AN INVESTIGATION OF CHAOTIC KOLMOGOROV FLOWS
AN INVESTIGATION OF CHAOTIC KOLMOGOROV FLOWS
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DOI：
10.1063/1.858074
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发表时间：
1991-04-01
期刊：
影响因子：
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通讯作者：
FITZMAURICE, N
中科院分区：
文献类型：
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作者：
PLATT, N;SIROVICH, L;FITZMAURICE, N
对由具有稳定空间周期力的不可压缩纳维-斯托克斯方程控制的二维流（称为柯尔莫哥洛夫流）进行了数值模拟。 详细研究了雷诺数 Re 变化时的流动行为及其过渡状态，以及许多流动特征。 当 Re 变化时，流动中会发生一系列分叉。 已经观察到两种主要的流动状态：对应于不同 Re 范围的小型和大型结构状态。 每个状态都包括许多周期性、混沌和再层化窗口。 此外，每个范围都包含一个具有非唯一混沌吸引子的混沌窗口。 在大尺度结构体系中发现了空间无序但时间稳定的状态。 不同情况的特征以时间功率谱、庞加莱截面以及可能的李雅普诺夫指数和李雅普诺夫维数的形式显示。
A two-dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number Re varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow have been observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of periodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with nonunique chaotic attractors. Spatially disordered, but temporally steady states have been discovered in the large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Lyapunov dimension.