Isotropic polarization of compressible flows

TL;DR

This paper investigates the polarization properties of compressible flows, revealing deviations from classical equipartition and the effects of acoustic modes on flow polarization and energy distribution.

Contribution

It uncovers the isotropic polarization characteristics of compressible flows and analyzes how acoustic modes influence helicity and energy distribution, extending previous incompressible flow theories.

Findings

Polarization involves both helical and acoustic modes.

Acoustic modes prevent negative temperature states in truncated systems.

Deviations from equipartition occur due to acoustic mode interactions.

Abstract

The helical absolute equilibrium of a compressible adiabatic flow presents not only the polarization between the two purely helical modes of opposite chiralities but also that between the vortical and acoustic modes, deviating from the equipartition predicted by {\sc Kraichnan, R. H.} [1955 The Journal of the Acoustical Society of America {\bf 27}, 438--441.]. Due to the existence of the acoustic mode, even if all Fourier modes of one chiral sector in the sharpened Helmholtz decomposition [{\sc Moses, H. E.} 1971 SIAM ~(Soc. Ind. Appl. Math.) J. Appl. Math. {\bf 21}, 114--130] are thoroughly truncated, leaving the system with positive definite helicity and energy, negative temperature and the corresponding large-scale concentration of vortical modes are not allowed, unlike the incompressible case.