Some physically significant consequences of recent advances in the theory of homogeneous statistical solutions of Navier–Stokes equations are presented. Invariance properties of families of those solutions are discussed and used to derive rigorously certain previously conjectured results, e.g., the Kolmogorov spectrum. Others include a reinterpretation of the von Karman–Howarth–Dryden equation that leads to the conditions for the existence of an inertial subrange. Further an application of Poincare´’s inequality produces a different view of intermittency. It is also suggested how a measurement of the two‐point triple velocity correlation could yield an accurate value of Kolmogorov’s constant.