The illusion of a Kolmogorov cascade

The theory of Kolmogorov, enunciated for very large Reynolds numbers, has progressively been shown to be inoperative for characterizing flows of practical relevance. Yet, in a recent study by Alves Portela et al. (J. Fluid Mech., vol. 896, 2020, A16), the turbulence statistics in the very near wake of a square prism at modest Reynolds numbers, reveal a significant portion of scales complying with a cascade of Kolmogorov type. By resorting to a generalized version of the Karman–Howarth–Kolmogorov equation, this intriguing observation is shown to be an illusion, hiding a measurable influence of coherent structures and statistical inhomogeneity. This striking conclusion highlights that a complete statistical theory of turbulence cannot dispense with the influence of large scales, possibly coherent, motions.