Covariant Lyapunov analysis of chaotic Kolmogorov flows

Masanobu Inubushi, Miki U. Kobayashi, Shin Ichi Takehiro, Michio Yamada

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    15 Citations (Scopus)


    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 Ginelli. 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.

    Original languageEnglish
    Article number016331
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Issue number1
    Publication statusPublished - 2012 Jan 31

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics


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