Covariant lyapunov analysis of chaotic kolmogorov flows and time-correlation function

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

    Research output: Contribution to journalConference article

    4 Citations (Scopus)

    Abstract

    We study a hyperbolic/non-hyperbolic transition of the flows on two-dimensional torus governed by the incompressible Navier-Stokes equation (Kolmogorov flows) using the method of covariant Lyapunov analysis developed by Ginelli et al.(2007) [1]. As the Reynolds number is increased, chaotic Kolmogorov flows become non-hyperbolic at a certain Reynolds number, where some new physical property is expected to appear in the long-time statistics of the fluid motion. Here we focus our attention on behaviors of the time-correlation function of vorticity across the transition point, and that the long-time asymptotic form of the correlation function changes at the Reynolds number close to that of the hyperbolic/non-hyperbolic transition, which suggests that the time-correlation function reflects the transition to non-hyperbolicity [3].

    Original languageEnglish
    Pages (from-to)244-248
    Number of pages5
    JournalProcedia IUTAM
    Volume5
    DOIs
    Publication statusPublished - 2012 Jan 1
    EventIUTAM Symposium on 50 Years of Chaos: Applied and Theoretical - Kyoto, Japan
    Duration: 2011 Nov 282011 Dec 2

    Keywords

    • Covariant lyapunov vector
    • Kolmogorov flow
    • Time-correlation function

    ASJC Scopus subject areas

    • Mechanical Engineering

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