Skip to main content
SpringerLink
Log in

Linear and nonlinear models for turbulence in the presence of waves

  • Conference paper
Book cover Fundamental Problematic Issues in Turbulence

Part of the book series: Trends in Mathematics ((TM))

  • 528 Accesses

Abstract

Some issues in turbulence description and modelling, with possible connection with stability analysis, are discussed in this paper. In the absence of a general theory for turbulence, the different issues will be illustrated by the case of‘weak’ turbulence, in which structuring effects, induced by the presence of body forces (e.g. Coriolis and buoyancy forces) or mean velocity or temperature gradients, play an essential role. Three points are addressed in the following.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Babin, A., MAHALOV, A. & Nicolaenko, B. 1996. Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Eur. J. Mech. B/Fluids 15, 291–300

    MathSciNet  MATH  Google Scholar 

  2. Batchelor, G.K. & Proudman, I. 1954. The effect of rapid distortion in a fluid in turbulent motion. Q. J. Mech. Appl. Maths, 7, 83

    Article  MathSciNet  MATH  Google Scholar 

  3. Bayly, B. J. 1986. Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57, 2160–2163

    Article  MathSciNet  Google Scholar 

  4. Benney, D. J. & Saffman, P. G. 1966. Nonlinear interactions of random waves in a dispersive medium. Proc. Roy. Soc. London A. 289, 301–320

    Article  Google Scholar 

  5. Caillol, P. & Zeitlin, V. 1998. On the stationary energy spectra of the stratified fluid in a weak turbulence regime. Proc. Monte Verita II Colloquium.

    Google Scholar 

  6. Cambon, C., Benoit, J. P., Shao, L. & Jacquin, L. 1994. Stability analysis and large eddy simulation of rotating turbulence with organized eddies. J. Fluid Mech.,278, 175–200

    Article  MathSciNet  MATH  Google Scholar 

  7. Cambon, C., Mansour, N. N. & Godeferd, F. S. 1997. Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332

    Article  MathSciNet  MATH  Google Scholar 

  8. Cambon, C. & Scott, J. F. 1998. Linear and nonlinear models of anisotropic turbulence. Ann. Rev. Fluid Mech. 61. To appear

    Google Scholar 

  9. Craik, A. D. D. & Criminale, W. O. 1986. Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier-Stokes equations. Proc. R. Soc. London A 406, 13.

    Article  MathSciNet  MATH  Google Scholar 

  10. Godeferd, F. S. & Cambon, C. 1994. Detailed investigation of energy transfers in homogeneous turbulence. Phys. Fluid 6, 2084–2100

    Article  MathSciNet  MATH  Google Scholar 

  11. Godeferd, F. S., Malik, N. A., Cambon, C. & Nicoleau, F. 1997. Eulerian and Lagrangian statistics in homogeneous stratified flows. Applied Scientific Research 57, 319–335

    Article  MATH  Google Scholar 

  12. Greenspan, H.P. 1968. The theory of rotating fluids. Cambridge University Press.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  14. Lee, J. M., Kim, J. & Moin, P. 1990. Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583

    Article  Google Scholar 

  15. Lifschitz, A. & Hameiri, E. 1991. Local stability conditions in fluid dynamics. Phys. Fluid A. 3, 2644–2651

    Article  MathSciNet  MATH  Google Scholar 

  16. Lumley, J. L. 1967. The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation, ed. A. M. Yaglom & V. I. Tatarski. Moscow: NAUCA

    Google Scholar 

  17. Monin, A. S. & Yaglom, A. M. 1975. Statistical Fluid Mechanics I. section 17.3, MIT Press

    Google Scholar 

  18. Orszag, S. A. Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.

    Google Scholar 

  19. Perry, A. E. & Chong, M. S. 1987 A study of eddying motions and flow patterns using critical point concepts. Ann. Rev. Fluid Mech. 19, 125–155.

    Article  Google Scholar 

  20. Rogers, M. M. 1991. The structure of a passive scalar field with a uniform gradient in rapidly sheared homogeneous turbulent flow. Phys. Fluid A. 3, 144–154

    Article  MATH  Google Scholar 

  21. Townsend, A. A. 1956. The structure of turbulent shear flow. Revised version 1976, Cambridge University Press.

    Google Scholar 

  22. Waleffe, F. 1993. Inertial transfers in the helical decomposition. Phys. Fluid A 5, 677–685

    Article  MATH  Google Scholar 

  23. Zakharov, V. E., L’vov,. S., Falkowich, G. 1992. Kolmogorov spectra of turbulence. I. Wave turbulence. Springer series in nonlinear dynamics. Springer Verlag

    Google Scholar 

Download references

Authors
  1. C. Cambon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Hydromechanics and Water Resources Management, ETH Hönggerberg, 8093, Zürich, Switzerland

    Albert Gyr  & Wolfgang Kinzelbach  & 

  2. Faculty of Engineering, Tel Aviv University, 69978, Tel Aviv, Israel

    Arkady Tsinober

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Basel AG

About this paper

Cite this paper

Cambon, C. (1999). Linear and nonlinear models for turbulence in the presence of waves. In: Gyr, A., Kinzelbach, W., Tsinober, A. (eds) Fundamental Problematic Issues in Turbulence. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8689-5_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8689-5_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9730-3

  • Online ISBN: 978-3-0348-8689-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation