被动指向矢混沌平流中出现的疤痕线
Emergent scar lines in chaotic advection of passive directors
摘要：
我们研究了由二维流体流平流的细长纤维的取向的空间场。这些被动指向矢的定向场在广泛的工业和地球物理流中是重要的。在混沌流中，我们引入了作为被动指向矢取向场中主导相干结构的涌现痕线。以前的工作已经确定了疤痕线的存在，其中方向在短距离内旋转π，但随着时间的推移，被确定的线消失了。其结果是，早期的工作集中在拓扑奇点的方向领域，我们发现在很长一段时间内发挥的作用可以忽略不计。我们使用的标准映射作为一个简单的时间周期二维（2D）流，产生拉格朗日混沌。这类流动产生持久的模式，被动标量平流，我们发现，一种不同的持久模式的发展中的被动导演方向场。我们确定的机制，紧急疤痕线增长，以主导这些模式在很长一段时间内在复杂的流量。在流体元素最近的拉伸垂直于先前的拉伸的地方形成了浮现的疤痕线。因此，这些疤痕线可以用它们的年龄来标记，定义为它们的拉伸达到最大值的时间。
英文摘要：
We examine the spatial field of orientations of slender fibers that are advected by a two-dimensional fluid flow. The orientation field of these passive directors are important in a wide range of industrial and geophysical flows. We introduce emergent scar lines as the dominant coherent structures in the orientation field of passive directors in chaotic flows. Previous work has identified the existence of scar lines where the orientation rotates by π over short distances, but the lines that were identified disappeared as time progressed. As a result, earlier work focused on topological singularities in the orientation field which we find to play a negligible role at long times. We use the standard map as a simple time-periodic two-dimensional (2D) flow that produces Lagrangian chaos. This class of flows produce persistent patterns in passive scalar advection, and we find that a different kind of persistent pattern develops in the passive director orientation field. We identify the mechanism by which emergent scar lines grow to dominate these patterns at long times in complex flows. Emergent scar lines form where the recent stretching of the fluid element is perpendicular to earlier stretching. Thus these scar lines can be labeled by their age, defined as the time since their stretching reached a maximum.
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