On the role of moderate Prandtl numbers in vertical natural convection

Direct numerical simulation (DNS) of temporally developing natural convection boundary layers is conducted at $ \textit{Pr} =4.16$ and $ \textit{Pr} =6$ . Results are compared with an existing DNS dataset for $ \textit{Pr} =0.71$ (Ke et al. J. Fluid Mech . 964, 2023, p. A24) to enable a direct assessment of Prandtl number effects across the range $0.71\leqslant \textit{Pr} \leqslant 6$ . The analysis reveals that the $ \textit{Pr}$ affects the flow through buoyancy forcing, which acts not only as the driving force but also modulates the local shear distribution via coupling with the momentum equation, thereby shifting the onset Rayleigh number of transition from the laminar regime. This transition is found to be characterised by the thermal boundary layer thickness $\delta _\theta$ , which provides a robust prediction of the critical Rayleigh number across $ \textit{Pr}$ , indicating a buoyancy instability consistent with the stability analysis (Ke et al. J. Fluid Mech . 988, 2024, p. A44; Ke et al. Intl J. Heat Mass Transfer 241, 2025, p. 126670). Further analysis in the turbulent regime suggests that while heat transfer becomes effectively independent of $ \textit{Pr}$ , the near-wall turbulence structure remains sensitive to $ \textit{Pr}$ due to persistent buoyancy effects. The skin friction coefficient scaling shows clear transition from a linear scaling with the bulk Reynolds number in the weakly turbulent regime to a log-law-type scaling with the bulk Reynolds number in the ultimate turbulent regime (Grossmann & Lohse J. Fluid Mech . 407, 2000, pp. 27–56). The premultiplied velocity spectra confirms the development of near-wall streaks that are characteristic of canonical shear-driven turbulence in this ultimate turbulent regime, with their spanwise spacing systematically broadening with increasing $ \textit{Pr}$ due to persistent buoyancy effects; while the spectral signature of the outer plume-like region appears largely $ \textit{Pr}$ -independent.