Effect of aspect-ratio on vortex distribution and heat transfer in rotating Rayleigh-B\'enard convection

TL;DR

This study investigates how the aspect ratio affects vortex formation and heat transfer in rotating Rayleigh-Bénard convection, revealing that strong rotation leads to aspect-ratio-independent heat transport due to vertically-aligned vortices.

Contribution

The paper provides new insights into the aspect-ratio independence of heat transfer in rotating convection, supported by numerical and experimental data across various aspect ratios and rotation rates.

Findings

Heat transfer becomes independent of aspect ratio at strong rotation.

Vertically-aligned vortices dominate heat transport in the rotating regime.

Vortex distribution features a vortex-depleted edge and an adjacent vortex-enhanced area.

Abstract

Numerical and experimental data for the heat transfer as function of the Rossby number Ro in turbulent rotating Rayleigh-B\'enard convection are presented for Prandtl number Pr=4.38 and Rayleigh number $Ra=2.91\times10^8$ up to $Ra=4.52\times10^9$. The aspect ratio \Gamma = D/L, where L is the height and D the diameter of the cylindrical sample, is varied between \Gamma=0.5 and \Gamma=2.0. Without rotation, where the aspect ratio influences the global large scale circulation, we see a small aspect-ratio dependence in the Nusselt number for $Ra=2.91\times10^8$. However, for stronger rotation, i.e. $1/Ro \gg 1/Ro_c$, the heat transport becomes independent of the aspect-ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically-aligned vortices. Since the vertically-aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when $1/Ro \gg 1/Ro_c$. In agreement with the results of Weiss et al. Phys. Rev. Lett., vol 105, 224501 (2010) we find a vortex-depleted area close to the sidewall. Here, we in addition show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.