Kolmogorov's 1941 (K41) framework remains central to the understanding of turbulent flows. However, in unsteady turbulence, K41's critical equilibrium assumption is expected to hold in an asymptotic manner, as the Reynolds number and wave numbers tend to infinity, rendering K41 not strictly valid at finite wave numbers. This work proposes a generalization of K41 for out-of-equilibrium effects and cascades far from initial conditions. The main result is a correction to the $-5/3$ law for out-of-equilibrium eddies, unrelated to intermittency effects. Experimental and numerical evidence is provided in support of the theoretical results.

• Received 1 November 2021
• Accepted 4 March 2022

DOI:https://doi.org/10.1103/PhysRevE.105.035109