Paper detail

On an alternative explanation of anomalous scaling and how well-defined is the concept of inertial range

The main point of this communication is that there is a small non-negligible amount of eddies-outliers/very strong events (comprising a significant subset of the tails of the PDF of velocity increments in the nominally-defined inertial range) for which viscosity/dissipation is of utmost importance at whatever high Reynolds number. These events contribute significantly to the values of higher-order structure functions and their anomalous scaling. Thus the anomalous scaling is not an attribute of the conventionally-defined inertial range, and the latter is not a well-defined concept. The claim above is supported by an analysis of high-Reynolds-number flows in which among other things it was possible to evaluate the instantaneous rate of energy dissipation.