In this paper we investigate whether the features of the nonequilibrium cascade, which have been identified in recent studies using high-fidelity tools, can be captured in the case of the classical dissipation scaling by turbulence closures based on the statistical description of freely decaying isotropic turbulence. Numerical results obtained using the eddy damped quasinormal Markovian (EDQNM) model over a very large range of Reynolds numbers (from $R{e}_{\lambda }=50$ up to $R{e}_{\lambda }={10}^6$) are analyzed to perform an extensive investigation of the scaling region identified as inertial range in Kolmogorov's theory. It is observed that EDQNM results are in agreement with the results of Lundgren's matched asymptotic expansion approach to the Kármán-Howarth equation. Both predict that the Kolmogorov inertial range equilibrium is never obtained irrespective of Reynolds number. Equilibrium is reached in the vicinity of the Taylor length $\lambda$ (which depends on viscosity) as Reynolds number tends to infinity and there is a gradual departure from equilibrium as the length scale moves away from $\lambda$, in particular towards scales larger than $\lambda$ all the way to the integral length scale.

• Received 20 December 2020
• Accepted 3 May 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.064602