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

Published online by Cambridge University Press:  08 January 2021

Ambrish Pandey Open the ORCID record for Ambrish Pandey [Opens in a new window]
Ambrish Pandey*
Affiliation:
Center for Space Science, New York University Abu Dhabi, PO Box 129188 Abu Dhabi, UAE
*
†Email address for correspondence: [email protected]
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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 $Ra^{-\beta (x)}$, 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 $Ra \geq 8 \times 10^{12}$ 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 (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.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A13
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© The Author(s), 2021. Published by Cambridge University Press

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References

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