Eur. Phys. J. B 73, 275-285 (2010)
https://doi.org/10.1140/epjb/e2009-00432-8

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

¹ Department of Theoretical Physics, St. Petersburg University, Ulyanovskaya 1, St. Petersburg, Petrodvorets, 198504, Russia
² Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
³ Faculty of Sciences, P.J. Šafarik University, Moyzesova 16, 040 01 Košice, Slovakia
⁴ Department of Military Technology, National Defence University, P.O. Box 7, 00861, Helsinki, Finland

Corresponding author: juha.honkonen@helsinki.fi

Received: 23 September 2009
Revised: 9 November 2009
Published online: 17 December 2009

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.