A key aspect of fluid mechanics concerns the frictionless phase-space dynamics of particles in an incompressible fluid. The issue, besides its theoretical interest in turbulence theory, is important in many applications, such as the pollutant dynamics in the atmosphere, a problem relevant for civil protection monitoring of air quality. Actually, both the numerical simulation of the ABL (atmospheric boundary layer) portion of the atmosphere and that of pollutant dynamics may generally require the correct definition of the Lagrangian dynamics which characterizes arbitrary fluid elements of incompressible thermofluids. We claim that particularly important for applications would be to consider these trajectories as phase-space trajectories. This involves, however, the unfolding of a fundamental theoretical problem up to now substantially unsolved: namely the determination of the exact frictionless dynamics of tracer particles in an incompressible fluid, treated either as a deterministic or a turbulent (i.e., stochastic) continuum. In this paper we intend to formulate the necessary theoretical framework to construct such a type of description. This is based on a phase-space inverse kinetic theory (IKT) approach recently developed for incompressible fluids (Tessarotto et al., 2004-2008). Our claim is that the conditional frictionless dynamics of a tracer particles - which corresponds to a prescribed velocity probability density and an arbitrary choice of the relevant fluid fields - can be exactly specified.
