Models for non-Gaussian variation, with applications to turbulence

Abstract

A new class of distributions, generalizing the Gaussian, the hyperbolic, and the so-called exponential power distributions, is introduced and studied to some extent. In particular, the possibilities are discussed of representing the distributions as mixtures of Gaussian distributions and of constructing a certain kind of stationary stochastic processes whose one dimensional distributions are of the type considered. A brief survey is given of the literature on observed distributions of velocities and velocity derivatives from turbulent fields with high Reynolds number and the applicability of the proposed distributions and processes for modelling turbulent velocity fields is discussed.