The Pr-dependence of the critical roughness height in two-dimensional turbulent Rayleigh-Benard convection

We carry out direct numerical simulations of turbulent Rayleigh-Benard convection in a square box with rough conducting plates over the Rayleigh number range 10(7) <= Ra <= 10(9) and the Prandtl number range 0.01 <= Pr <= 100. In Zhang et al. (J. Fluid Mech., vol. 836, 2018, R2), it was reported that while the measured Nusselt number Nu is enhanced at large roughness height h, the global heat transport is reduced at small h. The division between the two regimes yields a critical roughness height h(c), and we now focus on the effects of the Prandtl number (Pr) on h(c). Based on the variations of h(c), we identify three regimes for h(c)(Pr). For low Pr, thermal boundary layers become thinner with increasing Pr. This makes the boundary layers easier to be disrupted by rough elements, leading to the decrease of h(c) with increasing Pr. For moderate Pr, the corner-flow rolls become much more pronounced and suppress the global heat transport via the competition between the corner-flow rolls and the large-scale circulation (LSC). As a consequence, h(c) increases with increasing Pr due to the intensification of the corner-LSC competition. For high Pr, the convective flow transitions to the plume-controlled regime. As the rough elements trigger much stronger and more frequent plume emissions, hc again decreases with increasing Pr.