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 q th-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 µ 2 and d . The results derived from the model are in good agreement with those of experiments and a numerical simulation.