亚临界剪切流盆边界中混沌与分形的涌现
Emergence of chaos and fractality in the basin boundary of subcritical shear flow
浏览论文内容
中文总结 AI 辅助
研究泰勒-库埃特流亚临界区域，揭示亚临界剪切流盆边界边缘态变混沌的两步机制，即异宿缠结与异宿环的形成，表明边缘态特性对参数敏感。
中文摘要 AI 辅助
从剪切流亚临界转捩的动力学系统视角来看，分隔层流与湍流吸引子的盆边界，以及支配该边界上长期动力学的边缘态，具有根本重要性。当雷诺数从较小值升高时，相空间中会出现多种简单的精确相干结构（ECS），其中一种常扮演边缘态的角色。然而，在雷诺数更高时，盆边界和边缘态上的动力学对初始条件敏感，这已被大量数值与实验研究所证实。此转捩背后的机制仍不明确。为解决该问题，我们采用最小计算盒研究泰勒-库埃特流的亚临界区域，揭示了边缘态变为混沌的通用机制。该过程的第一步涉及行波型ECS与独立产生的混沌鞍之间异宿缠结的形成；这种相互作用使盆边界纳入该鞍，从而继承其分形结构，而边缘态本身仍为简单的ECS。边缘态向混沌的转捩需要第二步：形成包含该ECS与混沌鞍的异宿环。因此，在给定参数值下观察到简单的非混沌边缘态，无法保证在邻近参数值下仍会出现相同情况。
英文摘要
From a dynamical systems perspective of subcritical transition in shear flows, the basin boundary separating the laminar and turbulent attractors, along with the edge state that governs the long-term dynamics on that boundary, are of fundamental interest. As the Reynolds number is increased from small values, a multiplicity of simple exact coherent structures (ECS) appear in phase space, of which one often undertakes the role of the edge state. At higher values of the Reynolds number, however, the dynamics on the basin boundary and the edge state are sensitive to initial conditions, as shown by a wealth of numerical and experimental studies. The mechanism behind this transition remains unclear. To address this, we examine the subcritical regime of Taylor-Couette flow using a minimal computational box and reveal a generic mechanism whereby the edge state becomes chaotic. The first step in this process involves the formation of a heteroclinic tangle between a travelling-wave-type ECS and an independently engendered chaotic saddle. The interaction causes the basin boundary to incorporate the saddle, thus inheriting its fractal structure, while the edge state itself remains the simple ECS. The transition of the edge state to chaos requires a second step: the formation of a heteroclinic cycle involving the ECS and the chaotic saddle. In consequence, the observation of a simple non-chaotic edge state at given values of the parameters is no guarantee that the same situation will hold at nearby values.
