Evidence against ‘ultrahard’ thermal turbulence at very high Rayleigh numbers

Abstract

Several theories1,2,3,4,5 predict that a limiting and universal turbulent regime — ‘ultrahard’ turbulence — should occur at large Rayleigh numbers (Ra, the ratio between thermal driving and viscous dissipative forces) in Rayleigh–Benard thermal convection in a closed, rigid-walled cell. In this regime, viscosity becomes negligible, gravitationally driven buoyant plumes transport the heat and the thermal boundary layer, where the temperature profile is linear, controls the rate of thermal transport. The ultrahard state is predicted to support more efficient thermal transport than ‘hard’ (fully developed) turbulence: transport efficiency in the ultrahard state grows as Ra1/2, as opposed to Ra2/7 in the hard state6. The detection of a transition to the ultrahard state has been claimed in recent experiments using mercury7 and gaseous helium8. Here we report experiments on Rayleigh–Benard convection in mercury at high effective Rayleigh numbers, in which we see no evidence of a transition to an ultrahard state. Our results suggest that the limiting state of thermal turbulence at high Rayleigh numbers is ordinary hard turbulence.