Spatial structure of the thermal boundary layer in turbulent convection

We have measured the mean temperature profiles T̄(z) and the thermal layer thickness δₜₕ(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 2×10⁸ to 2×10¹⁰. 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 δₜₕ(x,0). Whereas those measured at different Ra do not have a universal form. Our results further reveal that the thermal layer thickness δₜₕ 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 δₜₕ with Ra is a function of x (and possibly a function of y as well), i.e. δₜₕ~ Ra^-β(x). Moreover, our results suggest that the thermal layer will eventually become uniform at very high Rayleigh numbers.