Acoustic multipole sources from the Boltzmann equation

TL;DR

This paper derives acoustic multipole source terms from the Boltzmann equation with particle sources, linking microscopic particle behavior to macroscopic wave phenomena in fluids.

Contribution

It introduces a method to derive acoustic multipole sources directly from the Boltzmann equation with particle source terms, connecting kinetic theory to wave equations.

Findings

Monopole and dipole sources emerge at the Euler level.

Quadrupole source appears at the Navier-Stokes level.

Quadrupole term is negligible in magnitude.

Abstract

By adding a particle source term in the Boltzmann equation of kinetic theory, it is possible to represent particles appearing and disappearing throughout the fluid with a specified distribution of particle velocities. By deriving the wave equation from this modified Boltzmann equation via the conservation equations of fluid mechanics, multipole source terms in the wave equation are found. These multipole source terms are given by the particle source term in the Boltzmann equation. To the Euler level in the momentum equation, a monopole and a dipole source term appear in the wave equation. To the Navier-Stokes level, a quadrupole term with negligible magnitude also appears.