Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation

Details Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation

2002-07-02

arxiv.org/abs/nlin/0207007v1

Int. Journ. Mod. Phys. B17 (2003) 2137-2170

Nonlinear Sciences

Chaotic Dynamics

20 pages, 3 figures

Scientific paper

10.1142/S0217979203018193

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, 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.

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