Viscous boundary layers at the sidewall of a convection cell

Abstract

Profiles of both the mean value and the standard deviation of the local fluctuating velocity were directly measured near the sidewall of a cubic convection cell using water as the working fluid. Scaling laws with the Rayleigh number Ra for various boundary layer quantities have been established over the range of Ra from ${10}^{8}$--${10}^{10}$ and were found to be substantially different from those near the horizontal conducting plates where large temperature gradients exist. This in turn signifies the interplay between the temperature and the velocity fields at the horizontal plates. The length scale associated with the root-mean-square velocity is found to be analogous to the thickness of the wall layer, while the length associated with the mean velocity is analogous to the thickness of the boundary layer, in conventional wall-bounded shear flows. Our measurements also reveal that the large-scale circulation is quite uniform over a large region on the sidewall plate.