Skip to main content
SpringerLink
Log in

Fourier analysis of wave turbulence in a thin elastic plate

  • Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V.E. Zakharov, V.S. L’vov, G. Falkovich, Kolmogorov Spectra of Turbulence (Springer, Berlin, 1992)

  2. A.C. Newell, S. Nazarenko, L. Biven, Physica D 152, 153, 520 (2001)

    Google Scholar 

  3. P. Denissenko, S. Lukaschuk, S. Nazarenko, Phys. Rev. Lett. 99, 014501 (2007)

    Article  ADS  Google Scholar 

  4. E. Herbert, N. Mordant, E. Falcon, e-print arXiv:1005.2000

  5. C. Connaughton, Physica D 238, 2282 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. G. Düring, C. Josserand, S.S. Rica, Phys. Rev. Lett. 97, 025503 (2006)

    Article  ADS  Google Scholar 

  7. A. Boudaoud, O. Cadot, B. Odille, C. Touzé, Phys. Rev. Lett. 100, 234504 (2008)

    Article  ADS  Google Scholar 

  8. N. Mordant, Phys. Rev. Lett. 100, 234505 (2008)

    Article  ADS  Google Scholar 

  9. P. Cobelli, P. Petitjeans, A. Maurel, V. Pagneux, N. Mordant, Phys. Rev. Lett. 103, 204301 (2009)

    Article  ADS  Google Scholar 

  10. L. Landau, Théorie de l’élasticité (MIR, Moscou, 1967)

  11. C. Connaughton, S. Nazarenko, A.C. Newell, Physica D 184, 86 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. E.A. Kartashova, Phys. Rev. Lett. 72, 2013 (1994)

    Article  ADS  Google Scholar 

  13. E. Kartashova, JETP Lett. 83, 283 (2006)

    Article  ADS  Google Scholar 

  14. E. Kartashova, Euro. Phys. lett. PL 87, 44001 (2009)

    Article  ADS  Google Scholar 

  15. P.J. Cobelli, A. Maurel, V. Pagneux, P. Petitjeans, Exp. Fluids 46, 1037 (2009)

    Article  Google Scholar 

  16. A. Maurel, P. Cobelli, V. Pagneux, P. Petitjeans, Appl. Opt. 48, 380 (2009)

    Article  ADS  Google Scholar 

  17. S. Nazarenko, J. Stat. Mech. 2, L02002 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Statistique, École Normale Supérieure & CNRS, 24 rue Lhomond, 75005, Paris, France

    N. Mordant

Authors
  1. N. Mordant
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Mordant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mordant, N. Fourier analysis of wave turbulence in a thin elastic plate. Eur. Phys. J. B 76, 537–545 (2010). https://doi.org/10.1140/epjb/e2010-00197-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2010-00197-y

Keywords

Search

Navigation