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

We present high-resolution numerical investigations of heat transport by two-dimensional (2D) turbulent Rayleigh–Bénard (RB) convection over the Rayleigh number range 10⁸ Ra 10¹⁰ and the Prandtl number range 0. 7 Pr 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≈ 2~ 3 for moderate $Ra$ .