Sensitivity of convective structures to mean flow boundary conditions: A correlation between symmetry and dynamics

International audienceVarious simple structures have been proposed for modeling the transition to time dependence of convective patterns in extended geometries. In order to further question their relevance to the dynamics of complex structures ͑textures͒, we introduce a change of boundary conditions from both an experimental and a theoretical side. It consists in keeping the same roll structure but in separating the boundaries of the mean flows from those of the roll flows. This induces negligible effects on symmetric structures ͑straight rolls and foci͒ but dramatic changes on asymmetric ones ͑focus pairs and textures͒, especially regarding the onset of time dependence. Both kinds of sensitivity to this change of boundary conditions are recovered from the Cross-Newell equations. They reveal a correlation between symmetry and dynamics that prevents symmetric structures from modeling asymmetric ones. On the opposite side, they point to focus pairs as a plausible prototype of the mechanisms of time-dependence at work in textures

Inhibition of phase turbulence close to onset of convection by permeable lateral boundary condition for the mean flow

International audienceWe show that the mechanisms which govern the onset of time dependence in usual Rayleigh-Bénard convection at low Prandtl number may be inhibited by a suitable choice of the lateral boundary condition for the sole mean flow. We first build a boundary condition which behaves like a rigid one for the roll flow and like a permeable one for the mean flow. We then observe that phase turbulence is inhibited close to the onset of convection. We understand this effect by solving the mean-flow field from the Cross-Newell equations. Our experimental result together with its interpretation demonstrates indirectly the existence of mean flows and enlightens the ways by which mean flows destabilize patterns

Front propagation in a regular vortex lattice : dependence on the vortex structure

International audienceWe investigate the dependence on the vortex structure of the propagation of fronts in stirred flows. For this, we consider a regular set of vortices whose structure is changed by varying both their boundary conditions and their aspect ratios. These configurations are investigated experimentally in autocatalytic solutions stirred by electroconvective flows and numerically from kinematic simulations based on the determination of the dominant Fourier mode of the vortex stream function in each of them. For free lateral boundary conditions, i.e. in an extended vortex lattice, it is found that both the flow structure and the front propagation negligibly depend on vortex aspect ratios. For rigid lateral boundary conditions, i.e. in a vortex chain, vortices involve a slight dependence on their aspect ratios which surprisingly yields a noticeable decrease of the enhancement of front velocity by flow advection. These different behaviors reveal a sensitivity of the mean front velocity on the flow sub-scales. It emphasizes the intrinsic multi-scale nature of front propagation in stirred flows and the need to take into account not only the intensity of vortex flows but also their inner structure to determine front propagation at a large scale. Differences between experiments and simulations suggest the occurrence of secondary flows in vortex chains at large velocity and large aspect ratios

Interaction of multiple particles with a solidification front : from compacted particle layer to particle trapping

The interaction of solidification fronts with objects such as particles, droplets, cells, or bubbles is a phenomenon with many natural and technological occurrences. For an object facing the front, it may yield various fates, from trapping to rejection, with large implications regarding the solidification pattern. However, whereas most situations involve multiple particles interacting with each other and the front, attention has focused almost exclusively on the interaction of a single, isolated object with the front. Here we address experimentally the interaction of multiple particles with a solidification front by performing solidification experiments of a monodisperse particle suspension in a Hele-Shaw cell, with precise control of growth conditions and real-time visualization. We evidence the growth of a particle layer ahead of the front at a close-packing volume fraction and we document its steady state value at various solidification velocities. We then extend single particle models to the situation of multiple particles by taking into account the additional force induced on an entering particle by viscous friction in the compacted particle layer. By a force balance model, this provides an indirect measure of the repelling mean thermomolecular pressure over a particle entering the front. The presence of multiple particles is found to increase it following a reduction of the thickness of the thin liquid film that separates particles and front. We anticipate the findings reported here to provide a relevant basis to understand many complex solidification situations in geophysics, engineering, biology, or food engineering, where multiple objects interact with the front and control the resulting solidification patterns.Comment: 13 pages, 10 figures, submitted to Langmui

Buckling Cascade of Thin Plates: Forms, Constraints and Similarity

We experimentally study compression of thin plates in rectangular boxes with variable height. A cascade of buckling is generated. It gives rise to a self-similar evolution of elastic reaction of plates with box height which surprisingly exhibits repetitive vanishing and negative stiffness. These features are understood from properties of Euler's equation for elastica

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures

Penta-Hepta Defect Motion in Hexagonal Patterns

Structure and dynamics of penta-hepta defects in hexagonal patterns is studied in the framework of coupled amplitude equations for underlying plane waves. Analytical solution for phase field of moving PHD is found in the far field, which generalizes the static solution due to Pismen and Nepomnyashchy (1993). The mobility tensor of PHD is calculated using combined analytical and numerical approach. The results for the velocity of PHD climbing in slightly non-optimal hexagonal patterns are compared with numerical simulations of amplitude equations. Interaction of penta-hepta defects in optimal hexagonal patterns is also considered.Comment: 4 pages, Postscript (submitted to PRL

Continuum-type stability balloon in oscillated granular layers

The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe patterns in a vertically oscillated granular layer. Molecular dynamics simulations show that the mechanism of the skew-varicose instability in granular patterns is similar to that in convection. These results suggest that pattern formation in granular media can be described by continuum models analogous to those used in fluid systems.Comment: 4 pages, 6 ps figs, submitted to PR

Chaotic advection and targeted mixing

The advection of passive tracers in an oscillating vortex chain is investigated. It is shown that by adding a suitable perturbation to the ideal flow, the induced chaotic advection exhibits two remarkable properties compared with a generic perturbation : Particles remain trapped within a specific domain bounded by two oscillating barriers (suppression of chaotic transport along the channel), and the stochastic sea seems to cover the whole domain (enhancement of mixing within the rolls)

Mean flow and spiral defect chaos in Rayleigh-Benard convection

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. Firstly, we show that, in the absence of mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wavenumbers that approach those uniquely selected by focus-type singularities, which, in the absence of mean flow, lie at the zig-zag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with Rayleigh number.Comment: 14 pages, 19 figure