The large-scale circulation (LSC) of fluid is one of the main concepts in turbulent thermal convection as it is known to be important in global heat and mass transport in the system. In turbulent Rayleigh–B'enard convection (RBC) in slender containers, the LSC is formed of several dynamically changing convective rolls that are stacked on top of each other. The present study reveals the following two important facts: {} the mechanism which causes the twisting and breaking of a single-roll LSC into multiple rolls is the elliptical instability and {} the heat and momentum transport in RBC, represented by the Nusselt (Nu) and Reynolds (Re) numbers, is always stronger (weaker) for smaller (larger) number $n$ of the rolls in the LSC structure. Direct numerical simulations support the findings for $n=1,...,4$ and the diameter-to-height aspect ratio of the cylindrical container $\Gamma =1/5$, the Prandtl number Pr~$=0.1$ and Rayleigh number Ra~$=5\times {10}^5$. Thus, Nu and Re are, respectively, 2.5 and 1.5 times larger for a single-roll LSC ($n=1$) than for a LSC with $n=4$ rolls.

中文翻译：

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有限湍流瑞利-贝纳德对流中大尺度环流的椭圆不稳定性和多辊流模式

流体的大规模循环（LSC）是湍流热对流的主要概念之一，因为众所周知，它对系统中的整体热量和质量传输很重要。在细长容器中的湍流瑞利-贝纳德对流（RBC）中，LSC由数个动态变化的对流辊形成，它们彼此堆叠在一起。本研究揭示了以下两个重要事实：{}导致单辊LSC扭曲和断裂成多辊的机理是椭圆不稳定性和{} RBC中的热和动量输运，由Nusselt（Nu ）和雷诺数（Re），对于较小（较大）的数字总是更强（更弱）$ñ$LSC结构中的卷的数量。直接数值模拟支持以下发现$ñ=\mathrm{1个}，。。。，4$ 圆柱容器的直径和高度的长宽比 $\Gamma =\mathrm{1个}/5$，Prandtl号Pr〜$=0.1$ 和瑞利数Ra〜$=5\times {10}^5$。因此，对于单辊LSC，Nu和Re分别大2.5倍和1.5倍（$ñ=\mathrm{1个}$）比具有 $ñ=4$ 劳斯莱斯。