标题： 平稳湍流的拓扑熵 显示英文标题

标题： Topological Entropy of Stationary Turbulent Flows

摘要： 拓扑熵作为量化高度混沌系统混合和复杂性的可行候选。 特别是在湍流中，这是通过流体物质线的指数拉伸率来确定的，这通常需要拉格朗日描述。 我们将最近的工作[A. Manoharan, S. Subramanian 和 A. Joy, arXiv:2412.08996]扩展到三维，并提出了一个精确的欧拉框架，用于稳态湍流中的拓扑熵，该框架不包含自由参数。 唯一的要求是局部应变率张量的特征值分布及其去相关时间。 这可以从固定位置的一个线探针中轻松获得，从而消除了因流动的混沌性质而仍然困难的拉格朗日粒子追踪的需要。 我们认为，我们的结果在旨在理解许多工业和自然流动中输运和混合的实验中具有很大的实用性。 显示英文摘要

摘要： Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically necessitates a Lagrangian description. We extend the recent work [A. Manoharan, S. Subramanian, and A. Joy, arXiv:2412.08996] to three dimensions, and present an exact Eulerian framework for the topological entropy in stationary turbulent flows that is devoid of free parameters. The only prerequisite is a distribution of eigenvalues of the local strain-rate tensor and their decorrelation times. This can be easily obtained from a single wire probe at a fixed location, thereby eliminating the need for Lagrangian particle tracking, which remains formidable due to chaotic nature of the flow. We believe that our results lend great utility in experiments aimed at understanding transport and mixing in many industrial and natural flows.