We derive a comprehensive statistical model for dispersion of passive or almost passive admixture particles such as fine particulate matter, aerosols, smoke and fumes, in turbulent flow. The model rests on the Markov limit for particle velocity. It is in accordance with the asymptotic structure of turbulence at large Reynolds number as described by Kolmogorov. The model consists of Langevin and diffusion equations in which the damping and diffusivity are expressed by expansions in powers of the reciprocal Kolmogorov constant C0. We derive solutions of O(C00) and O(C0-1). We truncate at O(C0-2) which is shown to result in an error of a few percent in predicted dispersion statistics for representative cases of turbulent flow. We reveal analogies and remarkable differences between the solutions of classical statistical mechanics and those of statistical turbulence.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2012|