Tailoring boundary geometry to optimize heat transport in turbulent convection

By tailoring the geometry of the upper boundary in turbulent Rayleigh-B\'enard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude and varying boundary wavelength $\lambda$, we find that the exponent $\beta$ in the Nusselt-Rayleigh scaling relation, $Nu-1 \propto Ra^\beta$, is maximized at $\lambda \equiv \lambda_{\text{max}} \approx (2 \pi)^{-1}$, but decays to the planar value in both the large ($\lambda \gg \lambda_{\text{max}}$) and small ($\lambda \ll \lambda_{\text{max}}$) wavelength limits. The changes in the exponent originate in the nature of the coupling between the boundary layer and the interior flow. We present a simple scaling argument embodying this coupling, which describes the maximal convective heat flux.