Spectral analysis of boundary layers in Rayleigh-Benard convection

TL;DR

This study combines experiments and simulations to analyze the turbulence and spectral characteristics of boundary layers in Rayleigh-Bénard convection across a wide range of Rayleigh numbers, revealing turbulence presence but non-classical boundary layer behavior.

Contribution

It provides a comprehensive spectral analysis of boundary layers in Rayleigh-Bénard convection through combined experimental and numerical methods over a broad Rayleigh number range.

Findings

Boundary layer and bulk velocity PDFs are nearly identical.

Spectra in boundary layer and bulk are continuous with wide active scales.

Boundary layers are turbulent but differ from classical shear-driven turbulence.

Abstract

A combined experimental and numerical study of the boundary layer in a 4:1 aspect-ratio Rayleigh-B\'{e}nard cell over a four-decade range of Rayleigh numbers has been undertaken aimed at gaining a better insight into the character of the boundary layers. The experiments involved the simultaneous Laser Doppler Anemometry (LDA) measurements of fluid velocity at two locations, i.e. in the boundary layer and far away from it in the bulk, for Rayleigh numbers varying between $1.6 \times 10^7$ and $2.4 \times 10^9$. In parallel, direct numerical simulations (DNS) have been performed for the same configuration for Rayleigh numbers between $7.0 \times 10^4$ and $7.7 \times 10^7$. The temperature and velocity probability density functions and the power spectra of the horizontal velocity fluctuations measured in the boundary layer and in the bulk flow are found to be practically identical. Except for the smallest Rayleigh numbers, the spectra in the boundary layer and in the bulk central region are continuous and have a wide range of active scales. This indicates that both the bulk and the boundary layers are turbulent in the $\textrm{Ra}$ number range considered. However, molecular effects can still be observed and the boundary layer does not behave like a classical shear-driven turbulent boundary layer.