Asymptotic formulae for the Lyapunov spectrum of fully-developed shell model turbulence

Details Asymptotic formulae for the Lyapunov spectrum of fully-developed shell model turbulence Asymptotic formulae for the Lyapunov spectrum of fully-developed shell model turbulence

1996-06-21

arxiv.org/abs/chao-dyn/9606009v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, PostScript file of 7 figures available upon request to yamada@ms.u-tokyo.ac.jp

Scientific paper

We study the scaling behavior of the Lyapunov spectra of a chaotic shell model for 3D turbulence. First, we quantify localization of the Lyapunov vectors in the wavenumber space by using the numerical results. Using dimensional arguments of Kolmogorov-type, we then deduce explicitly the asymptotic scaling behavior of the Lyapunov spectra. This in turn is confirmed by numerical results. This shell model may be regarded as a rare example of high-dimensional chaotic systems for which an analytic expression is known for the Lyapunov spectrum. Implications for the Navier-Stokes turbulence is given. In particular we conjecture that the distribution of Lyapunov exponents is {\it not} singular at null exponent.

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