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

Simulations of vibrated granular medium with impact velocity dependent restitution coefficient

We report numerical simulations of strongly vibrated granular materials designed to mimic recent experiments performed both in presence or absence of gravity. The coefficient of restitution used here depends on the impact velocity by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. We show that this model with impact velocity dependent restitution coefficient reproduce results that agree with experiments. We measure the scaling exponents of the granular temperature, collision frequency, impulse, and pressure with the vibrating piston velocity as the particle number increases. As the system changes from a homogeneous gas state at low density to a clustered state at high density, these exponents are all found to decrease continuously with the particle number. All these results differ significantly from classical inelastic hard sphere kinetic theory and previous simulations, both based on a constant restitution coefficient.Comment: to be published in Phys. Rev.

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.Comment: in press in Phys. Rev. E (2011

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.Comment: Europhysics Letters (2014) accepted in EP

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.Comment: Physical Review E (2013) submitted to PR

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.Comment: Journal of Fluid Mechanics (2013

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".Comment: Europhysics Letters (2013) in pres

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.Comment: Physical Review Letters (2014) in pres