On some properties of Lagrangian dispersion models with non-Gaussian noise

The properties of a stochastic model with non-Gaussian random noise describing turbulent dispersion have been investigated, with reference to its mathematical structure and to its behaviour simulating the inertial subrange. The process is Markovian, mean-square continuous and with delta-correlated increments. The model is influenced by the turbulence inhomogeneities also at the smallest scales, that is, it does not correctly simulate the existence of a well-developed inertial subrange. Some numerical computations have been performed confirming the theoretical results.