Stevens Richard J A M, Overkamp Jim, Lohse Detlef, Clercx Herman J H
Department of Science and Technology, University of Twente, Enschede, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056313. doi: 10.1103/PhysRevE.84.056313. Epub 2011 Nov 18.
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=2.91×10(8) up to Ra=4.52×10(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 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=2.91×10(8). However, for stronger rotation, i.e., 1/Ro>>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>>1/Ro(c). 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.
给出了普朗特数Pr = 4.38、瑞利数Ra = 2.91×10⁸直至Ra = 4.52×10⁹时，湍流旋转瑞利 - 贝纳德对流中热传递随罗斯比数Ro变化的数值和实验数据。纵横比Γ≡D/L，其中L是圆柱形样品的高度，D是其直径，在Γ = 0.5至2.0之间变化。在无旋转情况下，纵横比会影响整体大尺度环流，对于Ra = 2.91×10⁸，我们在努塞尔数中看到了小纵横比依赖性。然而，对于更强的旋转，即1/Ro>>1/Ro(c)，热传输变得与纵横比无关。我们对这一发现的解释如下：在旋转状态下，热量主要由垂直排列的涡旋传输。由于垂直排列的涡旋是局部的，纵横比在旋转状态下对热传输的影响可忽略不计。实际上，对涡旋统计的详细分析表明，当1/Ro>>1/Ro(c)时，被涡旋覆盖的水平面积分数与纵横比无关。与魏斯等人[《物理评论快报》105, 224501 (2010)]的结果一致，我们发现靠近侧壁处存在一个涡旋耗尽区域。在此我们表明，在涡旋耗尽边缘区域旁边还有一个涡旋浓度增强的区域，并且这两个区域的绝对宽度都与纵横比无关。
