Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection
AbstractWe report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, $C(r, \tau )$, in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured $C(r, \tau )$ have an elliptical curve shape and hence $C(r, \tau )$ can be related to $C({r}_{E} , 0)$ via ${ r}_{E}^{2} = (r\ensuremath{-} U\tau )^{2} + {V}^{2} {\tau }^{2} $ with $U$ and $V$ being two characteristic velocities. We further show that the fitted $U$ is proportional to the mean velocity of the flow, but the values of $V$ 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 $U$ and $V$ are approximately the same near the sidewall, while $U\simeq 0$ at the cell centre.
