Concentration fluctuations and relative dispersion PDF

In this paper, we consider the problem of the relative dispersion of particle pairs released in a homogeneous isotropic stationary turbulent field. A one-dimensional two-particle Lagrangian stochastic model is considered. Two Langevin equations for the particles separation (ΔΔ) and barycentre (Z)(Z) are presented and the results of the model simulations are discussed. The small-scale turbulence structure is analysed by reproducing the ΔΔ and ZZ mean square trends. These are compared with the theoretical predictions and with a new formula to verify the Richardson's t3t3-law and the existence of an intermediate subrange, respectively, whose extension depends on the initial separation. Concerning the separation probability density function (PDF), two different forms are found for small and long times, respectively, according to the classical turbulence theory and the results of previous Lagrangian stochastic models. The mean concentrations and concentration fluctuations predicted by the model are compared with a new formula based on the Richardson separation PDF and with the formula based on the Gaussian PDF.