Tailoring boundary geometry to optimize heat transport in turbulent convection

Abstract

By tailoring the geometry of the upper boundary in turbulent Rayleigh-Bénard 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 $λ$, we find that the exponent $β$ in the Nusselt-Rayleigh scaling relation, $Nu-1 \propto Ra^β$, is maximized at $λ\equiv λ_{\text{max}} \approx (2 π)^{-1}$, but decays to the planar value in both the large ($λ\gg λ_{\text{max}}$) and small ($λ\ll λ_{\text{max}}$) 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.