Experimental Investigation of Longitudinal Space-Time Correlations of the Velocity Field in Turbulent Rayleigh-B\'{e}nard Convection

TL;DR

This study experimentally analyzes the space-time correlations of velocity in turbulent Rayleigh-Bénard convection, validating an elliptic model for the correlation contours and revealing regional differences in characteristic velocities.

Contribution

It demonstrates the applicability of the elliptic model to turbulent thermal convection and quantifies the characteristic velocities across different regions of the convection cell.

Findings

Elliptic model accurately describes velocity correlations in turbulent convection.

Fitted characteristic velocity $eta$ correlates with mean flow velocity.

Region-specific differences in correlation parameters observed.

Abstract

We report an experimental investigation of the longitudinal space-time cross-correlation function of the velocity field, $C(r,\tau)$, in a cylindrical turbulent Rayleigh-B\'{e}nard convection cell using the particle image velocimetry (PIV) technique. We show that while the Taylor's frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows [He & Zhang, \emph{Phys. Rev. E} \textbf{73}, 055303(R) (2006)] is valid for the present velocity field for all over the cell, i.e., the isocorrelation contours of the measured $C(r,\tau)$ have a shape of elliptical curves and hence $C(r,\tau)$ can be related to $C(r_E,0)$ via $r_E^2=(r-\beta\tau)^2+\gamma^2\tau^2$ with $\beta$ and $\gamma$ being two characteristic velocities. We further show that the fitted $\beta$ is proportional to the mean velocity of the flow, but the values of $\gamma$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell's central region. It is found that $\beta$ and $\gamma$ are approximately the same near the sidewall, while $\beta\simeq0$ at cell center.