Mean velocity and temperature profiles in turbulent Rayleigh–Bénard convection at low Prandtl numbers. (5th May 2021)

• Record Type: Journal Article
• Authors: Xu, Wei; Wang, Yin; He, Xiaozhou; Wang, Xiaoping; Schumacher, Jörg; Huang, Shi-Di; Tong, Penger
• Is Part Of: Journal of fluid mechanics. Volume 918(2021)
• Publication Date: 2021-05-05
• Subjects: Bénard convection, -- buoyant boundary layers, -- turbulent convection; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.255
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : 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 $0.17\leq Pr\leq 4.4$ and the Rayleigh number ( $Ra$ ) varied in the range $5\times 10^8\leq Ra \leq 1\times 10^{10}$ . 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 $\nu _t$ . 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.