Skip to main content
SpringerLink
Log in

Strongly Anisotropic Turbulence, Statistical Theory and DNS

  • Conference paper
Turbulence and Interactions

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 105))

Abstract

Complete anisotropy of second-order statistics is parametrized in Fourier space, in terms of directional and polarization dependence. This description is shown to be useful to analyze homogeneous anisotropic turbulence, interacting with various body forces and/or in the presence of large-scale ‘mean’ gradients. As far as possible, both statistical theory, ranging from ‘Rapid Distortion Theory’ to nonlinear theories including it, and recent, often original, DNS data are investigated. Applications to strongly anisotropic turbulence are surveyed, in a rotating, then in a stably stratified fluid. The cases of homogeneous shear, simplified MHD with external magnetic field, and weakly compressible quasi-isentropic flows are touched upon using the same theoretical approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Batchelor, G.K.: The theory of homogeneous turbulence. Cambridge University Press, Cambridge (1953)

    MATH  Google Scholar 

  2. Cambon, C., Scott, J.F.: Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31, 1–53 (1999)

    Article  MathSciNet  Google Scholar 

  3. Cambon, C., Rubinstein, R.: Anisotropic developments for homogeneous shear flows. Phys. Fluids 18, 085106 (2006)

    Article  MathSciNet  Google Scholar 

  4. Kassinos, S., Reynolds, W.C., Rogers, M.: One-point turbulence structure tensors. J. Fluid Mech. 428, 213–248 (2000)

    Article  MathSciNet  Google Scholar 

  5. Arad, I., L’vov, V.S., Procaccia, I.: Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group. Phys. Rev. E 59, 6753–6765 (1999)

    Article  MathSciNet  Google Scholar 

  6. Written reports by Craya, Ph.D and P.S.T, in French, being unavailable or too abridged, more information can be obtained from the author upon request

    Google Scholar 

  7. Herring, J.R.: Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859–872 (1974)

    Article  MATH  Google Scholar 

  8. Townsend, A.A.: The structure of turbulent shear flow. Cambridge University Press, Cambridge (1956/1976)

    MATH  Google Scholar 

  9. 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. London Ser. A 406, 13–26 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Orszag, S.A.: Analytical theories of turbulence. J. Fluid Mech. 41, 363 (1970)

    Article  MATH  Google Scholar 

  11. Kaneda, Y.: Lagrangian Renormalized Approximation of Turbulence. Fluid Dynamic Research (to appear) (2006)

    Google Scholar 

  12. Kaneda, Y.: Present conference, keynote lecture

    Google Scholar 

  13. Cambon, C., Jacquin, L.: Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  14. Waleffe, F.: Inertial transfers in the helical decomposition. Phys. Fluids A 5, 677–685 (1993)

    Article  MATH  Google Scholar 

  15. Bos, W.J.T., Bertoglio, J.-P.: Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids 18, 071701 (2006)

    Article  Google Scholar 

  16. Brachet, M.: GDR turbulence, ESPI, Paris, France, November 26 (2005)

    Google Scholar 

  17. Bos, W.J.T., Bertoglio, J.-P.: A single-time two-point closure based on fluid particle displacements. Phys. Fluids 18, 031706 (2006)

    Article  Google Scholar 

  18. Godeferd, F.S., Lollini, L.: DNS of turbulence with confinment and rotation. J. Fluid Mech. 393, 257–308 (1999)

    Article  MATH  Google Scholar 

  19. Greenspan, H.P.: The theory of rotating fluids. Cambridge University Press, Cambridge (1968)

    MATH  Google Scholar 

  20. Cambon, C., Mansour, N.N., Godeferd, F.S.: Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  21. Bellet, F., Godeferd, F.S., Scott, J.F., Cambon, C.: Wave-turbulence in rapidly rotating flows. J. Fluid Mech. 552, 83–121 (2006)

    Article  MathSciNet  Google Scholar 

  22. Galtier, S.: A weak inertial wave-turbulence theory. Phys. Rev. E 68, 1–4 (2003)

    Article  Google Scholar 

  23. Cambon, C., Rubinstein, R., Godeferd, F.S.: Advances in wave-turbulence: rapidly rotating flows. New Journal of Physics 6, 73 (2004)

    Article  MathSciNet  Google Scholar 

  24. Jacquin, L., Leuchter, O., Cambon, C., Mathieu, J.: Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1–52 (1990)

    Article  MATH  Google Scholar 

  25. Bartello, P., Métais, O., Lesieur, M.: Coherent structures in rotating three-dimensional turbulence. J. Fluid Mech. 273, 1–29 (1994)

    Article  MathSciNet  Google Scholar 

  26. Morize, C., Moisy, F., Rabaud, M.: Decaying grid-generated turbulence in a rotating tank. Phys. Fluids 17(9), 095105 (2005)

    Article  Google Scholar 

  27. Gence, J.-N., Frick, C.: C. R. Acad. Sci. Paris. Série II b, vol. 329, p. 351 (2001)

    Google Scholar 

  28. Davidson, P.A., Stapelhurst, P.J., Dalziel, S.B.: On the evolution of eddies in a rapidly rotating system. J. Fluid Mech. 557, 135–144 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Liechtenstein, L., Godeferd, F.S., Cambon, C.: Nonlinear formation of structures in rotating stratified turbulence. Journal of Turbulence 6, 1–18 (2005)

    Article  MathSciNet  Google Scholar 

  30. Godeferd, F.S., Cambon, C.: Detailed investigation of energy transfers in homogeneous stratified turbulence. Phys. Fluids 6, 284–2100 (1994)

    Article  MathSciNet  Google Scholar 

  31. Riley, J.J., Metcalfe, R.W., Weissman, M.A.: DNS of homogeneous turbulence in density-stratified fluids. In: West, B.J. (ed.) Proc. of AIP Conference on Nonlinear Properties of Internal Waves, New York, pp. 79–112. American Institute of Physics (1981)

    Google Scholar 

  32. Godeferd, F.S., Staquet, C.: Statistical modelling and DNS of decaying stably-stratified turbulence, Part II: Large and small-scale anisotropy. J. Fluid Mech. 486, 115–159 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  33. Liechtenstein, L.: unpublished

    Google Scholar 

  34. Billant, P., Chomaz, J.-M.: Phys. Fluids.  13, 1645–1651 (2001)

    Google Scholar 

  35. Lindborg, E.: The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207–242 (2006)

    Article  MATH  Google Scholar 

  36. Charney, J.G.: Geostrophic turbulence. J. Atmos. Sci. 28, 1085–1087 (1971)

    Google Scholar 

  37. Herring, J.R.: J. Atmos. Sci.  37, 969–977 (1980)

    Google Scholar 

  38. Smith, L.M., Waleffe, F.: Generation of slow large-scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145–168 (2002)

    Article  MATH  Google Scholar 

  39. Lee, J.M., Kim, J., Moin, P.: Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583 (1990)

    Article  Google Scholar 

  40. Moffatt, K.: J. Fluid Mech.  28(3), 571–592 (1967)

    Google Scholar 

  41. Alboussière, T.: GDR dynamo, ENSL, Lyon, France, March 27 (2006)

    Google Scholar 

  42. Galtier, S., Nazarenko, S., Newell, A.C., Pouquet, A.: A weak turbulence theory for incompressible MHD. J. Plasma Physics 63, 447–488 (2000)

    Article  Google Scholar 

  43. Simone, A., Coleman, G.N., Cambon, C.: The effect of compressibility in turbulent shear flow: a RDT and DNS study. J. Fluid Mech. 330, 307–338 (1997)

    Article  MATH  Google Scholar 

  44. Fauchet, G., Shao, L., Wunenberger, R., Bertoglio, J.-P.: An improved two-point closure for weakly compressible turbulence. In: 11 Symp. Turb. Shear Flow, Grenoble, September 8–10 (1997)

    Google Scholar 

  45. Jacquin, L., Cambon, C., Blin, E.: Turbulence amplification by a shock wave and Rapid Distortion Theory. Phys. Fluids A 10, 2539–2550 (1993)

    Article  Google Scholar 

  46. Thacker, W.D., Sarkar, S., Gatski, T.B.: Analyzing the influence of compressibility on the rapid pressure-strain rate correlation in turbulent shear flow. TSFP4 meeting and TCFD journal (submitted)

    Google Scholar 

  47. Sarkar, S.: The stabilizing effect of compressibility in turbulent shear flows. J. Fluid Mech. 282, 163–286 (1995)

    Article  MATH  Google Scholar 

  48. 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)

    Article  MATH  Google Scholar 

  49. Cambon, C., Godeferd, F.S., Nicolleau, F., Vassilicos, J.C.: Turbulent diffusion in rapidly rotating flows with and without stable stratification. J. Fluid Mech. 499, 231–255 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  50. Benney, D.J., Newell, A.C.: Random Wave Closure. Studies in Applied Math. 48 (1969)

    Google Scholar 

  51. Dang, K., Roy, P.: Numerical simulation of homogeneous turbulence. In: Proc. Workshop on Macroscopic Modelling of Turbulent Flows and Fluid Mixtures. Springer, Heidelberg (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mécanique des Fluides et d’ Acoustique, École Centrale de Lyon, UCBL, INSA, CNRS, 69134, Ecully Cedex, France

    Claude Cambon

Authors
  1. Claude Cambon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. EPFL STI IGM LIN, Station 9, 1015, Lausanne, Switzerland

    Michel Deville

  2. ONERA, 29 Avenue de la Division Leclerc, 92322, Chatillon, France

    Thien-Hiep Lê

  3. Institut Jean Le Rond d’Alembert, Université Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris cedex 5, France

    Pierre Sagaut

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cambon, C. (2009). Strongly Anisotropic Turbulence, Statistical Theory and DNS. In: Deville, M., Lê, TH., Sagaut, P. (eds) Turbulence and Interactions. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00262-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00262-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00261-8

  • Online ISBN: 978-3-642-00262-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation