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By tailoring the geometry of the upper boundary in turbulentRayleigh-B\'enard convection we manipulate the boundary layer -- interior flowinteraction, and examine the heat transport using the Lattice Boltzmann method.For fixed amplitude and varying boundary wavelength $\lambda$, we find that theexponent $\beta$ in the Nusselt-Rayleigh scaling relation, $Nu-1 \proptoRa^\beta$, 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 thecoupling between the boundary layer and the interior flow. We present a simplescaling argument embodying this coupling, which describes the maximalconvective heat flux.

Tailoring boundary geometry to optimize heat transport in turbulent convection