Is turbulent mixing a self-convolution process?

Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulent flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be nonuniversal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In connection with this observation, advantages, shortcomings, and applicability of models for the PDF evolution based on a self-convolution mechanism are discussed.