Yuchou Hu

Apparatus for the study of Rayleigh–Bénard convection in gases under pressure

We review the history of experimental work on Rayleigh–Benard convection in gases, and then describe a modern apparatus that has been used in our experiments on gas convection. This system allows for the study of patterns in a cell with an aspect ratio (cell radius/fluid layer depth) as large as 100, with the cell thickness uniform to a fraction of a μm, and with the pressure controlled at the level of one part in 105. This level of control can yield a stability of the critical temperature difference for the convective onset of better than one part in 104. The convection patterns are visualized and the temperature field can be inferred using the shadowgraph technique. We describe the flow visualization and image processing necessary for this. Some interesting results obtained with the system are briefly summarized.

Experiments on three systems with non-variational aspects

Abstract We present recent experimental results for three pattern-forming systems in which non-variational effects play an important role. The first is thermal convection in a shallow horizontal layer of fluid with temperature-dependent properties. In this system, a hexagonal lattice of convection cells forms at onset. This lattice becomes unstable to rolls when the temperature difference is increased sufficiently. In the “roll” state, the roll are curved and the system forms stable rotating spirals. The rotating spiral states are associated with non-variational effects. Secondly, we discuss the formation of localized pulses in binary-mixture convection near onset. These pulses would not exist in a potential system. In narrow channels, they have been observed as stable states. In systems which are spatially extended in two dimensions they can form spontaneously, and can be long-lived. The third topic which we discuss is the Kuppers-Lortz instability in a thin horizontal layer of a Boussinesq fluid heated from below and rotated about a vertical axis. In this case, the pattern which forms immediately above the onset of convection is non-periodically time dependent even though the amplitude grows continuously from zero as the temperature difference is increased. The dominant mechanism of the instability is found to involve the motion of boundaries between coherent regions of convection rolls of a given orientation. The time dependence could not occur in a variational system. Since it occurs for arbitrarily small amplitudes, one might hope that it is amenable to theoretical analysis.

Spiral defect chaos in Rayleigh-Be´nard convection: defect population statistics

Abstract We report a number of observations regarding the populations of defects in the spiral-defect-chaos state of Rayleigh-Be´nard convection. The experiments were carried out using CO 2 at 32 bar with a Prandtl number σ = 0.98 in a cylindrical convection cell with radius-to-height ratio Γ = 52. The populations of spirals, targets, and sidewall foci were measured as functions of ɛ ≡Δ T /Δ T c −1 and were used to describe the transition to spiral-defect chaos. The probability distributions of the number and size of defects were determined and compared to Poisson and Gaussian distributions. The populations of spirals were further characterized by size and sense of winding (clockwise or counterclockwise) and the normalized difference is presented as a function of ɛ.