Log-Gamma Distribution Model of Intermittency in Turbulence

Abstract

A probability distribution for the logarithm of the breakdown coefficient ε_r⁄ε_l of energy dissipation density is shown, under the conditions of scale similarity, to be infinitely divisible, and the log-gamma distribution model of intermittency in fully developed turbulence is proposed. As a result, the intermittency exponent of the qth-order moment of the breakdown coefficient is derived to be μ_q=d {q−[ln (β⁄β+q)⁄ln (β⁄β+1)]}, where d denotes the space dimension, and β is a nondimensional parameter determined by the value of μ₂ and d. The results derived from the model are in good agreement with those of experiments and a numerical simulation.