TY - JOUR

T1 - Effect of aspect ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection

AU - Stevens, R.J.A.M.

AU - Overkamp, J.V.

AU - Lohse, D.

AU - Clercx, H.J.H.

PY - 2011

Y1 - 2011

N2 - Numerical and experimental data for the heat transfer as a function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number Pr=4.38 and the Rayleigh number Ra=2.91×108 up to Ra=4.52×109. The aspect ratio G=D/L, where L is the height and D the diameter of the cylindrical sample, is varied between G=0.5 and 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=2.91×108. However, for stronger rotation, i.e., 1/Ro»1/Roc, 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»1/Roc. In agreement with the results of Weiss et al. [ Phys. Rev. Lett. 105 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we 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.

AB - Numerical and experimental data for the heat transfer as a function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number Pr=4.38 and the Rayleigh number Ra=2.91×108 up to Ra=4.52×109. The aspect ratio G=D/L, where L is the height and D the diameter of the cylindrical sample, is varied between G=0.5 and 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=2.91×108. However, for stronger rotation, i.e., 1/Ro»1/Roc, 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»1/Roc. In agreement with the results of Weiss et al. [ Phys. Rev. Lett. 105 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we 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.

U2 - 10.1103/PhysRevE.84.056313

DO - 10.1103/PhysRevE.84.056313

M3 - Article

C2 - 22181504

VL - 84

SP - 056313-1/10

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

M1 - 056313

ER -