DOI: 10.1615/TSFP4
SPECTRAL EVOLUTION OF TURBULENCE IN THE LIMIT OF SLOW VARIATION
RÉSUMÉ
The ε equation is considered from the viewpoint of spectral evolution in a closure theory. The balance of vortex stretching and enstrophy destruction, on which the e equation depends, occurs whenever the spectrum can be described by parameters that vary slowly relative to the turbulence itself. The central question for modeling is whether these parameters satisfy closed equations of motion. A multiple scale analysis of a closure model in the slow variation limit, analogous to the Chapman-Enskog expansion of kinetic theory, suggests that a universal ε equation does not exist. Further evidence against this possibility is given by constructing self-similar states of turbulence evolution each of which is consistent with an ε equation with different constants.