arXiv subjects

Eric Falcon

Publications and source records attributed to Eric Falcon.

At least 73 records · Page 4Linked to original sources

arXiv2012

Decay of capillary wave turbulence

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent than the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.

physics.flu-dyn↗

arXiv2011

Instability of the origami of a ferrofluid drop in a magnetic field

Capillary origami is the wrapping of an usual fluid drop by a planar elastic membrane due to the interplay between capillary and elastic forces. Here, we use a drop of magnetic fluid whose shape is known to strongly depend on an applied magnetic field. We study the quasi-static and dynamical behaviors of such a magnetic capillary origami. We report the observation of an overturning instability that the origami undergoes at a critical magnetic field. This instability is triggered by an interplay between magnetic and gravitational energies in agreement with the theory presented here. Additional effects of elasticity and capillarity on this instability are also discussed.

physics.flu-dyn↗

arXiv2011

Experimental study of the inverse cascade in gravity wave turbulence

We perform experiments to study the inverse cascade regime of gravity wave turbulence on the surface of a fluid. Surface waves are forced at an intermediate scale corresponding to the gravity-capillary wavelength. In response to this forcing, waves at larger scales are observed. The spectrum of their amplitudes exhibits a frequency-power law at high enough forcing. Both observations are ascribed to the upscale wave action transfers of gravity wave turbulence. The spectrum exponent is close to the value predicted by the weak turbulence theory. The spectrum amplitude is found to scale linearly with the mean injected power. We measure also the distributions of the injected power fluctuations in the presence of upscale (inverse) transfers or in the presence of a downscale (direct) cascade in gravity wave turbulence.

physics.flu-dyn↗

arXiv2011

Observation of depth-induced properties in wave turbulence on the surface of a fluid

We report the observation of changes in the wave turbulence properties of gravity-capillary surface waves due to a finite depth effect. When the fluid depth is decreased, a hump is observed on the wave spectrum in the capillary regime at a scale that depends on the depth. The possible origin of this hump is discussed. In the gravity regime, the wave spectrum still shows a power law but with an exponent that strongly depends on the depth. A change in the scaling of the gravity spectrum with the mean injected power is also reported. Finally, the probability density function of the wave amplitude rescaled by its rms value is found to be independent of the fluid depth and to be well described by a Tayfun distribution.

physics.flu-dyn↗

arXiv2011

Wave turbulence on the surface of a ferrofluid in a horizontal magnetic field

We report observations of wave turbulence on the surface of a ferrofluid submitted to a magnetic field parallel to the fluid surface. The magnetic wave turbulence shows several differences compared to the normal field case reported recently. The inertial zone of the magnetic wave turbulence regime is notably found to be strongly increased with respect to the normal field case, and to be well described by our theoretical predictions. The dispersion relation of linear waves is also measured and differs from the normal field case due to the absence of the Rosensweig instability.

physics.flu-dyn↗

arXiv2010

Observation of nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid

We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space using an optical method. The full space-time power spectrum shows that the wave energy is localized on several branches in the wave-vector-frequency space. The number of branches depend on the power injected within the waves. The measurement of the nonlinear dispersion relation is found to be well described by a law suggesting that the energy transfer mechanisms involved in wave turbulence are not only restricted to purely resonant interaction between nonlinear waves. The power-law scaling of the spatial spectrum and the probability distribution of the wave amplitudes at a given wave number are also measured and compared to the theoretical predictions.

physics.flu-dyn↗

arXiv2010

Revealing intermittency in experimental data with steep power spectra

The statistics of signal increments are commonly used in order to test for possible intermittent properties in experimental or synthetic data. However, for signals with steep power spectra [i.e., $E(ω) \sim ω^{-n}$ with $n \geq 3$], the increments are poorly informative and the classical phenomenological relationship between the scaling exponents of the second-order structure function and of the power spectrum does not hold. We show that in these conditions the relevant quantities to compute are the second or higher degree differences of the signal. Using this statistical framework to analyze a synthetic signal and experimental data of wave turbulence on a fluid surface, we accurately characterize intermittency of these data with steep power spectra. The general application of this methodology to study intermittency of experimental signals with steep power spectra is discussed.

physics.data-an↗

arXiv2010

On the origin of intermittency in wave turbulence

Using standard signal processing tools, we experimentally report that intermittency of wave turbulence on the surface of a fluid occurs even when two typical large-scale coherent structures (gravity wave breakings and bursts of capillary waves on steep gravity waves) are not taken into account. We also show that intermittency depends on the power injected into the waves. The dependence of the power-law exponent of the gravity-wave spectrum on the forcing amplitude cannot be also ascribed to these coherent structures. Statistics of these both events are studied.

physics.flu-dyn↗

arXiv2010

Axisymmetric solitary waves on the surface of a ferrofluid

We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of axisymmetric linear waves propagating on the cylindrical ferrofluid layer that are found in good agreement with theoretical predictions.

physics.flu-dyn↗

arXiv2010

Laboratory Experiments on Wave Turbulence

This review paper is devoted to a presentation of recent progress in wave turbulence. I first present the context and state of the art of this field of research both experimentally and theoretically. I then focus on the case of wave turbulence on the surface of a fluid, and I discuss the main results obtained by our group: caracterization of the gravity and capillary wave turbulence regimes, the first observation of intermittency in wave turbulence, the occurrence of strong fluctuations of injected power in the fluid, the observation of a pure capillary wave turbulence in low gravity environment and the observation of magnetic wave turbulence on the surface of a ferrofluid. Finally, open questions in wave turbulence are discussed.

physics.flu-dyn↗

arXiv2009

Two-Dimensional Melting of a Crystal of Ferrofluid Spikes

We report the observation of the transition from an ordered solid-like phase to a disordered liquid-like phase of a lattice of spikes on a ferrofluid surface submitted to horizontal sinusoidal vibrations. The melting transition occurs for a critical spike displacement which is experimentally found to follow the Lindemann criterion, for two different lattice topologies (hexagonal and square) and over a wide range of lattice wavelengths. An intermediate hexatic-like phase between the solid and isotropic liquid phases is also observed and characterized by standard correlation functions. This dissipative out-of-equilibrium system exhibits strong similarities with 2D melting in solid-state physics.

cond-mat.soft↗

arXiv2009

Fluctuations of energy flux in a simple dissipative out-of-equilibrium system

We report the statistical properties of the fluctuations of the energy flux in an electronic RC circuit driven with a stochastic voltage. The fluctuations of the power injected in the circuit are measured as a function of the damping rate and the forcing parameters. We show that its distribution exhibits a cusp close to zero and two asymmetric exponential tails, the asymmetry being driven by the mean dissipation. This simple experiment allows to capture the qualitative features of the energy flux distribution observed in more complex dissipative systems. We also show that the large fluctuations of injected power averaged on a time lag do not verify the Fluctuation Theorem even for long averaging time. This is in contrast with the findings of previous experiments due to their small range of explored fluctuation amplitude. The injected power in a system of N components either correlated or not is also studied to mimic systems with large number of particles, such as in a dilute granular gas.

cond-mat.stat-mech↗

arXiv2009

Capillary wave turbulence on a spherical fluid surface in low gravity

We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container which is submitted to random forcing. The surface wave amplitude displays power-law spectrum over two decades in frequency, corresponding to wavelength from $mm$ to a few $cm$. This spectrum is found in roughly good agreement with wave turbulence theory. Such a large scale observation without gravity waves has never been reached during ground experiments. When the forcing is periodic, two-dimensional spherical patterns are observed on the fluid surface such as subharmonic stripes or hexagons with wavelength satisfying the capillary wave dispersion relation.

cond-mat.other↗

arXiv2008

Wave turbulence on the surface of a ferrofluid submitted to a magnetic field

We report the observation of wave turbulence on the surface of a ferrofluid mechanically forced and submitted to a static normal magnetic field. We show that magnetic surface waves arise only above a critical field. The power spectrum of their amplitudes displays a frequency-power law leading to the observation of a magnetic wave turbulence regime which is experimentally shown to involve a 4-wave interaction process. The existence of the regimes of gravity, magnetic and capillary wave turbulence is reported in the phase space parameters as well as a triple point of coexistence of these three regimes. Most of these features are understood using dimensional analysis or the dispersion relation of the ferrohydrodynamics surface waves.

physics.class-ph↗

arXiv2008

Fluctuations of energy flux in wave turbulence

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin type model.

physics.flu-dyn↗

arXiv2007

Some aspects of electrical conduction in granular systems of various dimensions

We report on measurements of the electrical conductivity in both a 2D triangular lattice of metallic beads and in a chain of beads. The voltage/current characteristics are qualitatively similar in both experiments. At low applied current, the voltage is found to increase logarithmically in a good agreement with a model of widely distributed resistances in series. At high enough current, the voltage saturates due to the local welding of microcontacts between beads. The frequency dependence of the saturation voltage gives an estimate of the size of these welded microcontacts. The DC value of the saturation voltage (~ 0.4 V per contact) gives an indirect measure of the number of welded contact carrying the current within the 2D lattice. Also, a new measurement technique provides a map of the current paths within the 2D lattice of beads. For an isotropic compression of the 2D granular medium, the current paths are localized in few discrete linear paths. This quasi-onedimensional nature of the electrical conductivity thus explains the similarity between the characteristics in the 1D and 2D systems.

cond-mat.other↗

arXiv2007

Simulations of dense granular gases without gravity with impact-velocity-dependent restitution coefficient

We report two-dimensional simulations of strongly vibrated granular materials without gravity. The coefficient of restitution depends on the impact velocity between particles by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. Use of this model of restitution coefficient leads to new unexpected behaviors. When the number of particles N is large, a loose cluster appears near the fixed wall, opposite the vibrating wall. The pressure exerted on the walls becomes independent of N, and linear in the vibration velocity V, quite as the granular temperature. The collision frequency at the vibrating wall becomes independent of both N and V, whereas at the fixed wall, it is linear in both N and V. These behaviors arise because the velocity-dependent restitution coefficient introduces a new time scale related to the collision velocity near the cross over from viscoelastic to plastic deformation.

cond-mat.other↗

arXiv2007

Observation of gravity-capillary wave turbulence

We report the observation of the cross-over between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.

cond-mat.other↗