A mean field prediction of the asymptotic state of decaying 2D turbulence

Abstract

We compare the quasi-stationary state obtained from a numerical integration of the two-dimensional Navier-Stokes equation, performed by Matthaeus et al. [Phys. Rev. Lett. 66, 2731 (1991)] with predictions of a mean field theory based on inviscid dynamics. We find that over a relatively short initial period, the theory does not apply, whereas at later stages its prediction for the quasi-stationary state is very good. We relate the failure and success of the inviscid theory to the relevance of viscous effects in the dynamics.