Limitations of random multipliers in describing turbulent energy dissipation

The intermittency of turbulent energy dissipation is often analyzed in terms of a product of random multipliers, each multiplier being the total dissipation in a subinterval r divided by the total dissipation in an interval λr. Recent experimental data of Pedrizzetti, Novikov, and Praskovsky [Phys. Rev. E 53, 475 (1996)] give extensive information on the statistics of these multipliers. In this paper we further analyze these statistics, with emphasis on the universal scaling exponents. We emphasize that the scaling exponents are sensitive to the location of the subinterval within the interval and that they reflect dependence of successive multipliers. We show that these two sensitivities are related and strongly limit the direct applicability of multiplier statistics to the statistics of the turbulent energy dissipation. We extend Novikov’s [Phys. Rev. E 51, R3303 (1994)] “gap theorem” on the high moments of the multiplier to the case when the multipliers are statistically dependent and discuss its relevance to the high moments of the turbulent energy dissipation.