No abstract

Classical and symmetrical horizontal convection is studied by means of direct numerical simulations for Rayleigh numbers Ra up to 3 × 10 12 and Prandtl numbers Pr = 0.1, 1 and 10. For both set-ups, a very good agreement in global quantities with respect to heat and momentum transport is attained. Similar to Shishkina & Wagner (Phys. Rev. Lett., vol. 116, 2016, 024302), we find Nusselt number Nu versus Ra scaling transitions in a region 10 8 Ra 10 11 . Above a critical Ra, the flow undergoes either a steady-oscillatory transition (small Pr) or a transition from steady state to a transient state with detaching plumes (large Pr). The onset of the oscillations takes place at Ra Pr −1 ≈ 5 × 10 9 and the onset of detaching plumes at Ra Pr 5/4 ≈ 9 × 10 10 . These onsets coincide with the onsets of scaling transitions.

Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting vs. plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ultimately ejecting dominated at . This is consistent with the trends observed in 3-D convection at lower Ra, and we therefore expect a similar crossover to also occur there. We identify the development of a turbulent mixing zone, connected to thermal plume emission, as the primary mechanism for the takeover. The mixing zone gradually extends vertically and horizontally, therefore becoming more and more dominant for the overall heat transfer.

This work addresses the effects of different thermal sidewall boundary conditions on the formation of flow states and heat transport in two- and three-dimensional Rayleigh–Bénard convection (RBC) by means of direct numerical simulations and steady-state analysis for Rayleigh numbers ${\textit {Ra}}$ up to $4\times 10^{10}$ and Prandtl numbers ${\textit {Pr}}=0.1,1$ and $10$ . We show that a linear temperature profile imposed at the conductive sidewall leads to a premature collapse of the single-roll state, whereas a sidewall maintained at a constant temperature enhances its stability. The collapse is caused by accelerated growth of the corner rolls with two distinct growth rate regimes determined by diffusion or convection for small or large ${\textit {Ra}}$ , respectively. Above the collapse of the single-roll state, we find the emergence of a double-roll state in two-dimensional RBC and a double-toroidal state in three-dimensional cylindrical RBC. These states are most prominent in RBC with conductive sidewalls. The different states are reflected in the global heat transport, so that the different thermal conditions at the sidewall lead to significant differences in the Nusselt number for small to moderate ${\textit {Ra}}$ . However, for larger ${\textit {Ra}}$ , the heat transport and flow dynamics become increasingly alike for different sidewalls and are almost indistinguishable for ${\textit {Ra}}>10^{9}$ . This suggests that the influence of imperfectly insulated sidewalls in RBC experiments is insignificant at very high ${\textit {Ra}}$ – provided that the mean sidewall temperature is controlled.