arXiv subjects

Eric Falcon

Publications and source records attributed to Eric Falcon.

At least 55 records · Page 3Linked to original sources

arXiv2019

Observation of the resonance frequencies of a stable torus of fluid

We report the first quantitative measurements of the resonance frequencies of a torus of fluid confined in a horizontal Hele-Shaw cell. By using the unwetting property of a metal liquid, we are able to generate a stable torus of fluid with an arbitrary aspect ratio. When subjected to vibrations, the torus displays azimuthal patterns at its outer periphery. These lobes oscillate radially, and their number n depends on the forcing frequency. We report the instability ''tongues'' of the patterns up to n = 25. These resonance frequencies are well explained by adapting to a fluid torus the usual drop model of Lord Rayleigh. This approach could be applied to the modeling of large-scale structures arisen transiently in vortex rings in various domains.

physics.flu-dyn↗

arXiv2019

Forced three-wave interactions of capillary-gravity surface waves

{Three-wave resonant interactions constitute an essential nonlinear mechanism coupling capillary surface waves. In a previous work, Haudin et al. [Phys. Rev E 93, 043110 (2016)], we have characterized experimentally the generation by this mechanism of a daughter wave, whose amplitude saturates due to the viscous dissipation. Here, we show experimentally the generation of a daughter wave verifying the resonant conditions, but not the dispersion relation.} By modeling the response of the free surface at the lowest nonlinear order, we explain this observation as a forced interaction. {The bandwidth of the linear transfer function of the free surface is indeed increased by the significant viscous dissipation.} The observation of free surface excitations not following the linear dispersion relation then becomes possible. This forced three-wave interaction mechanism could have important consequences for wave turbulence in experimental or natural systems with non negligible dissipation.

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↗

arXiv2018

Turbulence of capillary waves forced by steep gravity waves

We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free-surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness ($0.2-0.3$), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from large scale to small scale. Analysis of temporal fluctuations of spatial spectrum demonstrates that the capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of wave spectrum are found to be in agreement with those of the weakly nonlinear Wave Turbulence Theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with Wave Turbulence Theory. These results suggest that theoretical developments beyond the classic Wave Turbulence Theory are necessary to describe the dynamics and statistics of capillary waves in natural environment. In particular, in presence of broad scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions could be reconsidered.

physics.flu-dyn↗

arXiv2017

Dissipated power within a turbulent flow forced homogeneously by magnetic particles

We report measurements of global dissipated power within a turbulent flow homogeneously forced at small scale by a new forcing technique. The forcing is random in both time and space within the fluid by using magnetic particles in an alternating magnetic field. By measuring the growth rate of the fluid temperature, we show how the dissipated power is governed by the external control parameters (magnetic field, and number N of particles). We experimentally found that the mean dissipated power scales linearly with these parameters, as expected from the magnetic injected power scalings. These experimental results are well described by simple scaling arguments showing that the main origins of the energy dissipation are due to viscous turbulent friction of particles within the fluid and to the inelasticity of collisions. Finally, by measuring the particle collision statistics, we also show that the particle velocity is independent of N, and is only fixed by the magnetic "thermostat".

physics.flu-dyn↗

arXiv2017

Wave turbulence in a two-layer fluid: coupling between free surface and interface waves

We experimentally study gravity-capillary wave turbulence on the interface between two immiscible fluids of close density with free upper surface. We locally measure the wave height at the interface between both fluids by means of a highly sensitive laser Doppler vibrometer. We show that the inertial range of the capillary wave turbulence regime is significantly extended when the upper fluid depth is increased: The crossover frequency between the gravity and capillary wave turbulence regimes is found to decrease whereas the dissipative cut-off frequency of the spectrum is found to increase. We explain these observations by the progressive decoupling between waves propagating at the interface and the ones at the free surface, using the full dispersion relation of gravity-capillary waves in a two-layer fluid of finite depths. The cut-off evolution is due to the disappearance of parasitic capillaries responsible for the main wave dissipation for a single fluid.

physics.flu-dyn↗

arXiv2016

Tuning the resonant frequencies of a drop by a magnetic field

We report an experimental study of a magnetic liquid drop deposited on a superhydrophobic substrate and subjected to vertical vibrations in presence of a static magnetic field. It is well-known that a flattened drop of usual liquid displays oscillating lobes at its periphery when vibrated. By adding ferromagnetic nanoparticles to a water drop and varying the strength of the magnetic field, we are experimentally able to efficiently tune the resonant frequencies of the drop. By using conservation energy arguments, we show that the magnetic field contribution is equivalent to adding an effective negative surface tension to the drop. Our model is found in good agreement with the experiments with no fitting parameter.

physics.flu-dyn↗

arXiv2016

Experimental study of three-wave interactions among capillary-gravity surface waves

In propagating wave systems, three or four-wave resonant interactions constitute a classical non-linear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave-trains and we study their interaction. Using two optical methods, a local one (Laser Doppler Vibrometry) and a spatio-temporal one (Diffusive Light Photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wavenumber. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly non-linear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave-trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

physics.flu-dyn↗

arXiv2015

Transition to a labyrinthine phase in a driven granular medium

Labyrinthine patterns arise in two-dimensional physical systems submitted to competing interactions, ranging from the fields of solid-state physics to hydrodynamics. For systems of interacting particles, labyrinthine and stripe phases were studied in the context of colloidal particles confined into a monolayer, both numerically by means of Monte Carlo simulations and experimentally using superparamagnetic particles. Here we report an experimental observation of a labyrinthine phase in an out-of-equilibrium system constituted of macroscopic particles. Once sufficiently magnetized, they organize into short chains of particles in contact and randomly orientated. We characterize the transition from a granular gas state towards a solid labyrinthine phase, as a function of the ratio of the interaction strength to the kinetic agitation. Spatial local structure is analyzed by means of an accurate particle tracking. Moreover, we explain the formation of these chains using a simple model.

cond-mat.soft↗

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↗

arXiv2014

Direct numerical simulations of capillary wave turbulence

This work presents Direct Numerical Simulations of capillary wave turbulence solving the full 3D Navier Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency in good agreement with weak turbulence theory. By estimating the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction and dissipative times is also observed. These numerical results confirm the validity of weak turbulence approach to quantify out-of equilibrium wave statistics.

physics.flu-dyn↗

arXiv2014

Transition from a dissipative to a quasi-elastic system of particles with tunable repulsive interactions

A two-dimensional system of particles with tunable repulsive interactions is experimentally investigated. Soft ferromagnetic particles are placed on a vibrating rough plate and vertically confined, so that they perform a horizontal Brownian motion in a cell. When immersed in an external vertical magnetic field, the particles become magnetised and thus interact according to a dipolar repulsive law. As the amplitude of the magnetic field is increased, magnetic repulsion raises and the rate of inelastic collisions decreases. Studying the pair correlation function and the particle velocity distributions, we show that the typical properties of such a dissipative out-of-equilibrium granular gas are progressively lost, to approach those expected for a usual gas at thermodynamic equilibrium. For stronger interaction strengths, the system gradually solidifies towards a hexagonal crystal. This new setup could consequently be used as a model experimental system for out-of-equilibrium statistical physics, in which the distance to the quasi-elastic limit can be accurately controlled.

cond-mat.soft↗

arXiv2014

Generation of surface waves by an underwater moving bottom: Experiments and application to tsunami modelling

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes a sudden upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are usually neglected in tsunami warning systems. Our results display good agreement with a prevailing linear theory without fitting parameter. Based on our experimental data, we provide a new theoretical approach for the rapid kinematics limit that is applicable even for non-flat bottoms: a key step since most approaches assume a uniform depth. This approach can be easily appended to tsunami simulations under arbitrary topography.

physics.flu-dyn↗

arXiv2013

Nonlinear waves on the surface of a fluid covered by an elastic sheet

We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the dispersion relation of waves. When the forcing is increased, a significant nonlinear shift of the dispersion relation is observed. We show that this shift is due to an additional tension of the sheet induced by the transverse motion of a fundamental mode of the sheet. When the system is subjected to a random noise forcing at large scale, a regime of hydro-elastic wave turbulence is observed with a power-law spectrum of the scale in disagreement with the wave turbulence prediction. We show that the separation between relevant time scales is well satisfied at each scale of the turbulent cascade as expected theoretically. The wave field anisotropy, and finite size effects are also quantified and are not at the origin of the discrepancy. Finally, the dissipation is found to occur at all scales of the cascade contrary to the theoretical hypothesis, and could thus explain this disagreement.

physics.flu-dyn↗

arXiv2013

Energy flux measurement from the dissipated energy in capillary wave turbulence

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a fluid by changing its viscosity. We observe that the frequency power law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the fluid. Here, we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be non constant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

physics.flu-dyn↗

arXiv2013

Equation of state of a granular gas homogeneously driven by particle rotations

We report an experimental study of a dilute "gas" of magnetic particles subjected to a vertical alternating magnetic field in a 3D container. Due to the torque exerted by the field on the magnetic moment of each particle, a spatially homogeneous and chaotic forcing is reached where only rotational motions are driven. This forcing differs significantly from boundary-driven systems used in most previous experimental studies on non equilibrium dissipative granular gases. Here, no cluster formation occurs, and the equation of state displays strong analogy with the usual gas one apart from a geometric factor. Collision statistics is also measured and shows an exponential tail for the particle velocity distribution. Most of these observations are well explained by a simple model which uncovers out-of-equilibrium systems undergoing uniform "heating".

cond-mat.soft↗

arXiv2013

Space-Time Resolved Capillary Wave Turbulence

We report experiments on the full space and time resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of Diffusing Light Photography associated with a fast camera. Linear and nonlinear dispersion relations are extracted from the spatio-temporal power spectrum of wave amplitude. When wave turbulence regime is reached, we observe power-law spectra both in frequency and in wave number, whose exponents are found in agreement with the predictions of capillary wave turbulence theory. Finally, the temporal dynamics of the spatial energy spectrum highlight the occurrence of stochastic bursts transferring wave energy through the spatial scales.

physics.flu-dyn↗

arXiv2012

Gravity wave turbulence revealed by horizontal vibrations of the container

We experimentally study the role of the forcing on gravity-capillary wave turbulence. Previous laboratory experiments using spatially localized forcing (vibrating blades) have shown that the frequency power-law exponent of the gravity wave spectrum depends on the forcing parameters. By horizontally vibrating the whole container, we observe a spectrum exponent that does not depend on the forcing parameters for both gravity and capillary regimes. This spatially extended forcing leads to a gravity spectrum exponent in better agreement with the theory than by using a spatially localized forcing. The role of the vessel shape has been also studied. Finally, the wave spectrum is found to scale linearly with the injected power for both regimes whatever the forcing type used.

physics.flu-dyn↗