Evidence of a boundary layer instability at very high Rayleigh number

Institut NEEL, CNRS/UJF - BP 166, F-38042 Grenoble Cedex 9, France, EU

Received: 30 January 2008
Accepted: 4 June 2008

Abstract

In 1997, a Rayleigh-Bénard experiment evidenced a significant increase of the heat transport efficiency for Rayleigh numbers larger than Ra ~ 10¹² and interpreted this observation as the signature of Kraichnan's “Ultimate Regime” of convection. According to Kraichnan's 1962 prediction, the flow boundary layers above the cold and hot plates —in which most of the fluid temperature drop is localized— become unstable for large enough Ra and this instability boosts the heat transport compared to the other turbulent regimes. Using the same convection cell as in the 1997 experiment, we show that the reported heat transport increase is accompanied with enhanced and increasingly skewed temperature fluctuations of the bottom plate, which was heated at constant power levels. Thus, for , the bottom plate fluctuations can simply be accounted from those in the bulk of the flow. In particular, they share the same spectral density at low frequencies, as if the bottom plate was following the slow temperature fluctuations of the bulk, modulo a constant temperature drop across the bottom boundary layer. Conversely, to account for the plate's temperature fluctuations at higher Ra, we no-longer can ignore the fluctuations of the temperature drop across the boundary layer. These observations, consistent with a boundary layer instability, provide new evidence that the transition reported in 1997 corresponds to the triggering of the Ultimate Regime of convection.