A critical examination of the random displacement model of turbulent dispersion

Abstract

Although the random displacement model (RDM) represents the “diffusion limit” of the first-order Lagrangian stochastic (or “Langevin”) model of turbulent dispersion, we show that these provide distinct (numerical) solutions even for the case of a ground-level source, where intuition might suggest their solutions converge (i.e., the “far-field” model would suffice). We also demonstrate (analytically) that the discrete RDM does not preserve an initially well-mixed particle distribution—though the well-mixed ‘test state’ can be preserved to within an arbitrarily small error, by reducing the timestep. From a comparison with reference calculations calibrated to Project Prairie Grass, we conclude that the RDM provides in practice an adequate description of far-field dispersion, and so justifiably could be used as a replacement for grid-based Eulerian methods in simulation of medium- and long-range transport. However there can be an important loss of accuracy (for the test case examined, at least) if the timestep is not strictly limited, and we recommend instead the (generalized) Langevin treatment.