Spatial structure of the thermal boundary layer in turbulent convection

Abstract

We have measured the mean temperature profiles $\overline{T}(\mathrm{z})$ and the thermal layer thickness ${\ensuremath{\delta}}_{\mathrm{th}}(x,y)$ at various horizontal positions on the lower plate of a cylindrical convection cell, using water as the working fluid. The Rayleigh number Ra in the experiment varied from $2\ifmmode\times\else\texttimes\fi{}{10}^{8}$ to $2\ifmmode\times\else\texttimes\fi{}{10}^{10}$. The normalized vertical temperature profiles measured at various positions $x$ along the direction of large scale circulation and for the same Ra are found to be self-similar, once the vertical distance $z$ is scaled by the respective thermal layer thickness ${\ensuremath{\delta}}_{\mathrm{th}}(x,0)$. Whereas those measured at different Ra do not have a universal form. Our results further reveal that the thermal layer thickness ${\ensuremath{\delta}}_{\mathrm{th}}$ varied significantly in the two directions measured---along the large-scale circulation $(x)$ and perpendicular to it $(y)$. We found that the scaling exponent of ${\ensuremath{\delta}}_{\mathrm{th}}$ with Ra is a function of $x$ (and possibly a function of $y$ as well), i.e. ${\ensuremath{\delta}}_{\mathrm{th}}\ensuremath{\sim}$ Ra${}^{\ensuremath{-}\ensuremath{\beta}(x)}$. Moreover, our results suggest that the thermal layer will eventually become uniform at very high Rayleigh numbers.