Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-B\'{e}nard convection

TL;DR

This study demonstrates that in turbulent Rayleigh-Bénard convection, temperature and velocity boundary layer profiles align with classical laminar profiles when analyzed in fluctuating dynamical reference frames across a broad range of Rayleigh and Prandtl numbers.

Contribution

It provides experimental and numerical evidence that boundary layer profiles in turbulent convection match Prandtl-Blasius profiles in dynamically resampled frames.

Findings

Profiles agree with Prandtl-Blasius laminar boundary layers when resampled in fluctuating frames.

Results cover a wide range of Rayleigh and Prandtl numbers.

Both temperature and velocity profiles exhibit this behavior.

Abstract

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-B\'{e}nard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.