The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Bénard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough, the dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes, and an interior region away from the side walls. The latter is dominated by the shear of the large-scale circulation (LSC) roll, which fills the whole cell and continuously varies its orientation. The working fluid is liquid mercury or gallium at a Prandtl number $\text{Pr}=0.021$ for Rayleigh numbers $3\times {10}^5\le \text{Ra}\le 4\times {10}^8$. The generated turbulent momentum transfer corresponds to macroscopic flow Reynolds numbers with $1.8\times {10}^3\le \text{Re}\le 4.6\times {10}^4$. In highly resolved spectral element direct numerical simulations, we present the mean profiles of velocity, Reynolds stress, and temperature in inner viscous units and compare our findings with convection experiments and channel flow data. The complex three-dimensional and time-dependent structure of the LSC in the cell is compensated by a plane-by-plane symmetry transformation which aligns the horizontal velocity components and all its derivatives with the instantaneous orientation of the LSC. As a consequence, the torsion of the LSC is removed, and a streamwise direction in the shear flow can be defined. It is shown that the viscous boundary layers for the largest Rayleigh numbers are highly transitional and obey properties that are directly comparable to transitional channel flows at friction Reynolds numbers ${\text{Re}}_{\tau }\lesssim {10}^2$. The transitional character of the viscous boundary layer is also underlined by the strong enhancement of the fluctuations of the wall stress components with increasing Rayleigh number. An extrapolation of our analysis data suggests that the friction Reynolds number ${\text{Re}}_{\tau }$ in the velocity boundary layer can reach values of 200 for $\text{Ra}\gtrsim {10}^{11}$. Thus the viscous boundary layer in a liquid metal flow would become turbulent at a much lower Rayleigh number than for turbulent convection in gases and gas mixtures.

• Received 3 September 2016

DOI:https://doi.org/10.1103/PhysRevFluids.1.084402