Modelling concentration fluctuation moments for spherically symmetric mean concentration

Clarke and Mole (Environmetrics, 6 (1995) 607-617) presented a model for concentration fluctuation moments of a passive scalar dispersing in a turbulent flow. This followed Sullivan and Moseley's work in making use of the equation for the evolution of the concentration moments integrated over all space, together with Chatwin and Sullivan's (J. Fluid Mech., 212 (1990) 533-556) description relating higher moments to the mean concentration. The model incorporated a simple closure to express the concentration gradient in terms of the concentration. Numerical results were presented for 1, 2 and 3 spatial dimensions under the assumption that the spatial distribution of the mean concentration was spherically symmetric and Gaussian. Two simple functional forms were used for the spreading rate of the mean cloud. Here those results are briefly summarised. Some asymptotic large time results are also given for spherically symmetric mean concentration of general functional form, and numerical results are obtained for a number of different functional forms.