TURBULENCE MODELS AND PROBABILITY-DISTRIBUTIONS OF DISSIPATION AND RELEVANT QUANTITIES IN ISOTROPIC TURBULENCE

A generalized class of Cantor-set models are introduced in a deductive way to explain the intermittent and multifractal structure in the inertial range of isotropic turbulence. All such Cantor-set models are produced by taking the probability density of the stochastic ratio of averaged dissipations in the basic breakdown process with scale ratio A-1, Er/EAr, as a polynomial-delta-function, and it is proved that only some can guarantee the f-alpha-spectra with a non-negative f. The whole statistics of the dissipation density, its square root, and the scaling index-alpha which these models should imply are revealed, and typical models are compared with a recent direct numerical simulation to indicate promising applications.