Heteroclinic and homoclinic connections in a Kolmogorov-like flow
Heteroclinic and homoclinic connections in a Kolmogorov-like flow
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DOI：
10.1103/physreve.100.013112
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发表时间：
2019-07-25
影响因子：
2.4
通讯作者：
Grigoriev, Roman O.
中科院分区：
文献类型：
--
作者：
Suri, Balachandra;Pallantla, Ravi Kumar;Grigoriev, Roman O.
最近的研究表明，纳维-斯托克斯方程的不稳定循环解为湍流动力学提供了新的见解。在本研究中，我们计算了位于反演对称子空间中的弱湍流准二维柯尔莫哥洛夫流中此类解之间的动态连接的广泛网络。特别是，我们发现不同类型的解（平衡、周期和准周期轨道）之间存在许多孤立的异宿连接，以及形成高维连接流形的连接连续体。我们还计算了周期轨道的同宿连接，并提供了强有力的证据，证明相关的同宿缠结形成了支撑对称子空间中瞬态湍流的混沌排斥极。
Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion-symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different types of solutions-equilibria, periodic, and quasiperiodic orbits-as well as continua of connections forming higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient turbulence in the symmetric subspace.