Advertisement

Incompressible Homogeneous Anisotropic Turbulence: With Strain

  • Pierre Sagaut
  • Claude Cambon
Chapter

Abstract

This chapter deals with effects of mean strain, with a direct impact on energy production. Various experimental facilities are surveyed. In addition to the pure strain (irrotational mean flows, symmetric mean velocity gradient matrix), the case of more general mean flows is addressed. The essentials of Rapid Distortion Theory with mean-flow-advection are given, after a brief survey of Reynolds Stress Models. Governing equations for second-order statistics are compacted under generalized Lin equations, and a recent model derived from anisotropic EDQNM is rendered more tractable in terms of spherically averaged descriptors. Some typical results are reported and compared to experiments. The return to isotropy is investigated, both in terms of a threshold scale in a scale-by-scale analysis, and in term of the temporal relaxation of anisotropy indicators when the mean velocity gradient is suppressed. Finally, the experimental investigation near the stagnation point in a von Karman flow with exactly co-rotating discs, illustrates the recovery of the concepts of homogeneous anisotropic turbulence in such a flow, with careful measurements of mean velocity gradients and Reynolds stresses.

References

  1. Batchelor, G.K., Proudman, I.: The effect of rapid distortion in a fluid in turbulent motion. Q. J. Mech. Appl. Maths 2, 7–83 (1954)zbMATHGoogle Scholar
  2. Bayly, B.J.: Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57(17), 2160–2163 (1986)ADSMathSciNetCrossRefGoogle Scholar
  3. Bayly, B.J., Holm, D.D., Lifschitz, : Three-dimensional stability of elliptical vortex columns in external strain flows. Phil. Trans. R. Soc. Lond. A 354, 895–926 (1996)Google Scholar
  4. Cambon, C.: Etude spectrale d’un champ turbulent incompressible soumis à des effets couplés de déformation et rotation imposés extérieurement. Université Lyon I, France, Thèse de Doctorat d’Etat (1982)Google Scholar
  5. Cambon, C., Teissèdre, C., Jeandel, D.: Etude d’ effets couplés de rotation et de déformation sur une turbulence homogène. Journal de Mécanique Théorique et Appliquée 5, 629 (1985)ADSzbMATHGoogle Scholar
  6. Cambon, C., Mansour, N.N., Godeferd, F.S.: Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332 (1997)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. Cambon, C., Jeandel, D., Mathieu, J.: Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247–262 (1981)ADSCrossRefzbMATHGoogle Scholar
  8. Cambon, C., Scott, J.F.: Linear and nonlinear models of anisotropic turbulence. Ann. Rev. Fluid Mech. 31, 1–53 (1999)ADSMathSciNetCrossRefGoogle Scholar
  9. Cambon, C., Rubinstein, R.: Anisotropic developments for homogeneous shear flows. Phys. Fluids 18, 085106 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. Champagne, F.H., Harris, V.G., Corrsin, S.J.: Experiments on nearly homogeneous turbulent shear flows. J. Fluid Mech. 41, 81–139 (1970)Google Scholar
  11. Chen, J., Meneveau, C., Katz, J.: Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle. J. Fluid Mech. 562, 123–150 (2006)ADSCrossRefzbMATHGoogle Scholar
  12. Corrsin, S.: On local isotropy in turbulent shear flow, NACA RM 58B11 (1958)Google Scholar
  13. Courseau, P., Loiseau, M.: Contribution à l’ analyse de la turbulence homogène anisotrope. Journal de Mécanique 17(2) (1978)Google Scholar
  14. Craik, A.D.D., Criminale, W.O.: Evolution of wavelike disturbances in shear flows: a class of exact solutions of Navier–Stokes equations. Proc. R. Soc. Lond. Ser. A 406, 13–26 (1986)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. Gence, J.-N., Mathieu, J.: On the application of successive plane strains to grid-generated turbulence. J. Fluid Mech. 93, 501–513 (1979)ADSCrossRefGoogle Scholar
  16. Gence, J.N., Mathieu, J.: The return to isotropy of an homogeneous turbulence having been submitted to two successive plane strains. J. Fluid Mech.101, 555–566 (1980)Google 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. Hadzic, I., Hanjalic, K., Laurence, D.: Modeling the response of turbulence subjected to cyclic irrotational strain. Phys. Fluid 13(6), 1739–1747 (2001)ADSCrossRefzbMATHGoogle Scholar
  19. Hunt, J.C.R.: A theory of turbulent flow around two-dimensional bluff bodies. J. Fluid Mech. 61, 625–706 (1973)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. Hunt, J.C.R., Carruthers, D.J.: Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532 (1990)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. Ishihara, T., Yoshida, K., Kaneda, Y.: Anisotropic velocity correlation spectrum at small scale in a homogeneous turbulent shear flow. Phys. Rev. Lett. 88(15), 154501 (2002)ADSCrossRefGoogle Scholar
  22. Jacquin, L., Leuchter, O., Cambon, C., Mathieu, J.: Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1–52 (1990)ADSCrossRefzbMATHGoogle Scholar
  23. Kassinos, S.C., Reynolds, W.C., Rogers, M.M.: One-point turbulence structure tensors. J. Fluid Mech. 428, 213–248 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. Kevlahan, N.K.R., Hunt, J.C.R.: Nonlinear interactions in turbulence with strong irrotational straining. J. Fluid Mech. 337, 333–364 (1997)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. Leblanc, S., Godeferd, F.S.: An illustration of the link between ribs and hyperbolic instability. Phys. Fluids 11(2), 497–499 (1999)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. Leclaire, B. (2006). Etude théorique et expérimentale d’ un écoulement tournant dans une conduite, Ph. D. thesis, Thèse de l’ Ecole Polytechnique, 21 Dec 2006Google Scholar
  27. Lee, M.J.: Distortion of homogeneous turbulence by axisymmetric strain and dilatation. Phys. Fluids A 1(9), 1541–1557 (1989)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. Leuchter, O., Benoit, J. -P., Cambon, C.: . Homogeneous turbulence subjected to rotation-dominated plane distortion. Turb. Shear Flow 4, Delft, The Netherlands (1992)Google Scholar
  29. Lifschitz, A., Hameiri, E.: Local stability conditions in fluid dynamics. Phys. Fluids A 3, 2644–2641 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. Machicoane, N., Bonaventure, J., Volk, R.: Melting dynamics of large ice balls in a turbulent swirling flow. Phys. Fluids 25, 12 (2013)CrossRefGoogle Scholar
  31. Maréchal, P.: Contribution à l’ étude de la déformation plane de la turbulence. Université de Grenoble, France, Doctorat es Sciences (1970)Google Scholar
  32. Moffatt, H.K.: Interaction of turbulence with strong wind shear. In: Yaglom, A.M., Tatarski, V.I. (eds.) Colloquium on Atmospheric Turbulence and Radio Wave Propagation, pp. 139–156. Nauka, Moscow (1967)Google Scholar
  33. Mons, V., Meldi, M., Sagaut, P.: Numerical investigation on the partial return to isotropy of freely decaying homogeneous axisymmetric turbulence. Phys. Fluids 26, 025110 (2014)ADSCrossRefGoogle Scholar
  34. Mons, V., Cambon, C., Sagaut, P.: A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors. J. Fluid Mech. 788, 147–182 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. Nazarenko, S.V., Zakharov, V.E.: The role of he convective modes and sheared variables in the Hamiltonian-dynamics of uniform-shear-flow perturbations. Phys. Lett. A 191(5–6), 403–408 (1994)ADSCrossRefGoogle Scholar
  36. Ribner, H.S.: Convection of a pattern of vorticity through a shock wave. Technical report 1164, NACA (1953)Google Scholar
  37. Rogers, M.M., Moin, P.: The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66 (1987)ADSCrossRefGoogle Scholar
  38. Rogers, M.: The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow. Phys. Fluids A 3(1), 144–154 (1991)ADSCrossRefzbMATHGoogle Scholar
  39. Rose, W.G.: Results of an attempt to generate a homogeneous turbulent shear flow. J. Fluid Mech. 25, 97–120 (1966)ADSCrossRefGoogle Scholar
  40. Sreenivasan, K.R., Narasimha, R.: Rapid distortion theory of axisymmetric turbulence. J. Fluid Mech. 84(3), 497–516 (1978)ADSCrossRefzbMATHGoogle Scholar
  41. Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, Cambridge (1976)zbMATHGoogle Scholar
  42. Tucker, H.J., Reynolds, A.J.: The distortion of turbulence by irrotational plane strain. J. Fluid Mech. 32, 657–673 (1968)ADSCrossRefGoogle Scholar
  43. Yoshida, K., Ishihara, T., Kaneda, Y.: Anisotropic spectrum of homogeneous turbulent shear flow in a Lagrangian renormalized approximation. Phys. Fluids 15(8), 2385–2397 (2003)ADSMathSciNetCrossRefzbMATHGoogle 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