The non-equilibrium part of the inertial range in decaying homogeneous turbulence

¹ Université Grenoble Alpes, CNRS, Grenoble- INP, LEGI - F-38000, Grenoble, France
² Department of Aeronautics, Imperial College London - London, UK

^(a) Univ. Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille, FRE 2017 - LMFL - Laboratoire de Mécanique des fluides de Lille - Kampé de Feriet, F-59000 Lille, France; john-christos.vassilicos@centralelille.fr

Received: 18 July 2019
Accepted: 29 September 2019

Abstract

We use two related non-stationarity functions as measures of the degree of scale-by-scale non-equilibrium in homogeneous isotropic turbulence. The values of these functions indicate significant non-equilibrium at the upper end of the inertial range. Wind tunnel data confirm Lundgren's prediction that the two-point separation r where the second- and third-order structure functions are closest to their Kolmogorov scalings is proportional to the Taylor length-scale λ, and that both structure functions increasingly distance themselves from their Kolmogorov equilibrium form as r increases away from λ throughout the inertial range. With the upper end of the inertial range in non-equilibrium irrespective of Reynolds number, it is not possible to justify the Taylor-Kolmogorov turbulence dissipation scaling on the basis of Kolmogorov equilibrium.