Turbulent convection at very high Rayleigh numbers

Turbulent convection occurs when the Rayleigh number (Ra)-which quantifies the relative magnitude of thermal driving to dissipative forces in the flui d motion-becomes sufficiently high. Although many theoretical and experimen tal studies of turbulent convection exist, the basic properties of heat tra nsport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predict s that in such a state the Nusselt number (Nu), representing the global hea t transport, should scale as Nu proportional to Ra-beta with beta = 1/2. He re we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) less than or equal to Ra less than or equal to 10(7) ), using cryogenic helium gas as the working fluid. Our data, over the enti re range of Ra, can be described to the lowest order by a single power-law with scaling exponent beta close to 0.31. In particular, we rnd no evidence for a transition to the Ra-1/2 regime. We also study the variation of inte rnal temperature fluctuations with Ra, and probe velocity statistics indire ctly.