A Simple Relative Dispersion Model for Concentration Fluctuations in Contaminant Clouds

Abstract

The relative dispersion process for clouds of contaminant in generic atmospheric flow is considered. The properties of the separation distance for pairs of particles are simplified by implicitly averaging over the spatial domain of the dispersing cloud. Representative statistics and simplified sets of measurements for characterizing two-particle dispersion in complex flows are identified. A Lagrangian stochastic model of relative dispersion equivalent to processes in homogeneous and isotropic turbulence at high Reynolds numbers is derived. The model uses a new formulation for parameterizing the acceleration of separation, satisfies the criterion of conserving a well-mixed distribution of particle separations, and accounts explicitly for non-Gaussian statistics of the turbulence velocity differences. The results are in very good agreement with similarity theory in the inertial range and are consistent with uncorrelated velocities at length scales larger than the turbulence integral scale. The model is applied to the estimation of fluctuating concentration fields, which is relevant for representing the relative dispersion part of popular meandering plume and puff approaches. The dependence of mean-square concentration and concentration fluctuations on the source size is eliminated via a new scaling law for the time, which in fact determines a universal behavior for the concentration field. Simple formulas are derived that are consistent with previous theories, and they are successfully tested against numerical simulations.