Effect of aspect-ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection

Abstract

Numerical and experimental data for the heat transfer as function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for Prandtl number Pr=4.38 and Rayleigh number $Ra=2.91\times 10^8$ up to $Ra=4.52\times 10^9$. The aspect ratio Γ= D/L, where L is the height and D the diameter of the cylindrical sample, is varied between Γ=0.5 and Γ=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 $Ra=2.91\times 10^8$. However, for stronger rotation, i.e. $1/Ro\gg 1/R{o}_c$, 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 $1/Ro\gg 1/R{o}_c$. 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.

13 pages, 8 figures

References in corpus (6)

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• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Connecting flow structures and heat flux in turbulent Rayleigh-Bénard convection
• Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection
• The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-Bénard convection
• Heat transport in rotating convection without Ekman layers

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• Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number
• Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection
• Effects of rotation on the bulk turbulent convection
• Rapidly Rotating Wall-Mode Convection