Knot spectrum of turbulence
Knot spectrum of turbulence
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DOI：
10.1038/s41598-019-47103-w
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发表时间：
2019-07
影响因子：
4.6
通讯作者：
R. G. Cooper;M. Mesgarnezhad;A. Baggaley;A. Baggaley;C. Barenghi;C. Barenghi
中科院分区：
文献类型：
--
作者：
R. G. Cooper;M. Mesgarnezhad;A. Baggaley;A. Baggaley;C. Barenghi;C. Barenghi
湍流流体和等离子体中的流线、涡线和磁通量管表现出大量的卷曲、扭曲和连接，这就提出了一个问题，即它们的拓扑复杂性(通过重新连接不断地产生和破坏)是否可以量化。在超流氦中，涡度的离散(量子化)性质可以被用来与每个涡旋环关联一个称为亚历山大多项式的纽结不变量，其阶数表征了该涡旋环的拓扑结构。通过数值模拟纠缠的量子涡旋线的动力学，我们发现这种量子湍流总是包含非常大程度的涡结，这些涡结不断地形成、消失和重塑，产生了一种拓扑分布，我们用节谱及其标度律来量化这种分布。我们还发现与更广泛的文献中的结果相似，表明涡旋缠绕的打结几率随着涡旋长度的增加而增加，对于大分子来说，并且在特征长度以上饱和，就像对于翻滚的弦一样。
Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.