Isotropic polarization of compressible flows

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.

an Erratum or Clarification is added to a remark on Page 4

References in corpus (2)

• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Note on specific chiral ensembles of statistical hydrodynamics: "order function" for transition of turbulence transfer scenarios

Cited by in corpus (6)

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• Compressible helical turbulence: Fastened-structure geometry and statistics
• Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas
• Chirality, extended MHD statistics and solar wind turbulence
• Turbulence compressibility reduction with helicity
• Real Schur flow computations, helicity fastening effects and Bagua-pattern cyclones