Advertisement

Compressible Homogeneous Anisotropic Turbulence

  • Pierre Sagaut
  • Claude Cambon
Chapter

Abstract

This chapter is devoted to compressible homogeneous turbulence in the presence of shear and strain. The emphasis is put Rapid Distortion Theory results and more sophisticated nonlinear models. The case of pure plane shear is extensively discussed, including noise generation and the role of pressure in the spreading of compressible shear layers. The analysis in terms of coherent structures, including vortices and shocklets, is addressed.

References

  1. Blaisdell, G.A., Mansour, N.N. Reynolds, W.C.: Numerical simulation of compressible homogeneous turbulence. Report TF-50. Department of Mechanical Engineering, Stanford University, Stanford (1991)Google Scholar
  2. Blaisdell, G.A., Mansour, N.N., Reynolds, W.C.: Compressibility effects on the growth and structure of homogeneous turbulent shear flow. J. Fluid Mech. 256, 443–485 (1993)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. Blaisdell, G.A., Coleman, G.N., Mansour, N.N.: RDT for compressible homogeneous turbulence under isotropic mean strain. Phys. Fluids 8, 2692–2708 (1996)ADSCrossRefzbMATHGoogle Scholar
  4. Cambon, C., Teissèdre, C., Jeandel, D.: Etude d’ effets couplés de déformation et de rotation sur une turbulence homogène. J. de Mécanique Théorique et Appliquée 4(5), 629–657 (1985). (in French)ADSMathSciNetzbMATHGoogle Scholar
  5. Cambon, C., Mao, Y., Jeandel, D.: On the application of time dependent scaling to the modelling of turbulence undergoing compression. Eur. J. Mech. B/Fluids 6, 683–703 (1992)zbMATHGoogle Scholar
  6. Cambon, C., Coleman, G.N., Mansour, N.N.: Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite mach number. J. Fluid Mech. 257, 641–665 (1993)ADSCrossRefzbMATHGoogle Scholar
  7. Cambon, C., Rubinstein, R.: Anisotropic developments for homogeneous shear flows. Phys. Fluids 18, 085106 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. Craik, A.D.D., Allen, H.R.: J. Fluid Mech. 234, 613–627 (1992)ADSMathSciNetCrossRefGoogle Scholar
  9. Debiève, J.F., Gouin, H., Gaviglio, J.: Evolution in the reynolds stress tensor in a shock wave turbulence interaction, Indian. J. Technol. 20, 90–97 (1982)zbMATHGoogle Scholar
  10. Durbin, P.A., Zeman, O.: RDT for homogeneous compressed turbulence with application to modelling. J. Fluid Mech. 242, 349–370 (1992)ADSCrossRefzbMATHGoogle Scholar
  11. Eckhoff, K.S., Storesletten, L.: A note on the stability of steady inviscid helical gas flows. J. Fluid Mech. 89, 401 (1978)ADSCrossRefzbMATHGoogle Scholar
  12. Erlebacher, G., Sarkar, S.: Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence. Phys. Fluids 5(12), 3240–3254 (1993)ADSCrossRefzbMATHGoogle Scholar
  13. Fabre, D., Jacquin, L., Sesterhenn, J.: Linear interaction of a cylindrical entropy spot with a shock wave. Phys. Fluid 13(8), 1–20 (2001)CrossRefzbMATHGoogle Scholar
  14. Fauchet, G., Shao, L., Wunenberger, R., Bertoglio, J.P.: An improved two-point closure for weakly compressible turbulence. In: 11-th Symposium Turbulence Shear Flow, Grenoble, 8–10 September 1997Google Scholar
  15. Friedrich, R.: Effects of compressibility and heat release in turbulent wall-bounded and free shear flows. In: SIG4 ERCOFTAC and GST13 Workshop, Porquerolles, France, 1 June 2006Google Scholar
  16. Frisch, U.: Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge (1995)zbMATHGoogle Scholar
  17. Goldstein, M.E.: Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89(3), 433–468 (1978)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. Hamba, F.: Effects of pressure fluctuations on turbulence growth in compressible homogeneous shear flow. Phys. Fluids 11(6), 1623–1635 (1999)ADSCrossRefzbMATHGoogle Scholar
  19. Heinz, S.: Statistical Mechanics of Turbulent Flows. Springer, Berlin (2004)Google Scholar
  20. Hunt, J.C.R.: A theory of turbulent flow around two-dimensional bluff bodies. J. Fluid Mech. 61, 625–706 (1973)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. Jacquin, L., Cambon, C., Blin, E.: Turbulence amplification by a shock wave and rapid distortion theory. Phys. Fluids A 10, 2539–2550 (1993)ADSCrossRefzbMATHGoogle Scholar
  22. Jacquin, L., Mistral, S., Cruaud, F.: Mixing of a heated supersonic jet with a parallel stream. Advances in Turbulence V. Springer, Berlin (1996)Google Scholar
  23. Kovasznay, L.S.G.: Turbulence in supersonic flow. J. Aeronaut. Sci. 20, 657–682 (1953)CrossRefzbMATHGoogle Scholar
  24. Lele, S.K.: Compressibility effects on turbulence. Annu. Rev. fluid Mech. 26, 211–254 (1994)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. Lifschitz, A., Hameiri, E.: Local stability conditions in fluid dynamics. Phys. Fluids A 3, 2644–2641 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. Livescu, D., Madnia, C.K.: Small scale structure of homogeneous turbulent shear flow. Phys. Fluids 16(8), 2864–2876 (2004)ADSCrossRefzbMATHGoogle Scholar
  27. Lighthill, M.J.: Waves in Fluids. Cambridge University Press, Cambridge (1978)zbMATHGoogle Scholar
  28. Pantano, C., Sarkar, S.: A study of compressibility effects in the high-speed turbulent shear layer using DNS. J. Fluid Mech. 451, 329–371 (2002)ADSCrossRefzbMATHGoogle Scholar
  29. Ribner, H.S., Tucker, M.: Spectrum of turbulence in a contracting stream, In: NACA Report, No 113 (1953)Google Scholar
  30. Sabel’nikov, V.A.: Pressure fluctuations generated by uniform distortion of homogeneous turbulence. J. Mech. Sov. Res. 4, 46–56 (1975)Google Scholar
  31. Sarkar, S., Erlebacher, G., Hussaini, M.Y.: Direct simulation of compressible turbulence in a shear flow. Theor. Comput. Fluid Dyn. 2, 291–305 (1991)CrossRefzbMATHGoogle Scholar
  32. Sarkar, S.: The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282, 163–286 (1995)ADSCrossRefzbMATHGoogle Scholar
  33. Simone, A., Coleman, G.N., Cambon, C.: The effect of compressibility on turbulent shear flow: a RDT and DNS study. J. Fluid Mech. 330, 307–338 (1997)ADSCrossRefzbMATHGoogle Scholar
  34. Thacker, W.D., Sarkar, S., Gatski, T.B.: Analyzing the influence of compressibility on the rapid pressure-strain rate correlation in turbulent shear flows. Theor. Comput. Fluid Dyn. 21(3), 171–199 (2006).  https://doi.org/10.1007/s00162-007-0043-4 CrossRefzbMATHGoogle Scholar
  35. Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edition. Cambridge University Press, Cambridge (1976)zbMATHGoogle Scholar

Copyright information

© 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

Personalised recommendations