The $\frac{1}{2}$ power law is reported in a Rayleigh-Bénard experiment: ${\mathrm{Nu}\mathrm{\sim }\mathrm{Ra}}^{1/2},$ 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)].

• Received 12 October 2000

DOI:https://doi.org/10.1103/PhysRevE.63.045303