Relationships between higher moments of concentration and of dose in turbulent dispersion

Chatwin and Sullivan (1990) proposed simple results for the relationships between moments of scalar fluctuations in self-similar turbulent shear flows. They showed these relationships to be well satisfied by observations from a range of experiments. Here their theory is extended to the skewness, kurtosis and higher order equivalents. It is shown that the relationships between these normalised moments are parameter-free, and are identical to those for zero molecular diffusion. Experimental observations are presented which show a remarkable degree of collapse when these normalised moments are plotted against each other. The agreement with the theoretical results is reasonably good, and better than for some other standard statistical distributions which are commonly applied to such observations. This is true not only for the concentration, but also for generalised doses. It is concluded that the simple theory provides a satisfactory basis for a model of both the concentration and of dose. Furthermore, the results suggest that the concentration and the dose can be modelled through a perturbation to a two-state model.