Skip to main content

Pattern Formation in a Vibrated Granular Layer

  • Chapter
  • First Online:
Granular Gases

Part of the book series: Lecture Notes in Physics ((LNP,volume 564))

Abstract

We present a numericalstudy of a surface instability occuring in a bidimensional vibrated granular layer. The driving mechanism for the formation of stationary waves is closely followed. Two regimes of wavelength selection are identified: a dispersive regime and a saturation regime. For the latter, a connection is established between the pattern formation and an intrinsic instability occuring spontaneously in dissipative gases.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. H. M. Jaeger, S. R. Nageland R. P. Behringer, Rev. Mod. Phys. 68, 1259 (1996).

    Article  ADS  Google Scholar 

  2. E. Clément, “Granular Packing under Vibration” in Physics of Dry Granular Media, H. J. Herrmann, J.-P. Hovi and S. Luding, Kluwer Acad. Publisher, Dordrecht, Holland (1998) p.585.

    Google Scholar 

  3. F. Melo, P. Umbanhowar and H. Swinney, Phys. Rev. Lett. 72, 172 (1994); ibid 75, 3838 (1995).

    Article  ADS  Google Scholar 

  4. P. Umbanhowar, F. Melo and H. Swinney, Nature 382, 793 (1996).

    Article  ADS  Google Scholar 

  5. M. Faraday, Philos. Trans. R. Soc. 121, 299 (1831).

    Article  Google Scholar 

  6. S. Fauve, in Dynamics of non-linear and disordered systems, G. Martinez-Mekler and T. H. Seligman, World Scientific, Singapore, (1995) p.67.

    Book  Google Scholar 

  7. E. Clément, L. Vanel, J. Duran and J. Rajchenbach, Phys. Rev. E 53, 2972 (1996).

    Article  ADS  Google Scholar 

  8. S. Luding, E. Clément, J. Rajchenbach and J. Duran, Europhys. Lett, 36, 247 (1996).

    Article  ADS  Google Scholar 

  9. C. Bizon, M. D. Shattuck, J. B. Swift, W. D. McCormick and H. Swinney, Phys. Rev. Lett. 80, 57 (1998).

    Article  ADS  Google Scholar 

  10. K. M. Aoki and T. Akiyama, Phys. Rev. Lett. 77, 4166 (1996).

    Article  ADS  Google Scholar 

  11. T. Shinbrot, Nature (London) 389, 574 (1997).

    Article  ADS  Google Scholar 

  12. L. S. Tsimring and I. S. Aronson, Phys. Rev. Lett. 79, 213 (1997).

    Article  ADS  Google Scholar 

  13. D. H. Rothman, Phys. Rev. E. 57, 1239 (1998).

    Article  ADS  Google Scholar 

  14. E. Cerda, F. Melo and S. Rica, Phys. Rev. Lett.79, 4570 (1997).

    Article  ADS  Google Scholar 

  15. J. Eggers and H. Riecke, Phys. Rev. E 59, 4476 (1999).

    Article  ADS  Google Scholar 

  16. W. Goldsmith, Impact, the Theory and Physical Behavior of Colliding Solids (Edward Arnorl, London, 1960); O. Walton et al., J. Rheol. 30, 949 (1983). S. F. Foerster et al., Phys. Fluids 6, 1108 (1994). L. Labous et al. Phys. Rev. E 56, 5717 (1997).

    Google Scholar 

  17. B. Bernu and R. Mazighi, J. Phys. A 23, 5745 (1990); S. McNamara, W. R. Young, Phys. Fluids A 5, 34 (1993).

    Article  MATH  ADS  Google Scholar 

  18. S. Luding, H. J. Herrmann and A. Blumen, Phys. Rev. E 50, 3100 (1994).

    Article  ADS  Google Scholar 

  19. B. D. Lubachevsky, J. Comp. Phys. 94, 255 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. L. D. Landau and E. Lifschitz, Fluid Mechanics (Pergamon Press, London, 1963).

    MATH  Google Scholar 

  21. L. Labous, Thèse de doctorat, Université de Paris VI (1998).

    Google Scholar 

  22. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993); S. McNamara and W. R. Young, Phys. Rev.E 50, R28 (1994).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Clément, E., Labous, L. (2001). Pattern Formation in a Vibrated Granular Layer. In: Pöschel, T., Luding, S. (eds) Granular Gases. Lecture Notes in Physics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44506-4_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-44506-4_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41458-2

  • Online ISBN: 978-3-540-44506-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics