scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence

In turbulent Rayleigh–Bénard (RB) convection with regular, mono-scale, surface roughness, the scaling exponent x1D6FD in the relationship between the Nusselt number Nu and the Rayleigh number Ra, Nu Ra^x1D6FD can be 1/2 locally, provided that Ra is large enough to ensure that the thermal boundary layer thickness x1D706ₗ₁₃₇₀₃ is comparable to the roughness height. However, at even larger Ra, x1D706ₗ₁₃₇₀₃ becomes thin enough to follow the irregular surface and x1D6FD saturates back to the value for smooth walls (Zhu et al. , Phys. Rev. Lett. , vol. 119, 2017, 154501). In this paper, we prevent this saturation by employing multiscale roughness. We perform direct numerical simulations of two-dimensional RB convection using an immersed boundary method to capture the rough plates. We find that, for rough boundaries that contain three distinct length scales, a scaling exponent of x1D6FD=0. 49 0. 02 can be sustained for at least three decades of Ra. The physical reason is that the threshold Ra at which the scaling exponent x1D6FD saturates back to the smooth wall value is pushed to larger Ra, when the smaller roughness elements fully protrude through the thermal boundary layer. The multiscale roughness employed here may better resemble the irregular surfaces that are encountered in geophysical flows and in some industrial applications.