Dynamical aspects of vortex reconnection of perturbed anti-parallel vortex tubes
Dynamical aspects of vortex reconnection of perturbed anti-parallel vortex tubes
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DOI：
10.1017/s0022112093000291
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发表时间：
1993-01
影响因子：
3.7
通讯作者：
M. Shelley;D. Meiron;S. Orszag
中科院分区：
文献类型：
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作者：
M. Shelley;D. Meiron;S. Orszag
对涡旋重联现象进行了数值分析，并与Saffman最近提出的一种重联模型的预测结果进行了定性比较。在雷诺数Re = 1000 ~ 3500范围内，采用均匀网格和应变网格的谱方法对两个几乎平行的反向旋转涡旋管进行了数值模拟。采用均匀网格计算，Re≤1500，每个方向分辨率为128点。使用拉伸网格的计算在1500 < Re≤3500的范围内进行，每个方向的分辨率高达160点，并且在重新连接区域周围进行四倍拉伸。我们给出了最大涡度变化的结果，重新连接的时间，以及该流的其他诊断作为雷诺数的函数。从模型方程的数值模拟中，我们推断并证明了模型的精确解的存在性，并且模型的解在较晚的时间被更一般的初始条件所吸引。在无限雷诺数的极限下，该模型预测轴向应变的最终饱和，这一特征在Pumir & Siggia最近的工作中观察到，在我们的完整数值模拟中也观察到。在这方面，该模型捕获了观测到的涡旋拉伸的局部动力学。然而，由于模型中没有考虑外部流动的整体影响，该模型预测轴向应变最终衰减，最大涡量在后期线性增长。相反，从完整的模拟中，我们看到了无限雷诺数下轴向应变行为的可能出现。由于我们的模拟受到非局部效应的影响，我们确实观察到应变的饱和，但没有随后的衰减。分析还表明，该模型预测的重联时间随雷诺数的增加呈对数变化。与全数值模拟的比较表明，随着雷诺数的增加，重联时间的变化比模型预测的要慢得多。讨论了Saffman模型与模拟之间的其他一致点和不一致点，并从其与欧拉方程可能出现的近奇异行为的关系的角度讨论了重连。与Pumir & Siggia最近的数值结果一致，我们的结果表明，在这个初始条件下，涡度在有限时间内不会形成奇点。
The phenomenon of vortex reconnection is analysed numerically and the results are compared qualitatively with the predictions of a model of reconnection recently proposed by Saffman. Using spectral methods over both uniform and strained meshes, numerical simulations are performed of two nearly parallel, counter-rotating vortex tubes, over the range of Reynolds numbers Re = 1000–3500. The calculations utilizing a uniform mesh are performed for Re ≤ 1500 with a resolution of 128 points in each direction. The calculations utilizing a stretched mesh are performed for 1500 < Re ≤ 3500 with a resolution of up to 160 points in each direction and with a fourfold stretching about the region of reconnection. We present results for the variation of the maximum of vorticity, the time to reconnection, and other diagnostics of this flow as functions of the Reynolds number. From numerical simulation of the model equations, we infer and demonstrate the existence of exact solutions to the model to which its solutions arising from more general initial conditions are attracted at late times. In the limit of infinite Reynolds number, the model predicts eventual saturation of the axial strain, a feature observed in the recent work of Pumir & Siggia and also observed in our full numerical simulations. In this respect the model captures the observed local dynamics of vortex stretching. However, because the global effects of external flows are not included in the model, the model predicts that the axial strain eventually decays and the maximum vorticity grows linearly at late times. In contrast, from the full simulations, we see the possible emergence of the behaviour of the axial strain at infinite Reynolds number. As our simulations are affected by non-local effects, we do observe saturation of the strain but no subsequent decay. It is also shown analytically that the model predicts a reconnection time which varies logarithmically with increasing Reynolds number. Comparison with the full numerical simulations shows a much slower variation of the reconnection time with increasing Reynolds number than predicted by the model. Other points of agreement and disagreement between the Saffman model and the simulations are discussed, Reconnection is also discussed from the point of view of its relation to the possible onset of nearly singular behaviour of the Euler equation. In agreement with the recent numerical results of Pumir & Siggia, our results suggest that no singularity in the vorticity will form in a finite time for this initial condition.