Probabilistic models for particle and scalar transport in fluctuating flows: an evaluation of simple closure approximations

A generalized Fokker–Planck equation is used to describe the transport of discrete particles and fluid-points in fluctuating flows. Simple closure approximations for this equation are considered which allow free-field analytic solutions to be constructed. Results based on these solutions are compared with those obtained from simulation of the underlying, non-Markovian particle and fluid-point trajectories. The work validates the form of the generalized Fokker–Planck equation, and demonstrates the effectiveness of using models based on this equation to study such transport.