Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection
In thermal convection, roughness is often used as a means to enhance heat transport, expressed in Nusselt number. Yet there is no consensus on whether the Nusselt vs. Rayleigh number scaling exponent ($\mathrm{Nu} \sim \mathrm{Ra}^β$) increases or remains unchanged. Here we numerically investigate turbulent Rayleigh-Bénard convection over rough plates in two dimensions, up to $\mathrm{Ra}=10^{12}$. Varying the height and wavelength of the roughness elements with over 200 combinations, we reveal the existence of two universal regimes. In the first regime, the local effective scaling exponent can reach up to 1/2. However, this cannot be explained as the attainment of the so-called ultimate regime as suggested in previous studies, because a further increase in $\mathrm{Ra}$ leads to the second regime, in which the scaling saturates back to a value close to the smooth case. Counterintuitively, the transition from the first to the second regime corresponds to the competition between bulk and boundary layer flow: from the bulk-dominated regime back to the classical boundary-layer-controlled regime. Our study clearly demonstrates that the local $1/2$ scaling does not signal the onset of asymptotic ultimate thermal convection.