Transitional boundary layers in low-Prandtl-number convection

TL;DR

This paper investigates the transitional boundary layer behavior in low-Prandtl-number turbulent convection, revealing that viscous boundary layers become turbulent at relatively low Rayleigh numbers compared to gases.

Contribution

It provides the first detailed analysis of the transitional viscous boundary layers in low-Prandtl-number convection, linking boundary layer properties to turbulent channel flow characteristics.

Findings

Viscous boundary layers are highly transitional at large Rayleigh numbers.

Wall stress fluctuations increase significantly with Rayleigh number.

Boundary layer turbulence onset occurs at lower Rayleigh numbers than in gas flows.

Abstract

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Benard 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 Pr=0.021 for Rayleigh numbers between Ra=3e+5 and 4e+8. The generated turbulent momentum transfer corresponds to macroscopic flow Reynolds numbers with values between 1800 and 46000. 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 Re_tau slightly below 100. 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 Re_tau in the velocity boundary layer can reach values of 200 for Ra beyond 1e+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.