Cross-waves induced by the vertical oscillation of a fully immersed vertical plate

Capillary waves excited by the vertical oscillations of a thin elongated plate below an air-water interface are analyzed using time-resolved measurements of the surface topography. A parametric instability is observed above a well defined acceleration threshold, resulting in a so-called cross-wave, a staggered wave pattern localized near the wavemaker and oscillating at half the forcing frequency. This cross-wave, which is stationary along the wavemaker but propagative away from it, is described as the superposition of two almost anti-parallel propagating parametric waves making a small angle of the order of $20^\mathrm{o}$ with the wavemaker edge. This contrasts with the classical Faraday parametric waves, which are exactly stationnary because of the homogeneity of the forcing. Our observations suggest that the selection of the cross-wave angle results from a resonant mechanism between the two parametric waves and a characteristic length of the surface deformation above the wavemaker.Comment: to appear in Physics of Fluid

Instability patterns between counter-rotating disks

International audienceThe instability patterns in the flow between counter-rotating disks (radius to height ratio R/h from 3.8 to 20.9) are investigated experimentally by means of visualization and Particle Image Velocimetry. We restrict ourselves to the situation where the boundary layers remain stable, focusing on the shear layer instability that occurs only in the counter-rotating regime. The associated pattern is a combination of a circular chain of vortices, as observed by Lopez et al. (2002) at low aspect ratio, surrounded by a set of spiral arms, first described by Gauthier et al. (2002) in the case of high aspect ratio. Stability curve and critical modes are measured for the whole range of aspect ratios. From the measurement of a local Reynolds number based on the shear layer thickness, evidence is given that a free shear layer instability, with only weak curvature effect, is responsible for the observed patterns. Accordingly, the number of vortices is shown to scale as the shear layer radius, which results from the competition between the centrifugal effects of each disk

Wall effects on granular heap stability

We investigate the effects of lateral walls on the angle of movement and on the angle of repose of a granular pile. Our experimental results for beads immersed in water are similar to previous results obtained in air and to recent numerical simulations. All of these results, showing an increase of pile angles with a decreasing gap width, are explained by a model based on the redirection of stresses through the granular media. Two regimes are observed depending on the bead diameter. For large beads, the range of wall effects corresponds to a constant number of beads whereas it corresponds to a constant characteristic length for small beads as they aggregate via van der Waals forces

Granular Avalanches in Fluids

Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects, and on the grain/fluid density ratio r. In gas (r >> 1 and St > 1, e.g., the dry case), the amplitude and time duration of avalanches do not depend on any fluid effect. In liquids (r ~ 1), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These regimes are described by the analysis of the elementary motion of one grain

Sources and sinks separating domains of left- and right-traveling waves: Experiment versus amplitude equations

In many pattern forming systems that exhibit traveling waves, sources and sinks occur which separate patches of oppositely traveling waves. We show that simple qualitative features of their dynamics can be compared to predictions from coupled amplitude equations. In heated wire convection experiments, we find a discrepancy between the observed multiplicity of sources and theoretical predictions. The expression for the observed motion of sinks is incompatible with any amplitude equation description.Comment: 4 pages, RevTeX, 3 figur

Evidence for directed percolation universality at the onset of spatiotemporal intermittency in coupled circle maps

We consider a lattice of coupled circle maps, a model arising naturally in descriptions of solid state phenomena such as Josephson junction arrays. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation (DP), with the transition being to an unique absorbing state for low nonlinearities, and to weakly chaotic absorbing states for high nonlinearities. We find that the complete set of static exponents and spreading exponents at all critical points match those of DP very convincingly. Further, hyperscaling relations are fulfilled, leading to independent controls and consistency checks of the values of all the critical exponents. These results lend strong support to the conjecture that the onset of STI in deterministic models belongs to the DP universality class.Comment: Submitted to Physical Review