Additional Reminders: Compressible Turbulence Description

  • Pierre Sagaut
  • Claude Cambon


This chapter presents the specific features of the description of compressible turbulent flows: governing equations, Favre-averaging and Kovasznay decomposition of compressible disturbances as the sum of vortical, acoustic and entropy modes, along with Rankine–Hugoniot jump relations. Linearized jump relations are also discussed.


  1. Bayly, B.J., Levermore, C.D., Passot, T.: Density variations in weakly compressible flows. Phys. Fluids 4(5), 945–954 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. Chassaing, P., Antonia, R.A., Anselmet, F., Joly, L., Sarkar, S.: Variable density turbulence. Springer, Berlin (2002)CrossRefzbMATHGoogle Scholar
  3. Chomaz, J.M.: Global instabilities in spatially developing flows: Non-normality and non-linearity. Ann. Rev. Fluid Mech. 37, 357–392 (2005)ADSCrossRefzbMATHGoogle Scholar
  4. Chu, B.T.: On the energy transfer to small disturbances in fluid flow (part 1). Acta Mechanica 1, 215–234 (1965)CrossRefGoogle Scholar
  5. Chu, B.T., Kovasznay, L.S.G.: Non-linear interactions in a viscous heat-conducting compressible gas. J. Fluid Mech. 3, 494–514 (1957)ADSMathSciNetCrossRefGoogle Scholar
  6. Feiereisen, W.J., Reynolds, W.C., Ferziger, J.H.: Numerical simulation of compressible homogeneous turbulent shear flow, Report No TF 13, Stanford University (1981)Google Scholar
  7. Hayes, W.D.: The vorticity jump across a gasdynamic discontinuity. J. Fluid Mech. 2, 595–600 (1957)ADSCrossRefzbMATHGoogle Scholar
  8. Joseph George, K., Sujith, R.I.: On Chu’s disturbance energy. J. Sound Vib. 330, 5280–5291 (2011)ADSCrossRefGoogle Scholar
  9. Kovasznay, L.S.G.: Turbulence in supersonic flow. J. Aero. Sci. 20, 657–682 (1953)CrossRefzbMATHGoogle Scholar
  10. Zank, G.P., Matthaeus, W.H.: Nearly incompressible hydrodynamics and heat conduction. Phys. Rev. Lett. 64(11), 1243–1245 (1990)ADSCrossRefGoogle Scholar
  11. Zank, G.P., Matthaeus, W.H.: The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence and waves. Phys. Fluids 3(1), 69–82 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres, UMR CNRS 7340, Ecole Centrale de MarseilleAix-Marseille UniversitéMarseilleFrance
  2. 2.Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509Ecole Centrale de LyonÉcullyFrance

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