A Generalized Brownian Motion Model for Turbulent Relative Particle Dispersion

A generalized Brownian motion model has been applied to the turbulent relative particle dispersion problem (Shivamoggi [1]). The fluctuating pressure forces acting on a fluid particle are taken to follow an Uhlenbeck-Ornstein process while it appears plausible to take their correlation time to have a power-law dependence on the flow Reynolds number R$_{e}$. This ansatz provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-R$_{e}$ limit and disappears otherwise. It provides a determination of the Richardson-Obukhov constant g as a function of R$_{e}$, with an asymptotic constant value in the infinite-R$_{e}$ limit. This ansatz is further shown to be in quantitative agreement, in the small-R$_{e}$ limit, with the Batchelor-Townsend ansatz for the rate of change of the mean square interparticle separation in 3D FDT. [1] B.K. Shivamoggi: arXiv: 1208.5786 (2014).