Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow
Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow
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DOI：
10.1103/physreve.98.023105
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发表时间：
2018-08-13
影响因子：
2.4
通讯作者：
Schatz, Michael F.
中科院分区：
文献类型：
--
作者：
Suri, Balachandra;Tithof, Jeffrey;Schatz, Michael F.
最近的研究表明，Navier-Stokes方程的不稳定，非混沌的解决方案可能会提供深入的了解流体湍流。在这篇文章中，我们提出了一个相结合的实验和数值研究，探索不稳定的平衡解决方案及其不变的流形在弱湍流，电磁驱动，浅流体层的动力学作用。识别湍流演变减慢的时刻，我们计算31个不稳定平衡的一个现实的二维模型的流量。我们建立这些不稳定平衡的动力学相关性表明，他们是密切访问的湍流。我们还建立了动力学相关的不稳定流形，通过验证，他们的阴影湍流轨迹离开的不稳定平衡在状态空间中的大距离的邻域。
Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.