Recent Developments in Closure and Boundary Conditions for Lagrangian Stochastic Dispersion Models

Abstract

Until the definitive paper of Thomson (1987), arguably the most pressing problem in Lagrangian particle modelling was which form of the Langevin equation should be used for inhomogeneous, non-stationary, non Gaussian turbulence to ensure well-mixedness, i. e. to ensure that particle accumulations did not occur in regions of low turbulence. Since that time, the major topics of research in Lagrangian dispersion modelling have been associated with convectively unstable conditions. This review paper focuses on two recent topics: (1) the closure problem associated with specification of the probability density function (PDF) for vertical turbulent fluctuations, and (2) the most appropriate boundary conditions to apply at the ground and at the top of the convectively mixed layer, particularly when simulating the fumigation1 process. The reviewed studies emphasise the importance of turbulence and concentration data from a laboratory saline water tank (Hibberd and Sawford, 1994) for testing the closure schemes and the various methods for incorporating entrainment processes into stochastic models.