Turbulent thermal convection over fractal-like multi-scale roughness

In turbulent Rayleigh-Bénard convection, roughness is often used as a means to enhance heat transport. Yet the community is still debating on whether the Nusselt vs Rayleigh number scaling exponent (Nu∼Ra^β) increases or remains unchanged. In our previous study we have shown that for periodic roughness of the same size, the scaling exponent β can reach up to 1/2 for one decade in Ra, and then saturates back to a value close to the smooth wall case. In contrast, we now investigate Rayleigh-Bénard convection with surface roughness of three length scales. We find that the range of Ra in which the 1/2 exponent manifests can be extended substantially. The reason is that with multi-scale roughness, the state where a thin thermal boundary layer is uniformly distributed along the rough surfaces is very much delayed and can only be achieved at very high Ra.