Rayleigh-Benard Experiment in a Low Prandtl Number Fluid, Mercury

Abstract

Convective motions in horizontal liquid layers heated from below have been studied since 1900 [1]. But thermal convection is an ever new topic; it provides a simple experimental example of a non-linear physical system. Thus it allows testing the asymptotic models of convection and develops some insights into the problem of turbulence in fluids. In the basic equations two non-linear terms are present which drive the fluid into stationary convective motion, time dependent convective motion, and turbulent motion as the temperature difference across the layer is increased. The relative importance of these two non-linear advection terms of momentum and temperature is given by the Prandtl number. In this paper we give some recent experimental results on convection in mercury which is a low Prandtl number fluid (P = 0.031 at 273 K). In this case, the important non-linear term is the momentum advection term which leads to the oscillatory instability of bi- dimensional convection rolls. In our experiments, we measure the heat flux transitions at the onset of stationary convection and time dependent convection, and we compare our results with previous experimental works of ROSSBY [2] and KRISHNAMURTI [3], and computations of CLEVER and BUSSE [4]. We also measure a local parameter which is the temperature of the fluid at a given point, and we analyse its time dependence. For convection in small aspect ratio layers of mercury, we observe the characteristic behavior of non-linear dynamical systems (frequency locking, generation of subharmonics) but many routes to turbulence seem to be present for a given sample. This special behaviour is probably due to the low Prandtl number of mercury.