2009/05/31 by Marco Tessarotto, Claudio Cremaschini, Massimo Tessarotto · 8 citations
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Compressibility #Computer science #Dynamics (music) #Fluid Dynamics and Turbulent Flows #Fluid parcel #Geometry #Ideal (ethics) #Infinitesimal #Inverse #Lagrangian #Lagrangian and Eulerian specification of the flow field #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Newtonian fluid #Particle Dynamics in Fluid Flows #Perfect fluid #Phase Equilibria and Thermodynamics #Phase space #Physics #Space (punctuation) #Thermodynamics #physics.class-ph #physics.flu-dyn
paper · pdf · doi:10.1016/j.physa.2009.06.008
published in Physica A Statistical Mechanics and its Applications 388(18), 3737-3744 (Elsevier BV) · submitted to Physica A
arxiv created 2009/05/31 · openalex publication_date 2009/06/09 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually related to the so-called \it ideal tracer particles. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution. The goal of this paper is to show that the tracer-particle dynamics can be \it exactly established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) (Tessarotto et al., 2000-2008). As an example, the case of an incompressible Newtonian thermofluid is here considered.