Effect of slip length on flow dynamics and heat transport in two-dimensional Rayleigh–Bénard convection

Abstract

We report a direct numerical simulation (DNS) study of the heat transport and temperature profiles of the plume ejecting and impacting regions in the two-dimensional turbulent Rayleigh–Bénard (RB) convection with slippery plates and horizontally periodic boundary conditions. The numerical study is conducted in the parameter range of Rayleigh number $Ra$ from ${10}^7$ to ${10}^9$ and the slip length b from 0 (NS) to ∞ (FS) for the top and bottom plates. Two distinct flow patterns can be seen depending on b, namely convection roll state and zonal flow, which affect the Nusselt number $Nu$ and the Reynolds number $Re$. We show that the zonal flow occurs when the normalised slip length $b/{\lambda }_0\gtrsim 20$, where ${\lambda }_0$ is the thermal boundary layer thickness for the no-slip (NS) plates. $Nu$ and $Re$ increase with increasing $b/{\lambda }_0$, and can reach the optimum before the generation of the zonal flow. It is observed that $Nu\sim {Ra}^{{\gamma }_{Nu}}$ with the effective scaling exponent ${\gamma }_{Nu}=0.30\pm 0.01$ for the convection roll state, and ${\gamma }_{Nu}=0.16\pm 0.01$ for the zonal flow. Furthermore, for the convection roll state, the power-law scaling of the local heat flux is $Nu\sim {Ra}^{0.33}$ in the plume ejecting region, while in the plume impacting region, $Nu\sim {Ra}^{0.28}$ for varying slip length $b/{\lambda }_0$. The DNS data with different slippery plates for both plume ejecting and impacting regions agree well with the predicted temperature profiles by Huang et al. (J Fluid Mech. 2022;943:A2).

Keywords:

• Bénard convection
• zonal flow
• heat transfer
• temperature boundary layer profiles

Acknowledgments

We would like to offer our special thanks to W. Xu for the support of the computational work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 91952101], the Natural Science Foundation of Guangdong Province [grant number 2020A1515011094], and the Science, Technology and Innovation Commission of Shenzhen Municipality [grant number 20220818113020001].