- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Nonlinear dynamos at infinite magnetic Prandtl number

Alexandros Alexakis

  • Laboratoire de Physique Statistique de l’Ecole Normale Supérieure, UMR CNRS 8550, 24 Rue Lhomond, F-75006 Paris Cedex 05, France

PDF

Phys. Rev. E 83, 036301 – Published 3 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036301

Abstract

The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.

View figure in article

Article Text

References (39)

  1. Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon & Breach, London, 1990).
  2. F. Cattaneo, D. W. Hughes, and E. J. Kim, Phys. Rev. Lett. 76, 2057 (1996).
  3. J. Maksymczuk and A. D. Gilbert, Geophys. Astrophys. Fluid Dyn. 90, 127 (1998).
  4. F. Cattaneo and S. M. Tobias, J. Fluid Mech. 621, 205 (2009).
  5. A. Tilgner and A. Brandenburg, Mon. Not. R. Astron. Soc. 391, 1477 (2008).
  6. M. Schrinner, D. Schmitt, R. Cameron, and P. Hoyng, Geophys. J. Int. 182, 675 (2010).
  7. A. Courvoisier, D. W. Hughes, and M. R. E. Proctor, Proc. R. Soc. London A 466, 583 (2010).
  8. A. A. Schekochihin, S. C. Cowley, S. F. Taylor, G. W. Hammett, J. L. Maron, and J. C. McWilliams, Phys. Rev. Lett. 92, 084504 (2004).
  9. A. A. Schekochihin, S. C. Cowley, and J. L. Maron, Phys. Rev. Lett. 92, 064501 (2004).
  10. A. A. Schekochihin, J. L. Maron, S. C. Cowley, and J. C. McWilliams, Astrophys. J. 576, 806 (2002).
  11. A. A. Schekochihin, S. C. Cowley, and J. L. Maron, Phys. Rev. E 65, 016305 (2001).
  12. H. K. Moffatt, J. Fluid Mech. 35, 117 (1969).
  13. D. O. Gomez, P. D. Mininni, and P. Dmitruk, Adv. Space Res. 35, 899 (2005).
  14. D. O. Gomez, P. D. Mininni, and P. Dmitruk, Phys. Scr. T 116, 123 (2005).
  15. V. I. Arnold, C. R. Acad. Sci. Paris 261, 17 (1965).
  16. T. Dombre, U. Frisch, J. M. Greene, M. Henon, A. Mehr, and A. M. Soward, J. Fluid Mech. 167, 353 (1986).
  17. O. M. Podvigina and A. Pouquet, Physica D 75, 471 (1994).
  18. V. I. Arnold and E. I. Korkina, Vestn. Mosk. Univ., Ser. 1: Mat, Mekh. 3, 43 (1983).
  19. D. J. Galloway and U. Frisch, Geophys. Astrophys. Fluid Dyn. 36, 53 (1986).
  20. Y. T. Lau and J. M. Finn, Phys. Fluids B 5, 365 (1993).
  21. S. Childress and A. D. Gilbert, Stretch, Twist, Fold: The Fast Dynamo (Springer, New York, 1995).
  22. D. J. Galloway and M. R. E. Proctor, Nature (London) 356, 691 (1992).
  23. V. Archontis, Ph.D. thesis, Copenhagen University, 2000.
  24. V. Archontis, S. B. F. Dorch, and A. Nordlund, Astron. Astrophys. 397, 393 (2003).
  25. S. B. F. Dorch and V. Archontis, Sol. Phys. 224, 171 (2004).
  26. V. Archontis, S. B. F. Dorch, and A. Nordlund, Astron. Astrophys. 472, 715 (2007).
  27. R. Cameron and D. Galloway, Mon. Not. R. Astron. Soc. 365, 735 (2006).
  28. A. D. Gilbert, Y. Ponty, and V. Zheligovsky, DOI: .10.1080/03091929.2010.513332
  29. S. Fauve and F. Petrelis, C. R. Phys. 8, 87 (2007).
  30. S. Fauve and F. Petrelis, Eur. Phys. J. B 22, 273 (2001).
  31. S. I. Vainstein and F. Cattaneo, Astrophys. J. 393, 165 (1992).
  32. P. D. Mininni, Y. Ponty, D. C. Montgomery, J.-F. Pinton, H. Politano, and A. Pouquet, Astrophys. J. 626, 853 (2005).
  33. D. O. Gomez and P. D. Mininni, Nonlin. Processes Geophys. 11, 619 (2004).
  34. A. Pouquet, U. Frisch, and J. Leorat, J. Fluid Mech. 77, 321 (1976).
  35. A. D. Gilbert and P. L. Sulem, Geophys. Astrophys. Fluid Dyn. 51, 243 (1990).
  36. A. Brandenburg, Astrophys. J. 550, 824 (2001).
  37. A. Brandenburg, W. Dobler, and K. Subramanian, Astron. Nachr. 323, 99 (2002).
  38. A. D. Gilbert, Geophys. Astrophys. Fluid Dyn. 96, 135 (2002).
  39. A. Alexakis, P. D. Mininni, and A. Pouquet, Astrophys. J. 640, 335 (2006).

Outline

Information

Phys. Rev. E 83, 036301– Published 3 March, 2011
  • Received 29 October 2010

©2011 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation