On universal relations in 2-D turbulence

Abstract

A rigorous study of universal laws of 2-D turbulence is presentedfor time independent forcing at all length scales.Conditions for energy and enstrophy cascades are derived, both for a general force, and for one with a large gap in itsspectrum. It is shown in the gap case that either a direct cascade of enstrophyor an inverse cascade of energy must hold, provided the gap modes of the velocity has a nonzero ensemble average. Partial rigorous supportfor 2-D analogs of Kolmogorov's 3-D dissipation law, as well as thepower law for the distributionof energy are given.