Transition to the Ultimate State of Turbulent Rayleigh-Benard Convection

Abstract

Measurements of the Nusselt number Nu and of a Reynolds number Re(eff) for Rayleigh-Benard convection (RBC) over the Rayleigh-number range 10(12) less than or similar to & Ra less than or similar to 10(15) and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Gamma equivalent to D/L of a cylindrical sample was 0.50. For Ra less than or similar to 10(13) the data yielded Nu alpha Ra(gamma eff) with gamma(eff) similar or equal to 0.31 and Re(eff) alpha Ra(zeta eff) with zeta(eff) similar or equal to 0.43, consistent with classical turbulent RBC. After a transition region for 10(13) less than or similar to Ra less than or similar to 5x 10(14), where multistability occurred, we found gamma(eff) similar or equal to 0: 38 and zeta(eff) = zeta similar or equal to 0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.