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The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 313–320 | Cite as

Influence of time dependent flows on the threshold of the kinematic dynamo action

  • A. de la TorreEmail author
  • J. Burguete
  • C. Pérez-García
Article

Abstract.

A numerical study of the influence of slowly evolving velocity fields in the threshold of the dynamo action is presented. Using experimental time averaged velocity fields, harmonic variations are introduced in a kinematic code in order to characterize the response of the magnetic field to a broad range of frequencies. A critical frequency is found around ωc=200 where a transition is obtained. For large values of the frequency (i.e. smaller periods) the magnetic field can not see the velocity fluctuations and the response of the system corresponds to that of the mean flow. For smaller frequencies, the magnetic field sees the slow evolution of the velocity field, and reduces significatively its growth rates when compared to the mean value. This loss of efficiency is due to the dissipation that appears during the transition between the magnetic eigenvectors corresponding to each one of the velocity fields.

Keywords

Shear Layer European Physical Journal Special Topic Small Frequency Azimuthal Velocity Magnetic Reynolds Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. J. Larmor, Rep. Brit. Assoc. Adv. Sci., 159 (1919) Google Scholar
  2. H.K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, 1978) Google Scholar
  3. R. Moreau, Magnetohydrodynamics (Kluwer Academic Publishers, Dortrecht, 1990) Google Scholar
  4. S.I. Vainshtein, Ya.B. Zeldovich, Sov. Phys. Usp. 75, 159 (1972) Google Scholar
  5. H.K. Moffatt, Nature 341, 285 (1989) Google Scholar
  6. A. Gailitis, O. Lielausis, S. Dement'ev, E. Placatis, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, H. Hänel, G. Will, Phys. Rev. Lett. 84, 4365 (2000) Google Scholar
  7. A. Gailitis, O. Lielausis, S. Dement'ev, E. Placatis, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, H. Hänel, G. Will, Phys. Rev. Lett. 86, 3024 (2001) Google Scholar
  8. R. Stieglitz, U. Müller, Naturwissenschaften 87, 381 (2000) Google Scholar
  9. R. Stieglitz, U. Müller Phys. Fluids 13, 561 (2001) Google Scholar
  10. M. Bourgoin, L. Marié, F. Pétrélis, J. Burguete, A. Chiffaudel, F. Daviaud, S. Fauve, P. Odier, J.-F. Pinton, Phys. Fluids 14, 3046 (2002) Google Scholar
  11. F. Pétrélis, M. Bourgoin, L. Marié, J. Burguete, A. Chiffaudel, F. Daviaud, S. Fauve, P. Odier, J.-F. Pinton, Phys. Rev. Lett. 90, 174501 (2003) Google Scholar
  12. R. Monchaux et al., Phys. Rev. Lett. 98, 044502 (2007) Google Scholar
  13. M. Berhanu et al., Europhys Lett. (2007) (submitted) Google Scholar
  14. L. Marie, J. Burguete, F. Daviaud, J. Leorat, Eur. Phys. J B 33, 469 (2003) Google Scholar
  15. F. Ravelet, A. Chiffaudel, F. Daviaud, J. Leorat, Phys. Fluids 17, 117104 (2005) Google Scholar
  16. A. de la Torre, J. Burguete, Phys. Rev. Lett. [arXiv:physics/0702151] (submitted) Google Scholar
  17. D.J. Galloway, M.R.E. Proctor, Nature 356, 691 (1992) Google Scholar
  18. R. Hollerbach, D.J. Galloway, M.R.E. Proctor 74, 3145 (1995) Google Scholar
  19. F. Cattaneo, S.M. Tobias, Phys. Fluids 17, 127105 (2005) Google Scholar
  20. J. Léorat, Magnetohydrodynamics 31, 367 (1995) Google Scholar
  21. Yu. B. Ponomarenko, J. Appl. Mech. Tech. Phys. 14, 755 (1972) Google Scholar
  22. C. Normand, Phys. Fluids 15, 1606 (2003) Google Scholar
  23. M. Peyrot, F. Plunian, C. Normand, Phys. Fluids (2007) (submitted) Google Scholar
  24. F. Pétrélis, S. Fauve, Europhys. Lett. 76, 602 (2006) Google Scholar
  25. S. Fauve, F. Pétrélis, Peyresq Lectures on Nonlienar Phenomena, edited by J. Sepulchre (World Scientific, Singapore, 2003), pp. 1–64 Google Scholar
  26. J.P. Laval, P. Blaineau, N. Leprovost, B. Dubrulle, F. Daviaud, Phys. Rev. Lett. 96, 204503 (2006) Google Scholar
  27. A.P. Willis, D. Gubbins, Geophys. Astrophys. Fluid Dynam. 98, 537 (2004) Google Scholar
  28. U. Müller, R. Stieglitz and S. Horanyi, F. Busse, XXI ICTAM (CDROM Proceedings) ISBN 83-89687-01-1 (IPPT-PAN, Warsaw, 2004) Google Scholar
  29. F. Ravelet, L. Marie, A. Chiffaudel, F. Daviaud, Phys. Rev. Lett. 93, 164501 (2004) Google Scholar
  30. T. von Kármán, Z. Angew. Math. Mech. 1, 233 (1921) Google Scholar
  31. P. Zandbergen, D. Dijkstra, Ann. Rev. Fluid Mech. 19, 465 (1987) Google Scholar
  32. C. Nore, L.S. Tuckerman, O. Daube, S. Xin, J. Fluid Mech. 477, 51 (2003) Google Scholar
  33. C. Nore, L.M. Witkowski, E. Foucault, J. Pecheux, O. Daube, P. Le Quere, Phys. Fluids 18, 054102 (2006) Google Scholar
  34. C. Nore, F. Moisy, L. Quartier, Phys. Fluids 17, 064103 (2005) Google Scholar
  35. J. Léorat, Prog. Ser. Am. Inst. Astronaut. Aeronaut. 162, 282 (1994) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • A. de la Torre
    • 1
    Email author
  • J. Burguete
    • 1
  • C. Pérez-García
    • 1
  1. 1.Departamento de Física y Matemática AplicadaUniversidad de NavarraPamplonaSpain

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