On the Scale-Invariant Theory of Developed Hydrodynamic Turbulence Kolmogorov Type

  • Victor S. L’vov
Part of the NATO ASI Series book series (NSSB, volume 225)


The modern statistical theory of hydro dynamic turbilience goes back to the papers by Kraichnan and Wyld [1,2], who suggested to simulate excitation of stationary space-homogeneous developed hydrodynamic turbulence with the help of a space-distributed variable force f(r,t). According to the Kolmogorov-Obukhov’s universality hypothesis [3,4] one can believe that in the limit of a large Reynolds number, the properties of fine-scale part of the turbulence (in the inertial range) will not depend on the way of turbulence excitation, i.e. of the type of the boundary conditions for the liquid flow or characteristics of the exciting force f̄(r̄,t). Therefore, one can suppose that the force f̄ is a random force with a Gaussian statistics, it does not excite the mean flow: <f̄(r̄,t)> = 0, and its pair correlator D depends only on the coordinates and time difference:


Inertial Range Exciting Force Euler Velocity Lagrange Velocity Kolmogorov Turbulence 
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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Victor S. L’vov
    • 1
  1. 1.Siberian Branch of Academy of ScienceInstitute of Automation and ElectrometryNovosibirskU.S.S.R.

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