标题： 湍流 puff 的自复制：在混沌鞍点的边缘 显示英文标题

标题： Self-Replication of Turbulent Puffs: On the edge between chaotic saddles

摘要： 管道流动是亚临界流的一个典型例子，过渡到湍流需要有限的扰动。 雷诺数（$Re$）作为这一过渡的控制参数，在增加$Re$的过程中，从有序（层流）转变为混沌（湍流）相。 就在临界值$Re$之上，湍流可以无限持续，湍流通过称为脉冲的局域湍流结构的自我复制而扩散。 为了揭示这一过程背后的机制，我们考虑了一和二脉冲状态之间的转换，动态上是两个不同的混沌鞍点之间的转换。 我们使用直接数值模拟来探索这些鞍点之间的相空间边界，采用二分算法识别边界上的吸引态，称为边缘状态。 在$Re = 2200$处，我们还检查了两个鞍点之间的自发转换，展示了找到的边缘状态对脉冲自我复制的相关性。 我们的分析揭示，自我复制的过程遵循先前提出的分裂机制，找到的边缘状态作为其临界点。 此外，我们报告了较低$Re$值的结果，在此情况下，二分算法产生了不同类型的边缘状态。 由于在此$Re$下无法直接观察到分裂，自我复制机制仍然是一个未解之谜。 我们的分析表明未来研究如何解决这个问题，并为探究其他亚临界流中的湍流扩散机制铺平了道路。 显示英文摘要

摘要： Pipe flow is a canonical example of a subcritical flow, the transition to turbulence requiring a finite perturbation. The Reynolds number ($Re$) serves as the control parameter for this transition, going from the ordered (laminar) to the chaotic (turbulent) phase with increasing $Re$. Just above the critical $Re$, where turbulence can be sustained indefinitely, turbulence spreads via the self-replication of localized turbulent structures called puffs. To reveal the workings behind this process, we consider transitions between one and two-puff states, which dynamically are transitions between two distinct chaotic saddles. We use direct numerical simulations to explore the phase space boundary between these saddles, adapting a bisection algorithm to identify an attracting state on the boundary, termed an edge state. At $Re = 2200$, we also examine spontaneous transitions between the two saddles, demonstrating the relevance of the found edge state to puff self-replication. Our analysis reveals that the process of self-replication follows a previously proposed splitting mechanism, with the found edge state as its tipping point. Additionally, we report results for lower values of $Re$, where the bisection algorithm yields a different type of edge state. As we cannot directly observe splits at this $Re$, the self-replication mechanism here remains an open question. Our analysis suggests how this question could be addressed in future studies, and paves the way to probing the turbulence proliferation mechanism in other subcritical flows.