Phase-space Lagrangian dynamics of incompressible thermofluids

TL;DR

This paper develops an exact phase-space Lagrangian framework for ideal tracer particles in incompressible thermofluids, establishing a connection between fluid dynamics and classical dynamical systems through inverse kinetic theory.

Contribution

It introduces a novel exact method to define tracer-particle dynamics in ideal fluids using inverse kinetic theory, applicable to incompressible thermofluids.

Findings

Exact tracer-particle dynamics can be derived for incompressible thermofluids.

The approach links fluid dynamics to classical dynamical systems.

Application demonstrated on Newtonian thermofluids.

Abstract

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 \textit{et al.}, 2000-2008). As an example, the case of an incompressible Newtonian thermofluid is here considered.