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

TL;DR

This paper challenges the traditional view of the inertial range in turbulence, showing that strong outlier events with significant dissipation influence anomalous scaling, thus questioning the well-defined nature of the inertial range.

Contribution

It introduces an alternative explanation for anomalous scaling by highlighting the role of outlier events where viscosity is crucial, challenging the conventional inertial range concept.

Findings

Strong outlier events significantly affect higher-order structure functions.

Anomalous scaling is influenced by dissipation in events outside the inertial range.

The inertial range is not as well-defined as traditionally assumed.

Abstract

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.