Properties of the Measured Instantaneous Viscous Boundary Layer Thickness in Turbulent Rayleigh-Benard Convection.

We report measurements of the instantaneous viscous boundary layer (BL) thickness $\delta _{v}$(t) in turbulent Rayleigh-Benard convection. The instantaneous $\delta _{v}$(t) obtained from PIV-measured two-dimensional velocity field is found to exhibit intermittent fluctuations. It is also found that there is a clean separation of statistical behavior of $\delta _{v}$(t) below and above its most probable value $\delta _{v}^{mp}$: for $\delta _{v}$(t)$<\delta _{v}^{mp}$, it obeys a lognormal distribution and for $\delta _{v}$(t)$>\delta _{v}^{mp}$, the distribution of $\delta _{v}$(t) has an exponential tail. Our results reveal that the variation of $\delta _{v}$(t) responds negatively to the fluctuations of the large-scale mean flow velocity with a nonzero time delay; while close to the plate the horizontal velocity reflects the variation of $\delta _{v}$(t) with zero time delay. In the reference frame of the time-dependent thickness $\delta _{v}$(t), the conditional-averaged velocity profile agrees excellently with the theoretical Prandtl-Blasius laminar BL profile and the shape factor is found to be much closer to the theoretical value of the Blasius shear layer as compared to that obtained in the laboratory frame. It is further found that $\delta _{v}^{mp}$ scales as Re$^{0.5}$.