Journal of Statistical Physics

, Volume 93, Issue 3–4, pp 715–724 | Cite as

Scaling of the Irreducible SO(3)-Invariants of Velocity Correlations in Turbulence

  • Siegfried Grossmann
  • Detlef Lohse
  • Achim Reeh


The scaling behavior of the SO(3) irreducible amplitudes \(d_n^1 (r)\) of velocity structure tensors is numerically examined for Navier–Stokes turbulence. Here, l characterizes the irreducible representation by the index of the corresponding Legendre polynomial, and n denotes the tensorial rank, i.e., the order of the moment. For moments of different order n but with the same representation index l extended self-similarity (ESS) towards large scales is found. Intermittency seems to increase with l. We estimate that a crossover behavior between different inertial subrange scaling regimes in the longitudinal and transversal structure functions will hardly be detectable for achievable Reynolds numbers.

Fully developed turbulence SO(3) invariants of velocity correlations scaling exponents intermittency longitudinal vs. transversal velocity structure functions 


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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Siegfried Grossmann
    • 1
  • Detlef Lohse
    • 1
  • Achim Reeh
    • 1
  1. 1.Fachbereich Physik der Universität MarburgMarburgGermany;

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