  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 ($\mathrm{Nu} \sim
\mathrm{Ra}^\beta$) increases or remains unchanged. Here we numerically
investigate turbulent Rayleigh-B\'enard 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.
