Gaussian Lagrangian stochastic models for multi-particle dispersion

We have extended the “well-mixed” two-particle stochastic models for 3D Gaussian turbulence to n particles, and have performed calculations for clusters of n ⩽ 6 particles. The particle joint motions are Gaussian and are constrained by pair-wise spatial correlations. This neglects non-Gaussian properties of the two-point velocity distribution and also neglects multi-point correlations. It also takes no account of intermittency. Although the models do not predict the growth of the separation of particles in the cluster satisfactorily, we find that they do give a good representation of the shape statistics for the cluster in comparison with direct numerical simulation results. We conclude that the pair-wise spatial structure of the turbulence accounts for most of the observed characteristics of the shape of multi-particle clusters in turbulence, and that non-Gaussian and multi-point features of the turbulence are of secondary importance.