Temperature and velocity boundary layers in turbulent convection

Abstract

We experimentally study the temperature and velocity fields in high Rayleigh number (Ra) convection by making local measurements as a function of distance from the boundary in a cubic cell. The experiments are performed at two different Prandtl numbers (Pr). In water (Pr=6.6), we measure the thermal and viscous boundary layers for Ra=1\ifmmode\times\else\texttimes\fi{}${10}^{9}$. We also estimate the advective heat transport in the cell. In room temperature gas (Pr=0.7), we measure the thermal boundary layer for Ra from 5\ifmmode\times\else\texttimes\fi{}${10}^{5}$ to 1\ifmmode\times\else\texttimes\fi{}${10}^{11}$. Its thickness scales as ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}2/7}$ for Ra>2\ifmmode\times\else\texttimes\fi{}${10}^{7}$. We measure a second length scale at both Pr using the maximum cutoff frequency of the power spectrum, and demonstrate that it corresponds to the maximum velocity of the large scale circulation. In the gas, this length is consistent with a ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}1/2}$ scaling for Ra>2\ifmmode\times\else\texttimes\fi{}${10}^{9}$. We also present the temperature skewness and the effects of Pr.