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

Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano

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

Authors

Mazzino, Andrea

Muratore-Ginanneschi, Paolo

Musacchio, Stefano

Description

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