Yamada, M. and Ohkitani, K. (1998) Asymptotic formulas for the Lyapunov spectrum of fully developed shell model turbulence. Physical Review E, 57 (6). R6257-R6260. ISSN 1539-3755
Abstract
The scaling behavior of the Lyapunov spectrum of a chaotic shell model for three-dimensional turbulence is studied in detail. First, we characterize the localization property of the Lyapunov vectors in wave-number space by using numerical results. By combining this localization property with Kolmogorov’s dimensional argument, we deduce explicitly the asymptotic scaling law for the Lyapunov spectrum, which in turn is shown to agree well with the numerical results. This shell model is an example of high-dimensional chaotic systems for which an asymptotic scaling law is obtained for the Lyapunov spectrum. Implications of the present results for the Navier-Stokes turbulence are discussed. In particular, we conjecture that the distribution of Lyapunov exponents is not singular at null exponent.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©1998 American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Oct 2017 13:25 |
Last Modified: | 05 Oct 2017 13:25 |
Published Version: | https://doi.org/10.1103/PhysRevE.57.R6257 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevE.57.R6257 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:122075 |