Succession of Resonances to Achieve Internal Wave Turbulence.

We study experimentally the interaction of nonlinear internal waves in a stratified fluid confined in a trapezoidal tank. The setup has been designed to produce internal wave turbulence from monochromatic and polychromatic forcing through three processes. The first is a linear transfer in wavelength obtained by wave reflection on inclined slopes, leading to an internal wave attractor which has a broad wave number spectrum. Second is the broadbanded time-frequency spectrum of the trapezoidal geometry, as shown by the impulse response of the system. The third one is a nonlinear transfer in frequencies and wave vectors via triadic interactions, which results at large forcing amplitudes in a power law decay of the wave number power spectrum. This first experimental spectrum of internal wave turbulence displays a k^{-3} behavior.

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 Rayleigh. This approach could be applied to the modeling of large-scale structures arisen transiently in vortex rings in various domains.

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

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear 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 spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. 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 nonlinear 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.

Transition to a labyrinthine phase in a driven granular medium.

Labyrinthine patterns arise in two-dimensional physical systems submitted to competing interactions, in fields ranging from 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. The spatial local structure is analyzed by means of accurate particle tracking. Moreover, we explain the formation of these chains using a simple model.

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

Capillary origami is the wrapping of a 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 quasistatic 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.