The European Physical Journal B

, Volume 73, Issue 2, pp 275–285 | Cite as

Improved ɛ expansion in the theory of turbulence: summation of nearest singularities by inclusion of an infrared irrelevant operator

Statistical and Nonlinear Physics

Abstract

A method is put forward to improve the ε expansion in the theory of developed d-dimensional turbulence on the basis of the renormalization of random forcing in the stochastic Navier-Stokes equation. This renormalization takes into account additional divergences, which appear as d →2. In the nth order of the perturbation theory with the extended renormalization the first n terms of the usual ε expansion are correctly reproduced as well as the first n terms of the Laurent expansion in the parameter d-2 of the terms of the rest of the usual ε expansion. The Kolmogorov constant and skewness factor calculated in the one-loop approximation of the improved perturbation theory are in reasonable agreement with their recommended experimental values.

Keywords

Pair Correlation Function Composite Operator Renormalization Scheme Inertial Range Renormalization Constant 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsSt. Petersburg UniversitySt. Petersburg, PetrodvoretsRussia
  2. 2.Institute of Experimental Physics, Slovak Academy of SciencesKošiceSlovakia
  3. 3.Faculty of Sciences, P.J. Šafarik UniversityKošiceSlovakia
  4. 4.Department of Military TechnologyNational Defence UniversityHelsinkiFinland

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