JETP Letters

, Volume 103, Issue 3, pp 201–205 | Cite as

Nonlinear generation of vorticity in thin smectic films

  • V. M. Parfenyev
  • S. S. Vergeles
  • V. V. Lebedev
Nonlinear Phenomena

Abstract

We analyze a solenoidal motion in a vertically vibrated freely suspended thin smectic film. We demonstrate analytically that transverse oscillations of the film generate two-dimensional vortices in the plane of the film owing to hydrodynamic nonlinearity. An explicit expression for the vorticity of the in-plane film motion in terms of the film displacement is obtained. The air around the film is proven to play a crucial role, since it changes the dispersion relation of transverse oscillations and transmits viscous stresses to the film, modifying its bending motion. We propose possible experimental observations enabling to check our predictions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

11448_2016_1094_MOESM1_ESM.pdf (165 kb)
Supplementary material, approximately 165 KB.

References

  1. 1.
    M. Gharib and P. Derango, Physica D 37, 406 (1989).ADSCrossRefGoogle Scholar
  2. 2.
    Y. Couder, J. M. Chomaz, and M. Rabaud, Physica D 37, 384 (1989).ADSCrossRefGoogle Scholar
  3. 3.
    S. Taylor, Proc. R. Soc. London 27, 71 (1878).CrossRefGoogle Scholar
  4. 4.
    M. Airiau, DEA Report (ENS, Paris, 1986).Google Scholar
  5. 5.
    V. O. Afenchenko, A. B. Ezersky, S. V. Kiyashko, M. I. Rabinovich, and P. D. Weidman, Phys. Fluids 10, 390 (1998).ADSCrossRefGoogle Scholar
  6. 6.
    J. M. Vega, F. J. Higuera, and P. D. Weidman, J. Fluid Mech. 372, 213 (1998).ADSCrossRefGoogle Scholar
  7. 7.
    P. Pieranski, L. Beliard, J.-Ph. Tournellec, X. Leoncini, C. Furtlehner, H. Dumoulin, E. Riou, B. Jouvin, J.-P. Fénerol, Ph. Palaric, J. Heuving, B. Cartier, and I. Kraus, Physica A 194, 364 (1993).ADSCrossRefGoogle Scholar
  8. 8.
    S. V. Yablonskii, T. Oue, H. Nambu, A. S. Mikhailov, M. Ozaki, and K. Yoshino, Appl. Phys. Lett. 75, 64 (1999).ADSCrossRefGoogle Scholar
  9. 9.
    I. Kraus, Ch. Bahr, I. V. Chikina, and P. Pieranski, Phys. Rev. E 58, 610 (1998).ADSCrossRefGoogle Scholar
  10. 10.
    E. I. Kats and V. V. Lebedev, Fluctuational Effects in the Dynamics of Liquid Crystals (Springer, Berlin, 1993).Google Scholar
  11. 11.
    wwwjetplettersacru.Google Scholar
  12. 12.
    S. Uto, E. Tazoh, M. Ozaki, and K. Yoshino, J. Appl. Phys. 82, 2791 (1997).ADSCrossRefGoogle Scholar
  13. 13.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, 2nd ed. (Pergamon, Oxford, UK, 1987).Google Scholar
  14. 14.
    M. Chertkov, C. Connaughton, I. Kolokolov, and V. Lebedev, Phys. Rev. Lett 99, 084501 (2007).ADSCrossRefGoogle Scholar
  15. 15.
    H. Xia, M. Shats, and G. Falkovich, Phys. Fluids 21, 125101 (2009).ADSCrossRefGoogle Scholar
  16. 16.
    J. Laurie, G. Boffetta, G. Falkovich, I. Kolokolov, and V. Lebedev, Phys. Rev. Lett. 113, 254593 (2014).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  • V. M. Parfenyev
    • 1
  • S. S. Vergeles
    • 1
  • V. V. Lebedev
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

Personalised recommendations