Turbulence cascades across equilibrium spectra

Abstract

Recent work has suggested that the spectrum of fully developed turbulence is determined by the equilibrium statistics of the Euler equations. The problem is to reconcile this fact with the irreversible aspects of turbulence. The purpose of this paper is to show that a reconciliation is possible by producing simple systems whose spectrum can be deduced from an analysis at equilibrium, yet they exhibit an irreversible transfer of an appropriate variable from large scales to small scales and dissipation. The analysis includes the dependence of the spectrum on the rate of energy transfer. © 1996 The American Physical Society.