The field theoretic renormalization group is applied to the stochastic Navier--Stokes equation that describes fully developed fluid turbulence. The complete two-loop calculation of the renormalization constant, the beta function and the fixed point is performed. The ultraviolet correction exponent, the Kolmogorov constant and the inertial-range skewness factor are derived to second order of the ϵ expansion.
@article{arxiv.nlin/0205046,
title = {Renormalization group in the statistical theory of turbulence: Two-loop approximation},
author = {L. Ts. Adzhemyan and N. V. Antonov and M. V. Kompaniets and A. N. Vasil'ev},
journal= {arXiv preprint arXiv:nlin/0205046},
year = {2007}
}