On the scaling properties of 2d randomly stirred Navier--Stokes equation

Abstract

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

4 pages, 5 figures

References in corpus (2)

• An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
• Effects of forcing in three dimensional turbulent flows

Cited by in corpus (3)

• Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise
• Functional renormalisation group approach to shell models of turbulence
• Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment