Measured Instantaneous Viscous Boundary Layer in Turbulent Rayleigh-B\'{e}nard Convection

TL;DR

This study measures the instantaneous viscous boundary layer thickness in turbulent Rayleigh-Bénard convection, revealing intermittent fluctuations and their statistical properties, and shows how the mean velocity profile aligns with theoretical predictions when accounting for these fluctuations.

Contribution

First measurement of instantaneous viscous boundary layer thickness in turbulent convection, linking fluctuations to large-scale flow dynamics and validating theoretical profiles.

Findings

$ ext{delta}_v(t)$ exhibits lognormal and exponential tail distributions.

Boundary layer thickness fluctuations are driven by large-scale flow variations.

Resampling velocity profiles relative to $ ext{delta}_v(t)$ aligns with Prandtl-Blasius theory.

Abstract

We report measurements of the instantaneous viscous boundary layer (BL) thickness $\delta_v(t)$ in turbulent Rayleigh-B\'{e}nard convection. It is found that $\delta_v(t)$ obtained from the measured instantaneous two-dimensional velocity field exhibits intermittent fluctuations. For small values, $\delta_v(t)$ obeys a lognormal distribution, whereas for large values the distribution of $\delta_v(t)$ exhibits an exponential tail. The variation of $\delta_v(t)$ with time is found to be driven by the fluctuations of the large-scale mean flow velocity and the local horizontal velocities close to the plate can be used as an instant measure of this variation. It is further found that in the present parameter range of the experiment the mean velocity profile measured in the laboratory frame can be brought into coincidence with the theoretical Prandtl-Blasius laminar BL profile, if it is resampled relative to the time-dependent frame of $\delta_v(t)$.