Albert Libchaber

Scaling of hard thermal turbulence in Rayleigh-Bénard convection

An experimental study of Rayleigh-Benard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 10 7 Ra 12 ) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra . However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu , proportional to

Quasi-periodicity and dynamical systems: An experimentalist's view

Ra^{\frac{1}{3}}

An Experimental Study of the Saffman Taylor Instability

while experiment gives an index much closer to

Coherent structures in turbulent convection, an experimental study

\frac{2}{7}

The Dynamics and Interaction of Laminar Thermal Plumes

. A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.

Experimental Study of the Attractor of a Driven Rayleigh-Bénard System

Current theoretical and experimental work on quasiperiodicity is reviewed in this tutorial. The concept of universality and its relevance to experiments on nonlinear multifrequency systems is discussed. The reduction of experimental data using Poincare sections and the mathematical properties of the one-dimensional circle map are considered. Various dynamical systems technique for determining scaling and multifractal properties as well as other more traditional methods of analysis, are presented. Experimental observations that would support or refute the one-dimensional circle map model are emphasized. Experimental results are summarized, with emphasis on forced Rayleigh-Benard convection and solid-state systems. Accomplishments and open problems of the dynamical systems theory of quasiperiodicity are outlined. >

Turbulent convection in helium gas

When a gas is pushed into a viscous fluid through a Hele-Shaw cell, one observes, after a long transient, the formation of a finger which propagates steadily along the channel. This simple situation defines the Saffman Taylor1 problem. In spite of its simplicity, the limiting sizes of those fingers at large velocities and their stability has not been understood for a long time. A particularly striking fact observed in the experiments is that fingers occupy about one-half of the channel width at large velocities. In the model of Saffman and Taylor1, where surface tension is neglected, all finger sizes are allowed. Moreover, fingers of size 1/2 are found linearly unstable, which is also in direct conflict with experiment. The problem was then to understand how surface tension acts to select finger sizes and to ensure stability.

About thermal turbulence

We present results from a visualization experiment in Rayleigh-Benard convection in water at high Rayleigh number. We distinguish three kinds of coherent structures in the flow: waves along the boundary layers, plumes, and spiraling swirls. The waves originate from the interaction of plumes with the boundary layers. The spiraling swirls appear to be the result of a shear instability of the viscous boundary layer. We describe the “life cycle” of these structures in the cell, and when we focus on the waves and characterize them quantitatively using local temperature measurements.

Directional Solidification of Liquid Crystals

We present an experimental study of the dynamics and interactions of laminar plumes emitted from a localized heat source. The observations are explained by a simple model of the flow structure around a plume. Using sources and sinks in a uniform flow, we reproduce the experimental shapes and extract the scaling behavior of the size of the plume. The model describes the initial stage of the interaction between plumes.

Global University at the onset of chaos: Results of a forced Rayleigh-Bénard experiment☆

We present a study of the geometrical and measure properties of attractors generated by Rayleigh-Benard convection with two oscillators present. One oscillator was induced by the flow while the second was imposed externally. The winding number was tuned to two different irrational numbers. The evolution of the attractors with increasing non-linear coupling between the oscillators was examined. Their dynamical properties were extracted and compared with those of circle maps.