Scaling properties of the two-dimensional randomly stirred navier-stokes equation

Abstract

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2-2ε. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small ε regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all ε, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence. © 2007 The American Physical Society.