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

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

2007-01-09

arxiv.org/abs/nlin/0701017v1

Phys. Rev. Lett. Vol 99, (2007), 144502.

Nonlinear Sciences

Chaotic Dynamics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.99.144502

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.

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