The approach to Kolmogorov equilibrium

At the limit of infinite Reynolds number, the K41 framework yields, asymptotically, the -5/3 law for the inertial subrange of turbulence. The latter is assumed to be in equilibrium. However, in non-stationary conditions (e.g. decaying turbulence) a large portion of the cascade will not be in equilibrium, even when the Reynolds number is extremely large. There, the -5/3 law is expected not to be exact. This work proposes a correction to the -5/3 law for scales which are not in exact equilibrium. The correction becomes asymptotically negligible when the Reynolds number tends to infinity, and for scales which are of negligible size compared to the integral length scale, in agreement with K41. A link between the K41 framework and the k-epsilon model of turbulence is also proposed. Experimental (grid turbulence) and numerical (DNS) evidence are provided in support of the proposed theoretical predictions.