Mean velocity and temperature profiles in turbulent Rayleigh-Bénard convection at low Prandtl numbers

We report a direct numerical simulation (DNS) study of the mean velocity and temperature profiles in turbulent Rayleigh-Bénard convection (RBC) at low Prandtl numbers (Pr). The numerical study is conducted in a vertical thin disk with Pr varied in the range 0.17 ≤ Pr ≤ 4.4 and the Rayleigh number (Ra) varied in the range 5 × 10^8 ≤ Ra ≤ 1 × 10^10. By varying Pr from 4.4 to 0.17, we find a sharp change of flow patterns for the large-scale circulation (LSC) from a rigid-body rotation to a near-wall turbulent jet. We numerically examine the mean velocity equation in the bulk region and find that the mean horizontal velocity profile u(z) can be determined by a balance equation between the mean convection and turbulent diffusion with a constant turbulent viscosity νt. This balance equation admits a self-similarity jet solution, which fits the DNS data well. In the boundary-layer region, we find that both the mean temperature profile T(z) and u(z) can be determined by a balance equation between the molecular diffusion and turbulent diffusion. Within the viscous boundary layer, both u(z) and T(z) can be solved analytically and the analytical results agree well with the DNS data. Our careful characterisation of the mean velocity and temperature profiles in low-Pr RBC provides a further understanding of the intricate interplay between the LSC, plume emission and boundary-layer dynamics, and pinpoints the physical mechanism for the emergence of a pronounced LSC in low-Pr RBC.