The planforms and onset of convection with a temperature-dependent viscosity

Abstract

An experimental investigation was made of convection in a fluid with a strongly temperature-dependent viscosity. The determination of the critical Rayleigh number, Rc, using the appearance of convection to define onset, was complicated by the occurrence of subcritical instabilities initiated by horizontal temperature gradients at the side boundaries. The increase in Rc over the expected value was less than predicted by linear theory, probably owing to the effect of finite conductivity boundaries and the temperature dependence of other fluid properties. The stability of various convective planforms was studied as a function of Rayleigh number, wavenumber and viscosity variation using controlled initial conditions to specify the wavenumber and pattern, Rayleigh numbers of up to 63000 and viscosity variations of up to 1000. In addition to the rolls and hexagons seen in constant- and weakly temperature-dependent-viscosity fluid, a new planform of squares was observed at large viscosity variations. Experiments with viscosity variations of 50 and 1000 showed that hexagons and squares were stable at Rayleigh numbers less than 25000 over a limited range of wavenumbers, which was shifted to higher values with increasing viscosity variation. Temperature profiles through the layer revealed that this shift in wavenumber was associated with the development of a thick, stagnant, cold boundary layer which reduced the effective depth of the layer. Experiments with a fixed wavenumber showed that rolls were unstable at all Rayleigh numbers for a viscosity contrast greater than 40, whereas squares did not become stable until the viscosity contrast exceeded 6. At low viscosity variations and high Rayleigh numbers rolls became unstable to a bimodal pattern, but at high viscosity variations and a Rayleigh number of 25000 squares broke down into the spoke pattern, a convective flow not observed until Rayleigh numbers of around 100000 in a constant-viscosity fluid.