The dependence of relative dispersion on turbulence scales in Lagrangian Stochastic Models

The aim of the article is to investigate the relative dispersion properties of the Well Mixed class of Lagrangian Stochastic Models. Dimensional analysis shows that given a model in the class, its properties depend solely on a non-dimensional parameter, which measures the relative weight of Lagrangian-to-Eulerian scales. This parameter is formulated in terms of Kolmogorov constants, and model properties are then studied by modifying its value in a range that contains the experimental variability. Large variations are found for the quantity $g^*=2gC_0^{-1}$, where $g$ is the Richardson constant, and for the duration of the $t^3$ regime. Asymptotic analysis of model behaviour clarifies some inconsistencies in the literature and excludes the Ornstein-Uhlenbeck process from being considered a reliable model for relative dispersion.