Covariant Lyapunov analysis of chaotic Kolmogorov flows
Covariant Lyapunov analysis of chaotic Kolmogorov flows
复制标题
混沌 Kolmogorov 流的协变 Lyapunov 分析
DOI：
10.1103/physreve.85.016331
复制
发表时间：
2012
影响因子：
2.4
通讯作者：
Michio Yamada
中科院分区：
文献类型：
--
作者：
Masanobu Inubushi;Miki U. Kobayashi;Shin-ichi Takehiro;Michio Yamada
双曲性是动力系统理论中的一个重要概念；然而，我们对具体物理系统的双曲性知之甚少，包括由Navier-Stokes方程控制的流体运动。本文利用Ginelliet等人提出的协变Lyapunov向量方法，对二维环面上（Kolmogorov流）的Navier-Stokes方程的双曲性进行了数值研究。[j].科学通报，1999,13(2):481 - 481。我们计算了局部稳定流形和不稳定流形沿混沌解的轨道之间的夹角来评价其双曲性。我们发现混沌Kolmogorov流动的吸引子在小雷诺数下是双曲的，但在大雷诺数下局部稳定流形和不稳定流形之间的夹角较小，并且在一定雷诺数下吸引子表现为非双曲的。此外，我们还观察到了这些双曲性质与涡度和能量耗散率的时间相关性等物理性质之间的一些关系。
Hyperbolicity is an important concept in dynamical system theory; however, we know little about the hyperbolicity of concrete physical systems including fluid motions governed by the Navier-Stokes equations. Here, we study numerically the hyperbolicity of the Navier-Stokes equation on a two-dimensional torus (Kolmogorov flows) using the method of covariant Lyapunov vectors developed by Ginelliet al.[Phys. Rev. Lett. 99, 130601 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.130601]. We calculate the angle between the local stable and unstable manifolds along an orbit of chaotic solution to evaluate the hyperbolicity. We find that the attractor of chaotic Kolmogorov flows is hyperbolic at small Reynolds numbers, but that smaller angles between the local stable and unstable manifolds are observed at larger Reynolds numbers, and the attractor appears to be nonhyperbolic at a certain Reynolds numbers. Also, we observed some relations between these hyperbolic properties and physical properties such as time correlation of the vorticity and the energy dissipation rate.