Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh-B\'enard convection

TL;DR

This study uses two-dimensional simulations to link logarithmic mean temperature profiles in Rayleigh-Bénard convection boundary layers to thermal plume emissions, revealing a nuanced picture of boundary layer turbulence.

Contribution

It demonstrates that logarithmic temperature profiles are localized to plume-emitting regions, suggesting boundary layer turbulence is spatially heterogeneous and evolves gradually.

Findings

Logarithmic temperature profiles are observed only in plume-emitting regions.

The boundary layer exhibits both turbulent and non-turbulent regions.

Transition to fully turbulent boundary layers is gradual, linked to increased plume emission.

Abstract

Two-dimensional simulations of Rayleigh-B\'enard convection at $Ra = 5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission and support a perception that parts of the boundary layer can be turbulent, while others are not. The transition to the ultimate regime, in which the boundary layers are considered to be fully turbulent, can therefore be understood as a gradual increases in fraction of the plume-emitting ('turbulent') regions of the boundary layer.