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The main point of this communication is that there is a small non-negligibleamount of eddies-outliers/very strong events (comprising a significant subsetof the tails of the PDF of velocity increments in the nominally-definedinertial range) for which viscosity/dissipation is of utmost importance atwhatever high Reynolds number. These events contribute significantly to thevalues of higher-order structure functions and their anomalous scaling. Thusthe anomalous scaling is not an attribute of the conventionally-definedinertial range, and the latter is not a well-defined concept. The claim aboveis supported by an analysis of high-Reynolds-number flows in which among otherthings it was possible to evaluate the instantaneous rate of energydissipation.

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