On an alternative explanation of anomalous scaling and how inertial is the inertial range

There are a variety of models of higher statistics that have meager or nonexistent deductive support from the Navier-Stokes equations but can be made to give good fits to experimental measurements [1]. These include ‘explanations’ of what is called anomalous scaling, observed experimentally for higher-order structure functions of velocity and temperature increments, such that their scaling exponents, are nonlinear concave functions of the order p. Starting with refined similarity hypotheses by Kolmogorov and Oboukhov, numerous phenomenological models have been proposed to describe these deviations. The dominant of these models has been the multifractal formalism, others claimed the Reynolds number dependence as responsible. The common in all these approaches is the basic, widely accepted premise that in the inertial range, the viscosity plays in principle no role [2] so that nonlinear dependence of the algebraic scaling exponents on the moment order p is a manifestation of the inertial-range intermittency [3] with the inertial range defined as (with being the Kolmogorov and L - some integral scale). Thus the issue is directly related to what is called inertial (sub)range and how inertial it is.