Relative periodic orbits form the backbone of turbulent pipe flow
Relative periodic orbits form the backbone of turbulent pipe flow
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DOI：
10.1017/jfm.2017.699
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发表时间：
2017-12-25
影响因子：
3.7
通讯作者：
Cvitanovic, P.
中科院分区：
文献类型：
--
作者：
Budanur, N. B.;Short, K. Y.;Cvitanovic, P.
低维系统的混沌动力学，如Lorenz或Rossler流，是由嵌入在其奇怪吸引子中的无限周期轨道引导的。对于Navier-Stokes方程的无限维动力学是否也是如此，长期以来一直是人们猜测的问题，也是正在进行的研究的主题。周期解和相对周期解已被证明参与了向湍流的转变。它们与湍流动力学的相关性--具体地说，周期轨道在像Navier-Stokes方程这样的高维非线性系统中是否起到与在低维系统中相同的作用--是目前研究的重点。本文对能量和平均耗散接近湍流值的管流相对周期轨道进行了详细的研究。我们概述了几种降低系统平移对称性的方法。我们研究了R-e=2500的最小计算单元中的管道流动，并报告了借助于条分法找到的不变解库。对这些解的样本的不稳定流形的详细研究与相对周期轨道嵌入在混沌鞍座中并指导湍流动力学的图景是一致的。
The chaotic dynamics of low-dimensional systems, such as Lorenz or Rossler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier-Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics - specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier-Stokes equations as they do in lower-dimensional systems - is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at R-e = 2500, and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics.