Analysis of Lundgren's matched asymptotic expansion approach to the Kármán-Howarth equation using the eddy damped quasinormal Markovian turbulence closure

Abstract

Using the eddy damped quasinormal Markovian (EDQNM) model we obtain numerical predictions which comply remarkably well with the results of Lundgren's matched asymptotic expansion approach to the K\`arm\`an-Howarth equation. Both predict that a Kolmogorov inertial range equilibrium is not obtained. Equilibrium is only achieved in the vicinity of the Taylor length in the limit where the Reynolds number tends to infinity and the Taylor length is not in the inertial range given its explicit dependence on viscosity.