Thermal Boundary Layer Structure In Low-Prandtl-Number Turbulent Convection

We study the structure of the thermal boundary layer (BL) in Rayleigh-Benard convection for Prandtl number (Pr) 0.021 by conducting direct numerical simulations in a two-dimensional square box for Rayleigh numbers (Ra) up to 10(9). The large-scale circulation in the flow divides the horizontal plates into three distinct regions, and we observe that the local thermal BL thicknesses in the plume-ejection region are larger than those in the plume-impact and shear-dominated regions. Moreover, the local BL width decreases as Ra-beta(x), with beta(x) depending on the position at the plate. We find that the values of beta(x) are nearly the same in the impact and shear regions, and are larger in the ejection region. Thus, the local BL width decreases faster in the ejection region than in the shear and impact regions, and we estimate that the thermal BL structure would be uniform throughout the horizontal plate for Ra >= 8 x 10(12) in our low-Pr convection. We compare the thermal BL profiles measured at various positions at the plate with the Prandtl-Blasius-Pohlhausen (PBP) profile and find deviations everywhere for all the Rayleigh numbers. However, the dynamically rescaled profiles, as suggested by Zhou & Xia (Phys. Rev. Lett., vol. 104, 2010, 104301), agree well with the PBP profile in the shear and impact regions for all the Rayleigh numbers, whereas they still deviate in the ejection region. We also find that, despite the growing fluctuations with increasing Ra, thermal boundary layers in our low-Pr convection are transitional and not yet fully turbulent.