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

TL;DR

This paper investigates the non-equilibrium behavior at the upper end of the inertial range in decaying homogeneous turbulence, challenging classical Kolmogorov assumptions and confirming theoretical predictions with wind tunnel data.

Contribution

It introduces non-stationarity functions to measure scale-by-scale non-equilibrium and confirms the non-equilibrium state at the inertial range's upper end through experimental data.

Findings

Significant non-equilibrium at the upper inertial range.

Validation of Lundgren's prediction relating structure functions to the Taylor length scale.

Inability to justify Kolmogorov scaling based on equilibrium assumptions.

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 (2002, 2003) 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 $\lambda$, and that both structure functions increasingly distance themselves from their Kolmogorov equilibrium form as $r$ increases away from $\lambda$ 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.