1996/06/21 by M. Yamada, Michio Yamada, Yamada, M. +3
Economics, Econometrics and Finance · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9606009
8 pages, PostScript file of 7 figures available upon request to [email protected]
arxiv created 1996/06/21 · openalex publication_date 1996/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.