On Intermittency in Shell Models and in Turbulent Flows

  • Itamar Procaccia
  • Roberto Benzi
  • Luca Biferale
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 4)


We propose an approach to study the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by ‘Statistically Preserved Structures’ which are associated with statistical conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations, and it demonstrates that the scaling exponents of these nonlinear models are indeed anomalous. In order to adress the universality of these nonlinear model we study the statistical properties of a semi-infinite chain of passive vectors advecting each other and study the scaling exponents at the fixed point of this chain.


turbulence anomalous exponents statistically preserved structures shell models 


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Copyright information

© Springer 2008

Authors and Affiliations

  • Itamar Procaccia
    • 1
  • Roberto Benzi
    • 2
  • Luca Biferale
    • 2
  1. 1.The Department of Chemical PhysicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Dept. of Physics and INFNUniversity of Rome “Roma Tor Vergata”RomeItaly

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