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arXiv 2006.03528physics.flu-dyn
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$η=0.91$ TC turbulence中angular momentum转运的双重最大值

Double maxima of angular momentum transport in $η=0.91$ TC turbulence

Rodrigo Ezeta, Francesco Sacco, Dennis Bakhuis, Sander G. Huisman, Rodolfo Ostilla-Mónico, Roberto Verzicco, Chao Sun, Detlef Lohse

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Submitted to JFM
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摘要：

我们使用实验和直接数值模拟探测相空间的低曲率泰勒-库埃特（TC）流在附近的最终制度。圆柱半径比固定为$η=r_i/r_o=0.91$。无量纲剪切驱动（泰勒数$\text{Ta}$）的范围$10^7\leq\text{Ta}\leq10^{11}$探索的共同和反向旋转的配置。在$\text{Ta}$范围$10^8\leq\text{Ta}\leq10^{10}$，我们观察到两个局部最大值的角动量传输作为一个函数的圆柱旋转比，这可以被描述为“共同”和“反向旋转”，由于其位置或“宽”和“窄”，由于其形状。我们确认，宽峰是伴随着加强的大型结构，而窄峰出现时，驱动（Ta）是足够强的。正如Brauckmann \emph{et al.} ~（2016）在数值模拟中首次证明的那样，宽峰是由离心不稳定性产生的，窄峰是剪切不稳定性的结果。我们描述了随着流动变得更加湍流，峰值如何随$\text{Ta}$而变化。当边界层（BL）变成湍流时，接近向最终状态的过渡时，通常的反向旋转泰勒涡对结构破裂，局部出现稳定的不成对滚转。我们将这种状态归因于在向极限状态过渡的过程中潜在的滚转特性的变化。进一步改变$\text{Ta}\approx10^{10}$周围的流动结构，导致宽峰完全消失，窄峰移动。当边界层内部的局部光滑区域消失并且整个边界层变得活跃时，引起第二次转变。

英文摘要：

We use experiments and direct numerical simulations to probe the phase-space of low-curvature Taylor--Couette (TC) flow in the vicinity of the ultimate regime. The cylinder radius ratio is fixed at $η=r_i/r_o=0.91$. Non-dimensional shear drivings (Taylor numbers $\text{Ta}$) in the range $10^7\leq\text{Ta}\leq10^{11}$ are explored for both co- and counter-rotating configurations. In the $\text{Ta}$ range $10^8\leq\text{Ta}\leq10^{10}$, we observe two local maxima of the angular momentum transport as a function of the cylinder rotation ratio, which can be described as either as "co-" and "counter-rotating" due to their location or as "broad" and "narrow" due to their shape. We confirm that the broad peak is accompanied by the strengthening of the large-scale structures, and that the narrow peak appears once the driving (Ta) is strong enough. As first evidenced in numerical simulations by Brauckmann \emph{et al.}~(2016), the broad peak is produced by centrifugal instabilities and that the narrow peak is a consequence of shear instabilities. We describe how the peaks change with $\text{Ta}$ as the flow becomes more turbulent. Close to the transition to the ultimate regime when the boundary layers (BLs) become turbulent, the usual structure of counter-rotating Taylor vortex pairs breaks down and stable unpaired rolls appear locally. We attribute this state to changes in the underlying roll characteristics during the transition to the ultimate regime. Further changes in the flow structure around $\text{Ta}\approx10^{10}$ cause the broad peak to disappear completely and the narrow peak to move. This second transition is caused when the regions inside the BLs which are locally smooth regions disappear and the whole boundary layer becomes active.

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