Thermal boundary layer structure in low-Prandtl-number turbulent convection

Abstract

We study the structure of the thermal boundary layer (BL) in Rayleigh-Bénard 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 $R{a}^{-\beta (x)}$, with $\beta (x)$ depending on the position at the plate. We find that $\beta (x)$ are nearly the same in impact and shear regions and are smaller than those in the ejection region. Thus, the local BL width decreases faster in the ejection region than those in the shear and impact regions, and we estimate that the thermal BL structure would be uniform throughout the horizontal plate for $Ra\ge 8\times 10^{12}$ 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 ({\it 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.

35 pages, 20 figures; published in Journal of Fluid Mechanics

References in corpus (9)

• Comparison between two and three dimensional Rayleigh-Bénard convection
• Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection
• Boundary layer structure in turbulent Rayleigh-Benard convection
• Scaling of large-scale quantities in Rayleigh-Bénard convection
• Global and local statistics in turbulent convection at low Prandtl numbers
• Local boundary layer scales in turbulent Rayleigh-Benard convection
• Transitional boundary layers in low-Prandtl-number convection
• Logarithmic temperature profiles of turbulent Rayleigh-Bénard convection in the classical and ultimate state for a Prandtl number of 0.8
• Mean Temperature Profiles in Turbulent Thermal Convection

Cited by in corpus (4)

• Flow states and heat transport in liquid metal convection
• Non-Boussinesq low-Prandtl number convection with a temperature-dependent thermal diffusivity
• Non-Boussinesq convection at low Prandtl numbers relevant to the Sun
• Convective heat transport in slender cells is close to that in wider cells at high Rayleigh and Prandtl numbers