Transition between Different Symmetries in Rayleigh-Benard Convection

Abstract

Convective patterns with different symmetries can develop in RayleighBénard convection. When the transport coefficients of the fluid are temperature dependent (non-Boussinesq conditions) a hexagonal pattern is stable near threshold, but it is replaced by a pattern of rolls when the heating rate is increased still further. We present here recent experimental results on the transition between a hexagonal pattern and a pattern of rolls in convection in pure water under non-Boussinesq conditions. The convective cell is cylindrical with a liquid depth d = 2.00 mm and a diameter D = 72 mm. This gives an aspect ratio F = D/2d = 18. The Prandtl number of water at the mean temperature of 28°C is P = 5.81. The general features of the pattern are determined qualitatively by a shadowgraph technique. Heat-flow and optical measurements enable us to obtain quantitatively local and global characteristics of the pattern. The optical technique is based on the deflections of a laser beam that crosses the fluid layer in the vertical direction. This technique allow us to reconstruct the temperature field averaged on the vertical direction. More details about the experimental set-up can be found elsewhere.¹

On leave from Dpto. Física, Univ. Autónoma de Barcelona.