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

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.