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 β function, the fixed point and the ultraviolet correction exponent is performed. The Kolmogorov constant and the inertial-range skewness factor, derived to second order of the \eps expansion, are in a good agreement with the experiment. The possibility of the extrapolation of the \eps expansion beyond the threshold where the sweeping effects become important is demonstrated on the example of a Galilean-invariant quantity, the equal-time pair correlation function of the velocity field. The extension to the d-dimensional case is briefly discussed.
@article{arxiv.nlin/0207007,
title = {Renormalization-group approach to the stochastic Navier--Stokes equation: 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/0207007},
year = {2009}
}