Edge of chaos in a parallel shear flow
Edge of chaos in a parallel shear flow
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DOI：
10.1103/physrevlett.96.174101
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发表时间：
2006-05-05
影响因子：
8.6
通讯作者：
Eckhardt, B
中科院分区：
文献类型：
--
作者：
Skufca, JD;Yorke, JA;Eckhardt, B
本文研究了稳定层流和瞬态湍流共存的平行剪切流的Galerkin表示中层流和湍流状态之间的转换。在初始条件下，寿命表现出强烈的波动和对初始条件的敏感依赖的区域与寿命平滑变化的区域被相空间中的一个物体分开，我们称之为“混沌边缘”。我们描述了识别和跟踪边缘的技术，我们的结果表明边缘是一个表面。当雷诺数较低时，表面重合于周期轨道的稳定流形，而当雷诺数较高时，表面重合于高维混沌物体的稳定集。
We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth variation of lifetimes by an object in phase space which we call the "edge of chaos." We describe techniques to identify and follow the edge, and our results indicate that the edge is a surface. For low Reynolds numbers we find that the surface coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.