Large volume limit of the distribution of characteristic exponents in turbulence View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1982-06

AUTHORS

David Ruelle

ABSTRACT

For spatially extended conservative or dissipative physical systems, it appears natural that a density of characteristic exponents per unit volume should exist when the volume tends to infinity. In the case of a turbulent viscous fluid, however, this simple idea is complicated by the phenomenon of intermittency. In the present paper we obtain rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation. These bounds have a reasonable large volume behavior. For two-dimensional fluids a particularly striking result is obtained: the total information creation is bounded above by a fixed multiple of the total energy dissipation (at fixed viscosity). The distribution of characteristic exponents is estimated in an intermittent model of turbulence (see [7]), and it is found that a change of behavior occurs at the valueD=2.6 of the self-similarity dimension. More... »

PAGES

287-302

References to SciGraph publications

  • 1978-03. An inequality for the entropy of differentiable maps in BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, NEW SERIES
  • 1981. On the dimension of the compact invariant sets of certain non-linear maps in DYNAMICAL SYSTEMS AND TURBULENCE, WARWICK 1980
  • 1981-06. Some relations between dimension and Lyapounov exponents in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1976. Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3+B in TURBULENCE AND NAVIER STOKES EQUATIONS
  • 1983. Lyapounov exponents and stable manifolds for compact transformations in GEOMETRIC DYNAMICS
  • 1982-12. The evolution of a turbulent vortex in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1979-12. A proof of Oseledec’s multiplicative ergodic theorem in ISRAEL JOURNAL OF MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01218566

    DOI

    http://dx.doi.org/10.1007/bf01218566

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1015368360


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