The expansion of clusters of particles in the atmosphere

Abstract

Abstract In this paper, the problem of the spatial expansion of a cluster of particles under the action of turbulence is investigated. The basic difficulty, that this form of diffusion depends on the Lagrangian properties of the turbulent field, is met by the assumption that the Lagrangian and Eulerian time‐correlograms are functionally similar. In consequence, it is possible to solve the equation governing the cluster's expansion to give prediction laws expressed only in terms of easily measured parameters of the turbulence. The application of the full solution is lengthy but a simple working approximation follows from the fact that over an important part of the expansion at which the size of the cluster is of the same order of magnitude as the Eulerian length‐scale, the rate of expansion is approximately constant and is proportional to the square of the intensity of turbulence whilst independent of the length scale itself. Experiments to test these formulae have been carried out on the diffusion of clusters of Lycopodium spores over a few hundred metres downwind travel near the ground, and the diffusion of long crosswind clouds of aircraft‐released fluorescent particles, sampled along the vertical, after several kilometres travel in the free atmosphere. Whilst the experiments are few in number and the conditions often did not strictly conform to the conditions of isotropy and homogeneity required by the theory, the results are satisfactorily consistent with the prediction formulae and imply an effectively constant ratio between the scales of the Lagrangian and Eulerian time‐correlograms.