title: Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
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 4-2ε 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 ε = 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 ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
authors.affiliation: Laboratory of Physical Properties, Department of Rural Engineering, Technical University of Madrid, Av. Complutense s/n, 28040 Madrid, Spain. carlos.mejia@upm.es
authors.forename: Carlos
authors.initials: C
authors.lastname: Mejía-Monasterio
authors.forename: Paolo
authors.initials: P
authors.lastname: Muratore-Ginanneschi
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*; D013269:Stochastic Processes