arXiv subjects

Eric Falcon

Publications and source records attributed to Eric Falcon.

At least 37 records · Page 2Linked to original sources

arXiv2022

Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence

We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the fluid using centimetric magnetic particles. We measure the statistics of the fluid velocity field at scales larger than the forcing scale (energy spectra, velocity distributions, and energy flux spectrum). In particular, we show that the large-scale dynamics are in statistical equilibrium and can be described with an effective temperature, although not isolated from the turbulent Kolmogorov cascade. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. Our work paves the way to use equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.

physics.flu-dyn↗

arXiv2022

Wave spectroscopy in a driven granular material

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we study fluid-like and crystal-like two-dimensional states in a driven granular material. In our experimental device, a tunable magnetic field induces and controls remote interactions between the granular particles. We use high-speed video recordings to analyse the velocity fluctuations of individual particles in stationary regime. Using statistical averaging, we find that the particles self-organize into collective excitations characterized by dispersion relations in the frequency-wavenumber space. These findings thus reveal that mechanical waves analogous to condensed matter phonons propagate in driven granular media. When the magnetic coupling is weak, the waves are longitudinal, as expected for a fluid-like phase. When the coupling is stronger, both longitudinal and transverse waves propagate, which is typically seen in solid-like phases. We model the dispersion relations using the spatial distribution of particles and their interaction potential. Finally, we infer the elastic parameters of the granular assembly from equivalent sound velocities, thus realizing the spectroscopy of a granular material.

cond-mat.soft↗

arXiv2022

Experimental observation of periodic Korteweg-de Vries solitons along a torus of fluid

We report on the experimental observation of solitons propagating along a torus of fluid. We show that such a periodic system leads to significant differences compared to the classical plane geometry. In particular, we highlight the observation of subsonic elevation solitons, and a nonlinear dependence of the soliton velocity on its amplitude. The soliton profile, velocity, collision, and dissipation are characterized using high resolution space-time measurements. By imposing periodic boundary conditions onto Korteweg-de Vries (KdV) equation, we recover these observations. A nonlinear spectral analysis of solitons (periodic inverse scattering transform) is also implemented and experimentally validated in this periodic geometry. Our work thus reveals the importance of periodicity for studying solitons and could be applied to other fields involving periodic systems governed by a KdV equation.

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↗

arXiv2022

Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence

We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillarywave turbulence to anisotropic magneto-capillary wave turbulence is observed for an increasing field. At high enough field, wave turbulence becomes highly anisotropic, cascading mainly perpendicularly to the field direction, in good agreement with the prediction of a phenomenological model, and with anisotropic Alfv{é}n wave turbulence. Although surface waves on a magnetic fluid are different from Alfv{é}n waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.

physics.plasm-ph↗

arXiv2021

Three-dimensional turbulence generated homogeneously by magnetic particles

Three-dimensional turbulence is usually studied experimentally by using a spatially localized forcing at large scales (e.g. via rotating blades or oscillating grids), often in a deterministic way. Here, we report an original technique where the fluid is forced in volume, randomly in space and time, using small magnetic particles remotely driven. Such a forcing generates almost no mean flow and is closer to those of direct numerical simulations of isotropic homogeneous turbulence. We compute the energy spectra and structure functions using local and spatiotemporal flow velocity measurements. The energy dissipation rate is also evaluated consistently in five different ways. Our experimental results confirm the stationary, homogeneous and isotropic features of such turbulence, and in particular the Tennekes' model for which the Tennekes' constant is experimentally estimated.

physics.flu-dyn↗

arXiv2021

Experimental quasi-1D capillary-wave turbulence

Wave turbulence in quasi-1D geometry is usually not investigated experimentally since low-order resonant wave interactions are theoretically prohibited. Here, we report on the first observation of unidirectional capillary-wave turbulence on the surface of a fluid in a canal. We also show that five-wave interactions are the lowest-order resonant process subsisting at small scales, and are thus probably the one generating such quasi-1D capillary wave turbulence. We show that the wave spectrum is compatible with the corresponding dimensional analysis prediction. The main assumptions of weak turbulence theory are also verified experimentally. Quasi-1D wave turbulence could be thus highlighted in other fields of wave turbulence.

physics.flu-dyn↗

arXiv2021

Experimental Dispersion Relation of Surface Waves Along a Torus of Fluid

We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatio-temporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous and sloshing modes. Standing azimuthal waves are also studied leading to polygon-like patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.

nlin.PS↗

arXiv2021

Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering

Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. As an exact breather solution of the one-dimensional focusing nonlinear Schrödinger equation with nonzero boundary conditions, the PS can be viewed as a soliton on finite background, i.e. a nonlinear superposition of a soliton and a monochromatic wave. A recent mathematical work showed that both nonzero boundary conditions and solitonic content are not pre-requisites for the PS occurrence. Instead, it has been demonstrated that PS can emerge locally, as an asymptotic structure arising from the propagation of an arbitrary large decaying pulse, independently of its solitonic content. This mathematical discovery has changed the widely accepted paradigm of the solitonic nature of rogue waves by enabling the PS to emerge from a partially radiative or even completely solitonless initial data. In this work, we realize the mathematically predicted universal mechanism of the local PS emergence in a water tank experiment with a particular aim to control the point of the PS occurrence in space-time by imposing an appropriately chosen initial chirp. By employing the inverse scattering transform for the synthesis of the initial data, we are able to engineer a localized wave packet with a prescribed solitonic and radiative content. This enabled us to control the position of the emergence of the rogue wave by adjusting the inverse scattering spectrum. The proposed method of the nonlinear spectral engineering is found to be robust to higher-order nonlinear effects inevitable in realistic wave propagation conditions.

nlin.PS↗

arXiv2021

Experiments in Surface Gravity-Capillary Wave Turbulence

The last decade has seen a significant increase in the number of studies devoted to wave turbulence. Many deal with water waves, as modeling of ocean waves has historically motivated the development of weak turbulence theory, which adresses the dynamics of a random ensemble of weakly nonlinear waves in interaction. Recent advances in experiments have shown that this theoretical picture is too idealized to capture experimental observations. While gravity dominates much of the oceanic spectrum, waves observed in the laboratory are in fact gravity-capillary waves, due to the restricted size of wave basins. This richer physics induces many interleaved physical effects far beyond the theoretical framework, notably in the vicinity of the gravity-capillary crossover. These include dissipation, finite-system size effects, and finite nonlinearity effects. Simultaneous space-and-time resolved techniques, now available, open the way for a much more advanced analysis of these effects.

physics.flu-dyn↗

arXiv2021

Nonlinear dispersion relation in integrable turbulence

The concept of Nonlinear dispersion relation (NDR) is used in various fields of Physics (nonlinear optics, hydrodynamics, hydroelasticity, mechanics, quantum optics, plasma physics,...) to characterize fundamental phenomena induced by nonlinearity such as wave frequency shift or turbulence. Nonlinear random waves described by the onedimensional nonlinear Schrodinger equation (1DNLSE) exhibit a remarkable form of turbulence called "integrable turbulence" where solitons play a key role. Surprisingly, little attention has been paid to the NDR of such universal wave systems up to a very recent theoretical study. Here, by using an original strategy, we report the accurate measurement of NDR of the slowly varying envelop of the waves in one-dimensional deep water waves experiments. We characterize precisely the frequency shift and the broadening of the NDR, which interestingly reveals the presence of solitons and of high order effects. Our results highlight the relevance of the NDR in the context of integrable turbulence.

physics.flu-dyn↗

arXiv2020

Numerical Simulation of Collinear Capillary-Wave Turbulence

We report on direct numerical simulation of quasi-one-dimensional bidirectional capillary-wave turbulence. Although nontrivial three-wave and four-wave resonant interactions are absent in this peculiar geometry, we show that an energy transfer between scales still occurs concentrated around the linear dispersion relation that is broadened by nonlinearity. The wave spectrum displays a clear wave number power-law scaling that is found to be in good agreement with the dimensionally prediction for capillary-wave turbulence involving four-wave interactions. The carried out high-order correlation analysis (bicoherence and tricoherence) confirms quantitatively the dominant role of four-wave quasi-resonant interactions. The Kolmogorov-Zakharov spectrum constant is also estimated numerically. We interpret our results as the first numerical observation of anisotropic capillary-wave turbulence in which four-wave interactions play a dominant role

physics.flu-dyn↗

arXiv2020

Saturation of the inverse cascade in surface gravity wave turbulence

We report on the observation of surface gravity wave turbulence at scales larger than the forcing ones in a large basin. In addition to the downscale transfer usually reported in gravity wave turbulence, an upscale transfer is observed, interpreted as the inverse cascade of weak turbulence theory. A steady state is achieved when the inverse cascade reaches a scale in between the forcing wavelength and the basin size, but far from the latter. This inverse cascade saturation, which depends on the wave steepness, is probably due to the emergence of nonlinear dissipative structures such as sharp-crested waves.

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↗

arXiv2020

Tuning the distance to the equipartition by controlling the collision rate in a driven granular gas experiment

In a granular gas experiment of magnetized particles confined in a thin layer, the rate of dissipative collisions is tuned by adjusting the amplitude of an external magnetic field. The velocity statistics are analyzed using the dynamic and static structure factors of transverse velocity modes. Using the fluctuating hydrodynamics theory we measure the deviation from kinetic energy equipartition in this out-of-equilibrium system as a function of the dissipative collision rate. When the collision rate is decreased, the distance to equipartition becomes smaller meaning that the dynamical properties of this granular gas approach by analogy those of a molecular gas in thermal equilibrium.

cond-mat.soft↗

arXiv2020

Capillary wave turbulence experiments in microgravity

Using the FLUIDICS (Fluid Dynamics in Space) experiment in the International Space Station, turbulence of capillary waves at the air-water interface is experimentally investigated in weightlessness. Capillary waves are excited in a spherical container partially filled with water and undergoing sinusoidal or random oscillations. The fluctuations of the interface, recorded with two capacitive probes are analyzed by means of the frequency power spectrum of wave elevation. For high enough forcing amplitudes, we report power-law spectra with exponents close to the prediction of weak wave turbulence theory. However, in this experiment the free-surface steepness is not small compared to 1 and thus the investigated regimes correspond to strongly nonlinear wave turbulence.

physics.flu-dyn↗

arXiv2019

Wave turbulence on the surface of a fluid in a high-gravity environment

We report on the observation of gravity-capillary wave turbulence on the surface of a fluid in a high-gravity environment. By using a large-diameter centrifuge, the effective gravity acceleration is tuned up to 20 times the Earth gravity. The transition frequency between the gravity and capillary regimes is thus increased up to one decade as predicted theoretically. A frequency power-law wave spectrum is observed in each regime and is found to be independent of the gravity level and of the wave steepness. While the timescale separation required by weak turbulence is well verified experimentally regardless of the gravity level, the nonlinear and dissipation timescales are found to be independent of the scale, as a result of the finite size effects of the system (large-scale container modes) that are not taken currently into account theoretically.

physics.flu-dyn↗