In developing this study, the authors started from the fact that there are a number of empirical concepts used to describe the intermittency in a fully developed turbulence. In their view, intermittency is a measure of non-uniformity of the energy cascade, and it is useful for many statistical laws of a fully developed turbulence. An example at hand: the power law for the energy density function, as a function of energy dissipation rate per unit mass, the integral scale and a dimension of a set that carries turbulent energy dissipation. Due to the intermittency, the deterministic counterparts of the power laws appear in a form of bounds to account for possible corrections, even though the intermittency itself has not been mathematically defined.
In the present study the authors give definitions and introduce in precise mathematical terms the empirical concepts such as active turbulent region, volume, eddies, and energy dissipation set. Another concern of the authors is the use of rigorous definitions of the above-mentioned empirical concepts for deterministic fields to justify intermittency corrections to statistical laws without the use of viscous dissipation. Also, these definitions are used to recover scaling laws for the energy spectrum and second-order structure functions with proper intermittency correction.