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Bistability and chaos in the Taylor-Green dynamo

Rakesh K. Yadav1,*, Mahendra K. Verma1, and Pankaj Wahi2

  • 1Department of Physics, Indian Institute of Technology, Kanpur 208016, India
  • 2Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India

  • *yadav.r.k.87@gmail.com
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Phys. Rev. E 85, 036301 – Published 6 March, 2012Erratum Phys. Rev. E 85, 049906 (2012)

DOI: https://doi.org/10.1103/PhysRevE.85.036301

Abstract

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

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Erratum

Erratum: Bistability and chaos in the Taylor-Green dynamo [Phys. Rev. E 85, 036301 (2012)]

Rakesh K. Yadav, Mahendra K. Verma, and Pankaj Wahi
Phys. Rev. E 85, 049906 (2012)

Article Text

References (34)

  1. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, 1978).
  2. F. Krause and K. H. Radler, Mean-field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980).
  3. A. Brandenburg and K. Subramanian, Phys. Rep. 417, 1 (2005).
  4. Y. Ponty, J. P. Laval, B. Dubrulle, F. Daviaud, and J. F. Pinton, Phys. Rev. Lett. 99, 224501 (2007).
  5. G. Nigro and P. Veltri, Astrophys. J. Lett. 740, L37 (2011).
  6. V. Morin and E. Dormy, Int. J. Mod. Phys. B 23, 5467 (2009).
  7. R. Yadav, M. Chandra, M. K. Verma, S. Paul, and P. Wahi, Europhys. Lett. 91, 69001 (2010).
  8. G. Sahoo, D. Mitra, and R. Pandit, Phys. Rev. E 81, 036317 (2010).
  9. R. Monchaux, M. Berhanu, M. Bourgoin, M. Moulin, P. Odier, J. Pinton, R. Volk, S. Fauve, N. Mordant, F. Pétrélis et al., Phys. Rev. Lett. 98, 044502 (2007).
  10. P. H. Roberts and G. A. Glatzmaier, Rev. Mod. Phys. 72, 1081 (2000).
  11. M. Ossendrijver, Astron. Astrophys. Rev. 11, 287 (2003).
  12. F. Pétrélis, N. Mordant, and S. Fauve, Geophys. Astrophys. Fluid Dyn. 101, 289 (2007).
  13. P. H. Roberts, Geophys. Astrophys. Fluid Dyn. 44, 3 (1988).
  14. M. G. S. Pierre, in Solar and Planetary Dynamos, edited by M. R. E. Proctor, P. C. Matthews, and A. M. Ruchlidge (Cambridge University Press, Cambridge, 1993), pp. 295–302.
  15. S. Stellmach and U. Hansen, Phys. Rev. E 70, 056312 (2004).
  16. W. Kuang and J. Bloxham, J. Comput. Phys. 153, 51 (1999).
  17. G. Krstulovic, G. Thorner, J.-P. Vest, S. Fauve, and M. Brachet, Phys. Rev. E 84, 066318 (2011).
  18. Y. Ponty, P. D. Mininni, D. C. Montgomery, J. F. Pinton, H. Politano, and A. Pouquet, Phys. Rev. Lett. 94, 164502 (2005).
  19. C. Nore, M. E. Brachet, H. Politano, and A. Pouquet, Phys. Plasmas 4, 1 (1997).
  20. P. Mininni, Y. Ponty, D. Montgomery, J. Pinton, H. Politano, and A. Pouquet, Astrophys. J. 626, 853 (2005).
  21. B. Dubrulle, P. Blaineau, O. M. Lopes, F. Daviaud, J. Laval, and R. Dolganov, New J. Phys. 9, 308 (2007).
  22. E. Dormy and A. M. Soward, Mathematical Aspects of Natural Dynamos (CRC Press, Boca Raton, 2007).
  23. N. O. Weiss, Geophys. Astrophys. Fluid Dyn. 105, 256 (2010).
  24. M. K. Verma, e-print arXiv:1103.2517.
  25. F. Pétrélis and S. Fauve, J. Phys.: Condens. Matter 20, 494203 (2008).
  26. W. Kuang, W. Jiang, and T. Wang, Geophys. Res. Lett. 35, L14204 (2008).
  27. P. Pal, P. Wahi, S. Paul, M. K. Verma, K. Kumar, and P. K. Mishra, Europhys. Lett. 87, 54003 (2009).
  28. A. Kageyama and T. Sato, Phys. Rev. E 55, 4617 (1997).
  29. S. Childress and A. M. Soward, Phys. Rev. Lett. 29, 837 (1972).
  30. J. Morin, E. Dormy, M. Schrinner, and J.-F. Donati, MNRAS Lett. 418, L133 (2011).
  31. B. Sreenivasan and C. A. Jones, J. Fluid Mech. 688, 5 (2011).
  32. R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Oxford University Press, Oxford, 1994).
  33. F. Stefani, A. Gailitis, and G. Gerbeth, Astron. Nachr. 332, 4 (2011).
  34. S. Aumaître, M. Berhanu, M. Bourgoin, A. Chiffaudel, F. Daviaud, B. Dubrulle, S. Fauve, L. Marié, R. Monchaux, N. Mordant et al., C. R. Phys. 9, 689 (2008).

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Phys. Rev. E 85, 036301– Published 6 March, 2012
  • Received 22 September 2011

©2012 American Physical Society

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