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It is established that there is a time asymptotic dependency of the higher order moments of concentration on the lowest three moments through statistical analysis of field plume releases [Mole and Clarke, 1995]. A microscale model of a diffusion layer randomly buffeted by supercloud size eddies and a model of advection and diffusion in a deterministic helical eddy both demonstrated that this slaving of the higher moments to lower moments obtains time-asymptotically and collapses with all intermittency factors onto a universal curve for kurtosis against skewness. In this article, this universality with residence time and intermittency factor obtains in two distinct plume models for transverse dispersion – diffusion within a 1-D lamellae structure and during advection by a 2-D random streamfunction. In the latter case, some evidence for Chatwin's closure hypothesis relating the expectation of the norm square of the gradient of the concentration, conditional at a given concentration, and the pdf of concentration, is presented. At early residence times in the plume, the power law hypothesis is consistent with simulations to a good degree. At intermediate residence times, however, there are apparently two branches to the proposed relationship, one matching Chatwin's hypothesis. Although not tested here, at long residence times the hypothesis should hold under the simulation scheme as it asymptotes to the assumptions of Chatwin's theory. Copyright © 2001 John Wiley & Sons, Ltd.

The paper derives the probability density function of concentration for a simple model of the turbulent diffusion process presented by Zimmerman and Chatwin (1995). Relationships with other work are discovered, and some implications for future research are assessed.

A new viewpoint on the evolution of scalar dispersion in a turbulent flow is taken by considering diffusion of a passive scalar where the measuring device is stochastically positioned. This is a model of a dispersion process where mixing at small scales occurs by molecular diffusion and large scale motions are rigid in regards to the internal cloud structure. Numerical results for the first four central moments are presented, and are shown to be consistent with theoretical approximations for both small and large times. The plot of kurtosis against skewness collapses onto a quadratic curve close to those discussed by Mole and Clarke, and others. The present work suggests that this robust feature has a rather simple basis in physics, and further research is proposed that will critically test this interpretation.