Tracer-particle dynamics in MHD fluids

Abstract

A key issue in fluid dynamics is the unique definition of the phase-space Lagrangian dynamics characterizing prescribed ideal fluids (i.e., continua), which is related to the dynamics of so-called \textit{ideal tracer particles} (ITP) moving in the same fluids. These are by definition particles of infinitesimal size which do not produce significant perturbations of the fluid fields and do not interact among themselves. For Navier-Stokes (NS) fluids, the discovery by Tessarotto et al. (2005-2009) of the phase-space dynamical system advancing in time the state of the fluid, has made possible, \textit{in the case NS fluids}, the actual definition of these trajectories. In this paper we intend to pose the problem in the case of compressible/incompressible magnetofluids based on the inverse kinetic theory which can be developed for their phase-space statistical description (see also accompanying paper) \ We propose the conjecture of the existence of a subset of ITP's (i.e., particular solutions of the phase-space dynamical system), denoted as \textit{thermal ideal tracer particles} (TITP). These particles are characterized by a relative velocity with respect to the fluid, whose magnitude is determined, by the kinetic pressure (in turn, related to the fluid pressure).