Experimental study of non-Boussinesq Rayleigh–Bénard convection at high Rayleigh and Prandtl numbers

Abstract

A set of experiments is performed, in which a layer of fluid is heated from below and cooled from above, in order to study convection at high Rayleigh numbers (Ra) and Prandtl numbers (Pr). The working fluid, corn syrup, has a viscosity that depends strongly on temperature. Viscosity within the fluid layer varies by a factor of 6 to 1.8×103 in the various experiments. A total of 28 experiments are performed for 104<Ra<108 and Pr sufficiently large, 103<Pr<106, that the Reynolds number (Re) is less than 1; here, values of Ra and Pr are based on material properties at the average of the temperatures at the top and bottom of the fluid layer. As Ra increases above O(105), flow changes from steady to time-dependent. As Ra increases further, large scale flow is gradually replaced by isolated rising and sinking plumes. At Ra>O(107), there is no evidence for any large scale circulation, and flow consists only of plumes. Plumes have mushroom-shaped “heads” and continuous “tails” attached to their respective thermal boundary layers. The characteristic frequency for the formation of these plumes is consistent with a Ra2/3 scaling. In the experiments at the largest Ra, the Nusselt number (Nu) is lower than expected, based on an extrapolation of the Nu–Ra relationship determined at lower Ra; at the highest Ra, Re→1, and the lower-than-expected Nu is attributed to inertial effects that reduce plume head speeds.