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In this article we deal with the turbulent regimes of Rayleigh–Bénard convection, namely the 2/7 regime and beyond. An experiment with He at low temperature allows us to explore a large Rayleigh number (Ra) range up to 2×1014, under Boussinesq conditions, while the Prandtl number (Pr) is equal to and larger than 0.7. Calorimetric measurements evidence a departure from the 2/7 regime above Ra=1011 toward a new regime where the heat transfer is enhanced. Local measurements with two nearby thermometers allows us to relate this change to a laminar–turbulent transition of the velocity boundary layer induced by the large-scale flow near the walls of the cell. The features of the observed new regime match those of the ultimate regime predicted by R. Kraichnan [Phys. Fluids 5, 1374 (1962)] at moderate Pr; in particular, our experimental data show that the thermal boundary layer lies inside the viscous sublayer of the turbulent boundary layer.

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The 1/2 power law is reported in a Rayleigh-Bénard experiment: Nu approximately Ra(1/2), where Ra and Nu are the Rayleigh and Nusselt numbers. This observation is coherent with the predictions of the ultimate convection regime, characterized by fully turbulent heat transfers. Ordered rough boundaries are used to cancel the correction due to the thickness variation of the viscous sublayer, and the observation of the asymptotic regime is therefore possible. This result supports the interpretation of a laminar-turbulent boundary-layer transition to account for the observation of Chavanne et al. of a new regime [X. Chavanne et al., Phys. Rev. Lett. 79, 3648 (1997)].

We present velocity spectra measured in three cryogenic liquid 4He steady flows: grid and wake flows in a pressurized wind tunnel capable of achieving mean velocities up to 5 m/s at temperatures above and below the superfluid transition, down to 1.7 K, and a "chunk" turbulence flow at 1.55 K, capable of sustaining mean superfluid velocities up to 1.3 m/s. Depending on the flows, the stagnation pressure probes used for anemometry are resolving from one to two decades of the inertial regime of the turbulent cascade. We do not find any evidence that the second order statistics of turbulence below the superfluid transition differ from the ones of classical turbulence, above the transition.Comment: 13 pages, 9 figure

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