Citation
Mejia-Monasterio, Carlos and Muratore-Ginanneschi, Paolo
(2012).
A non-perturbative renormalization group study of the stochastic NavierStokes equation.
"Physical Review E", v. 86
(n. 1);
pp..
ISSN 1539-3755.
https://doi.org/10.1103/PhysRevE.86.016315.
Abstract
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4−2 ɛ of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ɛ=2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ɛ dependence of the scaling dimension of the eddy diffusivity at ɛ=3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.