Isotropic polarization of compressible flows

The helical absolute equilibrium of a compressible adiabatic flow presents not only polarization between two purely helical modes of opposite chiralities but also that between vortical and acoustic modes, deviating from the equipartition predicted by Kraichnan ( J. Acoust. Soc. Am. , vol. 27, 1955, pp. 438–441). Owing to the existence of the acoustic mode, even if all the Fourier modes of one chiral sector in the sharpened Helmholtz decomposition (Moses, SIAM J. Appl. Maths , vol. 21, 1971, pp. 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 in the incompressible case.