Local boundary layer scales in turbulent Rayleigh-Benard convection

TL;DR

This paper introduces local boundary layer scales in turbulent Rayleigh-Benard convection, linking them to flux fluctuations and spatial inhomogeneities, and explores their scaling behavior with Rayleigh number.

Contribution

It defines and analyzes local boundary layer scales based on shear stress, extending classical concepts to turbulent convection and examining their scaling and transitional behavior.

Findings

Inner and outer boundary layer scales are linked to classical turbulence scales.

Outer temperature boundary layer scale aligns with standard thermal boundary layer thickness.

Friction coefficient indicates transitional boundary layer behavior.

Abstract

We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh-Benard convection. These scales are directly connected to the highly intermittent fluctuations of the fluxes of momentum and heat at the isothermal top and bottom walls and are statistically distributed around the corresponding mean thickness scales. The local boundary layer scales also reflect the strong spatial inhomogeneities of both boundary layers due to the large-scale, but complex and intermittent, circulation that builds up in closed convection cells. Similar to turbulent boundary layers, we define inner scales based on local shear stress which can be consistently extended to the classical viscous scales in bulk turbulence, e.g. the Kolmogorov scale, and outer scales based on slopes at the wall. We discuss the consequences of our generalization, in particular the scaling of our inner and outer boundary layer thicknesses and the resulting shear Reynolds number with respect to Rayleigh number. The mean outer thickness scale for the temperature field is close to the standard definition of a thermal boundary layer thickness. In the case of the velocity field, under certain conditions the outer scale follows a similar scaling as the Prandtl-Blasius type definition with respect to Rayleigh number, but differs quantitatively. The friction coefficient c_epsilon scaling is found to fall right between the laminar and turbulent limits which indicates that the boundary layer exhibits transitional behavior. Additionally, we conduct an analysis of the recently suggested dissipation layer thickness scales versus Rayleigh number and find a transition in the scaling. We also performed one study of aspect ratio equal to three in the case of Ra=1e+8.