experimentally, how the soliton is affected by the disorder, in the context of Anderson localization, and how localization depends on nonlinearity. For weak soliton amplitudes, the localization length is found in quantitative agreement with a linear shallow-water theory. For higher amplitudes, this spatial attenuation of the soliton amplitude is found to be enhanced. Behind the leading soliton slowed down by the topography, different experimentally unreported dynamics occur: Fission into backward and forward nondispersive pulses for the periodic case, and scattering into dispersive waves for the random case. Our findings open doors to potential applications regarding ocean coastal protection against large-amplitude waves.

physics.flu-dyn↗

arXiv2024

Freely Decaying Saffman Turbulence Experimentally Generated by Magnetic Stirrers

We investigate experimentally the decay of three-dimensional hydrodynamic turbulence, initially generated by the erratic motions of centimeter-size magnetic stirrers in a closed container. Such zero-mean-flow homogeneous isotropic turbulence is well suited to test Saffman's model and Batchelor's model of freely decaying turbulence. Here, we report a consistent set of experimental measurements (temporal decay of the turbulent kinetic energy, of the energy dissipation rate, and growth of the integral scale) strongly supporting the Saffman model. We also measure the conservation of the Saffman invariant at early times of the decay and show that the energy spectrum scales as $k^{2}$ at large scales and keeps its self-similar shape during the decay. This letter thus presents the first experimental evidence of the validity of the connection between the Saffman invariant and the $k^{2}$-energy spectrum of the large scales. The final decay regime closely corresponds to Saffman's model when the container size is sufficiently large.

physics.flu-dyn↗

arXiv2024

Effects of nonlinearity on Anderson localization of surface gravity waves

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.

cond-mat.dis-nn↗

arXiv2024

Nonlinear dynamics of a hanging string with a freely pivoting attached mass

We show that the natural resonant frequency of a suspended flexible string is significantly modified (by one order of magnitude) by adding a freely pivoting attached mass at its lower end. This articulated system then exhibits complex nonlinear dynamics such as bending oscillations, similar to those of a swing becoming slack, thereby strongly modifying the system resonance that is found to be controlled by the length of the pivoting mass. The dynamics is experimentally studied using a remote and noninvasive magnetic parametric forcing. To do so, a permanent magnet is suspended by a flexible string above a vertically oscillating conductive plate. Harmonic and period-doubling instabilities are experimentally reported and are modeled using the Hill equation, leading to analytical solutions that accurately describe the experimentally observed tonguelike instability curves.

nlin.PS↗

arXiv2024

Experimental study of three-dimensional turbulence under a free surface

In many environmental flows, an air-water free surface interacts with a turbulent flow in the water phase. To mimic this situation, we propose an original experimental setup, based on the Randomly Actuated Synthetic Jet Array (RASJA) forcing used to study turbulence with almost no mean flow. By using a central pump connected to jets, we generate a turbulent flow of tunable intensity, with good isotropy and horizontal homogeneity, up to a maximal turbulent Reynolds number of $8800$. The aim here is to characterize how turbulence is modified by the presence of a free surface. We show that the free surface affects turbulence for fluid depths smaller than the integral length. We report that the turbulent fluctuations become strongly anisotropic when approaching the free surface. The vertical velocity fluctuations decrease close to the surface whereas the horizontal ones increase, as reported in previous theoretical predictions and numerical observations. We also observe a strong enhancement of the amplitude of the temporal and spatial power spectra of the horizontal velocity at large scales, showing the strengthening of these velocity fluctuations near the free surface. Besides, these behaviors are studied for various levels of turbulence.

physics.flu-dyn↗

arXiv2023

A numerical direct scattering method for the periodic sine-Gordon equation

We propose a procedure for computing the direct scattering transform of the periodic sine-Gordon equation. This procedure, previously used within the periodic Korteweg-de Vries equation framework, is implemented for the case of the sine-Gordon equation and is validated numerically. In particular, we show that this algorithm works well with signals involving topological solitons, such as kink or anti-kink solitons, but also for non-topological solitons, such as breathers. It has also the ability to distinguish between these different solutions of the sine-Gordon equation within the complex plane of the eigenvalue spectrum of the scattering problem. The complex trace of the scattering matrix is made numerically accessible, and the influence of breathers on the latter is highlighted. Finally, periodic solutions of the sine-Gordon equation and their spectral signatures are explored in both the large-amplitude (cnoidal-like waves) and low-amplitude (radiative modes) limits.

nlin.PS↗

arXiv2023

Experimental evidence of random shock-wave intermittency

We report the experimental observation of intermittency in a regime dominated by random shock waves on the surface of a fluid. We achieved such a nondispersive surface-wave field using a magnetic fluid subjected to a high external magnetic field. We found that the small-scale intermittency of the wave-amplitude fluctuations is due to shock waves, leading to much more intense intermittency than previously reported in three-dimensional hydrodynamics turbulence or in wave turbulence. The statistical properties of intermittency are found to be in good agreement with the predictions of a Burgerslike intermittency model. Such experimental evidence of random shock-wave intermittency could lead to applications in various fields.

physics.flu-dyn↗

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↗

arXiv2023

Statistics of a 2D immersed granular gas magnetically forced in volume

We present an experimental study of the dynamics of a set of magnets within a fluid in which a remote torque applied by a vertical oscillating magnetic field transfers angular momentum to individual magnets. This system differs from previous experimental studies of granular gas where the energy is injected by vibrating the boundaries. Here, we do not observe any cluster formation, orientational correlation and equipartition of the energy. The magnets' linear velocity distributions are stretched exponentials, similar to 3D boundary-forced dry granular gas systems, but the exponent does not depend on the number of magnets. The value of the exponent of the stretched exponential distributions is close to the value of 3/2 previously derived theoretically. Our results also show that the conversion rate of angular momentum into linear momentum during the collisions controls the dynamics of this homogenously-forced granular gas. We report the differences between this homogeneously-forced granular gas, ideal gas, and nonequilibrium boundary-forced dissipative granular gas.

cond-mat.soft↗

arXiv2023

Evidence of experimental three-wave resonant interactions between two dispersion branches

We report the observation of nonlinear three-wave resonant interactions between two different branches of the dispersion relation of hydrodynamic waves, namely the gravity-capillary and sloshing modes. These atypical interactions are investigated within a torus of fluid for which the sloshing mode can be easily excited. A triadic resonance instability is then observed due to this three-wave two-branch interaction mechanism. An exponential growth of the instability and phase locking are evidenced. The efficiency of this interaction is found to be maximal when the gravity-capillary phase velocity matches the group velocity of the sloshing mode. For a stronger forcing, additional waves are generated by a cascade of three-wave interactions populating the wave spectrum. Such a three-wave two-branch interaction mechanism is probably not restricted to hydrodynamics and could be of interest in other systems involving several propagation modes.

physics.flu-dyn↗

arXiv2023

Transition from wave turbulence to acousticlike shock-wave regime

We report on the experimental observation of a transition from a dispersive wave turbulence regime to a nondispersive regime involving shock waves on the surface of a fluid. We use a magnetic fluid in a canal subjected to an external horizontal magnetic field to tune the dispersivity of the system. For a low magnetic field, gravity-capillary wave turbulence is observed, whereas for a high enough field, random steep coherent structures arise which are found to be shock waves. These shock waves create singularities in the second-order difference of the surface elevation, leading to an $\omega^{-4}$ frequency power spectrum. This spectrum is also found to be controlled by the number and amplitude of the shocks and is well captured by a model based on a random Dirac-$\delta$ distribution (Kuznetsov-like spectrum). Finally, the shock-amplitude statistics exhibits a power-law distribution with an exponent close to the predictions of the one-dimensional random-forced Burgers equation. This shock-wave regime, discovered here for surface waves, thus paves the way to better explore their properties.

physics.flu-dyn↗

arXiv2023

Axisymmetric gravity-capillary standing waves on the surface of a fluid

We report on the experimental study of axisymmetric gravity-capillary standing waves generated by a vertically vibrating ring partially immersed into a fluid. Different regimes of standing waves are highlighted at the basin center depending on the forcing parameters: linear, nonlinear, and ejection regimes. For weak forcing, the standing waves display a resonant response, close to a natural frequency of the circular basin, predicted by the linear theory. For stronger forcing, we observed that the experimental spatial profile of standing waves breaks the up-down symmetry, and is well described by a third-order nonlinear theory. When the forcing is further increased, the maximum height of the axisymmetric wave crest at the basin center is found to increase linearly with its wavelength, due to the saturation of its steepness, a result well captured by a proposed model.

physics.flu-dyn↗