On the dynamical content of Lagrangian stochastic models in the well-mixed class

摘要

It is shown how the correspondence between Lagrangian stochastic models and second-moment closures of the scalar-flux equation can be exploited to distinguish between Lagrangian stochastic models in the well-mixed class. It is found that physicallyrealistic closures of the scalar-flux equation correspond to Lagrangian stochastic models that have non-zero 'spin' and so produce spiralling tracer-particle trajectories, whilst 'zero-spin' models correspond to the isotropic-production model of scalar-fluxes. Lagrangian stochastic models consistent with rapid distortion theory and Speziale's transformation rule for the Reynolds stress equations in the extreme limit of two-dimensional turbulence are also shown to have non-zero spin. The residual non-uniqueness associated with satisfaction of the well-mixed condition and the specification of mean spin is shown to be related to the helicity of tracer-particle trajectories. Investigations are also made of the influence upon turbulent dispersion of time-dependent spin and of mean rotations of the fluctuating Lagrangian acceleration vector (i.e., second-order spin).