  In this paper, a generalized Brownian motion model has been applied to
describe the relative particle dispersion problem in more realistic turbulent
flows. The fluctuating pressure forces acting on a fluid particle are taken to
be a colored noise and follow a stationary process and are described by the
Uhlenbeck-Ornstein model while it appears plausible to take their correlation
time to have a power-law dependence on the flow Reynolds number $R_e$, thus
introducing a bridge between the Lagrangian quantities and the Eulerian
parameters for this problem. This ansatz is in qualitative agreement with the
possibility of a connection speculated earlier by Corrsin [26] between the
white-noise representation for the fluctuating pressure forces and the
large-$R_e$ assumption in the Kolmogorov [4] theory for the 3D fully developed
turbulence (FDT) as well as the argument of Monin and Yaglom [23] and the
result of Sawford [13] and Borgas and Sawford [24] that the Lagrangian
acceleration is delta-function auto-correlated in the infinite-$R_e$ limit. It
also provides an insight into the result that the Richardson-Obukhov scaling
holds only in the infinite-$R_e$ limit and disappears otherwise. This ansatz
further confirms the Lin-Reid [18] conjecture regarding the connection between
the fluctuating pressure-force parameter and the energy dissipation rate in
turbulence and leads to an $R_e$-dependent explicit relation between the two
speculated by Lin and Reid [18]. More specifically, this ansatz 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. It is shown to
lead to full agreement, in the small-$R_e$ limit as well, with the
Batchelor-Townsend [27] scaling for the rate of change of the mean square
interparticle separation in 3D FDT, hence validating its soundness further.
