Boundary layer length scales in convective turbulence

Abstract

Profiles of both the mean value and the standard deviation of the local fluctuating velocity in turbulent convection in water have been directly measured using a light scattering technique. Scaling laws with the Rayleigh number Ra for various boundary layer quantities have been established over the range of Ra from $2.4\ifmmode\times\else\texttimes\fi{}{10}^{7}$ to $1.1\ifmmode\times\else\texttimes\fi{}{10}^{11}$, while the variation of the Prandtl number was kept at minimum $(\mathrm{Pr}\ensuremath{\simeq}7)$. In particular, a new boundary layer length scale is identified from the standard deviation profile, and is found to scale as ${\ensuremath{\delta}}_{\ensuremath{\sigma}}\ensuremath{\sim}{\mathrm{Ra}}^{\ensuremath{-}0.25}$, whereas the velocity boundary layer thickness ${\ensuremath{\delta}}_{v}\ensuremath{\sim}{\mathrm{Ra}}^{\ensuremath{-}0.16}$.