2012/08/28 by Bhimsen K. Shivamoggi, Shivamoggi, Bhimsen
Engineering · Environmental Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Hydrology and Drought Analysis #Mathematical Physics (math-ph) #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.1208.5786
openalex publication_date 2012/08/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper, a generalized Brownian motion model has been applied to\ndescribe the relative particle dispersion problem in more realistic turbulent\nflows. The fluctuating pressure forces acting on a fluid particle are taken to\nbe a colored noise and follow a stationary process and are described by the\nUhlenbeck-Ornstein model while it appears plausible to take their correlation\ntime to have a power-law dependence on the flow Reynolds number Re, thus\nintroducing a bridge between the Lagrangian quantities and the Eulerian\nparameters for this problem. This ansatz is in qualitative agreement with the\npossibility of a connection speculated earlier by Corrsin [26] between the\nwhite-noise representation for the fluctuating pressure forces and the\nlarge-Re assumption in the Kolmogorov [4] theory for the 3D fully developed\nturbulence (FDT) as well as the argument of Monin and Yaglom [23] and the\nresult of Sawford [13] and Borgas and Sawford [24] that the Lagrangian\nacceleration is delta-function auto-correlated in the infinite-Re limit. It\nalso provides an insight into the result that the Richardson-Obukhov scaling\nholds only in the infinite-Re limit and disappears otherwise. This ansatz\nfurther confirms the Lin-Reid [18] conjecture regarding the connection between\nthe fluctuating pressure-force parameter and the energy dissipation rate in\nturbulence and leads to an Re-dependent explicit relation between the two\nspeculated by Lin and Reid [18]. More specifically, this ansatz provides a\ndetermination of the Richardson-Obukhov constant g as a function of Re,\nwith an asymptotic constant value in the infinite-Re limit. It is shown to\nlead to full agreement, in the small-Re limit as well, with the\nBatchelor-Townsend [27] scaling for the rate of change of the mean square\ninterparticle separation in 3D FDT, hence validating its soundness further.\n