Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection

Abstract

AbstractWe present high-resolution numerical investigations of heat transport by two-dimensional (2D) turbulent Rayleigh–Bénard (RB) convection over the Rayleigh number range $1{0}^{8} \leqslant Ra\leqslant 1{0}^{10} $ and the Prandtl number range $0. 7\leqslant Pr\leqslant 10$. We find that there exists strong counter-gradient local heat flux with magnitude much larger than the global Nusselt number $Nu$ of the system. Two mechanisms for generating counter-gradient heat transport are identified: one is due to the bulk dynamics and the other is due to the competition between the corner-flow rolls and the large-scale circulation (LSC). While the magnitude of the former is found to increase with increasing Prandtl number, that of the latter maximizes at medium $Pr$. We further reveal that the corner–LSC competition leads to the anomalous $Nu$–$Pr$ relation in 2D RB convection, i.e. $Nu(Pr)$ minimizes, rather than maximizes as in the three-dimensional cylindrical case, at $Pr\approx 2\sim 3$ for moderate $Ra$.