Relative dispersion and Lagrangian correlations in inhomogeneous turbulence: experimental and numerical study

This work explores two aspects of the motion of particles inside a turbulent fluid flow: relative dispersion and Lagrangian correlations. These are studied experimentally, by means of custom-made miniaturized radiosondes launched in clusters to obtain data about the turbulence in the atmospheric boundary layer, and numerically, by means of Direct Numerical Simulations of a cloud's border region, modeled as a turbulent mixing layer in which the advected Lagrangian particles are water droplets. Relative dispersion is one of the open problems of fluid turbulence, concerning how fast particles are spread apart by the fluid flow. The relevant theoretical framework is Kolmogorov's and Obukhov's K41 theory, but this only holds for the case of stationary, homogeneous, isotropic turbulence. However, real flows rarely hold these properties, and thus studies of dispersion far from these ideal conditions are necessary both for theoretical insight into real turbulence and for correct modelling of real-world phenomena and forecasting. Our experimental results are compared with those from K41, in terms of the exponents and coefficients found for the dispersion laws, and deviations are found that can be explained in terms of the inhomogeneities inherently contained in atmospheric turbulence. On the numerical side, preliminary studies are conducted on the currently available simulations, that lack the necessary features to allow for definitive investigation, in order to pave the way for newer upcoming simulations. Lagrangian correlations are a far less explored branch in the study of turbulence, and while some specific studies have been conducted there is no solid and widely recognized theoretical framework to interpret them. We thus present novel results about these quantities both for velocity components, which are what most studies investigate, and other relevant quantities for the cases of the cloud border simulations and the radiosondes released in the atmosphere. Simmetrically with respect to the discussion on dispersion, results on Lagrangian correlations see a stronger contribution from the numerical simulations.