arXiv 1907.024512019-07-04physics.flu-dyn

旋转湍流对流中的急剧转变：拉格朗日加速度统计揭示了第二个临界Rossby数

Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number

Kim M. J. Alards, Rudie P. J. Kunnen, Richard J. A. M. Stevens, Detlef Lohse, Federico Toschi., Herman J. H. Clercx

备注：: 16 pages, 9 Figures
发表信息：: Phys. Rev. Fluids 4, 074601 (2019)
DOI：: 10.1103/PhysRevFluids.4.074601

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摘要：

在RB对流与普朗特数$Pr\gtrsim 1$的流体，旋转超过一个临界（小）的旋转速率是已知的，会导致突然增强的热传递，这可以解释为在对流单元的顶部和底部板附近的BL动力学的字符的变化。也就是说，随着旋转速率的增加，BL签名突然从Prandtl-Blasius型转变为Ekman型。已知随着旋转速率的增加，从恒定的热传递到几乎线性增加的热传递的转变是急剧的，并且临界Rossby数$Ro_{c}$通常发生在$2.3\lesssim Ro_{c}\lesssim 2.9$范围内（对于瑞利数$Ra=1.3\times 10^9$、$Pr=6.7$和具有纵横比$Γ=\frac{D}{H}=1$的对流单元，$D$是单元的直径，$H$是单元的高度）。热传递中的急剧转变的解释指向占主导地位的流动结构的变化。在$1/Ro\lesssim 1/Ro_c$（慢旋转），发现了著名的LSC：由许多单独的热羽流组成的单个充满区域的对流卷。在$1/Ro\gtrsim 1/Ro_c$（快速旋转）时，LSC消失，取而代之的是与旋转轴对齐的涡旋羽流。在本文中，通过数值研究拉格朗日加速度统计，有关的小尺度特性的流结构，我们揭示了这些不同的主导流结构之间的过渡发生在第二个临界Rossby数，$Ro_{c_2}\approx 2.25$（不同的$Ro_{c_1}\approx 2.7$的急剧过渡的努塞尔数$Nu$ ;这两个值为我们目前的数值研究的参数设置）。当收集顶板附近的拉格朗日示踪剂的统计数据时，发现这些示踪剂的水平加速度的均方根（rms）值和峰度在$Ro_{c_2}$处显示出突然增加。

英文摘要：

In RB convection for fluids with Prandtl number $Pr\gtrsim 1$, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the BL dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl--Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number $Ro_{c}$ occurs typically in the range $2.3\lesssim Ro_{c}\lesssim 2.9$ (for Rayleigh number $Ra=1.3\times 10^9$, $Pr=6.7$, and a convection cell with aspect ratio $Γ=\frac{D}{H}=1$, with $D$ the diameter and $H$ the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At $1/Ro\lesssim 1/Ro_c$ (slow rotation), the well-known LSC is found: a single domain-filling convection roll made up of many individual thermal plumes. At $1/Ro\gtrsim 1/Ro_c$ (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, $Ro_{c_2}\approx 2.25$ (different from $Ro_{c_1}\approx 2.7$ for the sharp transition in the Nusselt number $Nu$; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at $Ro_{c_2}$.

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