On the Well-Mixed Condition and Consistency Issues in Hybrid Eulerian/Lagrangian Stochastic Models of Dispersion

Abstract

We clarify issues related to the expression of Lagrangian stochastic models used for atmospheric dispersion applications. Two aspects are addressed: the need to verify the well-mixed criterion and the correspondence between Eulerian and Lagrangian turbulence models when they are combined in practical simulations. In particular, it is recalled that the fulfillment of the well-mixed criterion depends only on the proper incorporation of the mean pressure-gradient term as the mean drift term of the Langevin equation. New consistency issues between duplicate fields within Eulerian/Lagrangian hybrid formulations are also brought out, especially regarding turbulence models, boundary conditions, and divergence-free condition. Such hybrid methods, where mean flow quantities calculated with an Eulerian approach are provided to the Lagrangian approach, are commonly used in atmospheric dispersion simulations for their numerical efficiency. Nevertheless, it is shown that serious inconsistencies can result from coupling Eulerian and Lagrangian models that do not correspond to the same level of description of the fluid turbulence.