Anomalous scaling of structure functions and dynamic constraints on turbulence simulations

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The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as Re 4, and not as Re 3 expected from Kolmogorov's theory, where Re is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier-Stokes equations, and some problems of principle associated with existing LES models are highlighted.

Original languageEnglish (US)
Pages (from-to)823-841
Number of pages19
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Dec 2005


  • Anomalous scaling
  • Direct numerical simulations
  • Hydrodynamic turbulence
  • Large eddy simulations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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