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

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.