Lagrangian chaos and the fast kinematic dynamo problem

  • Edward Ott
Plasma And turbulence
Part of the Lecture Notes in Physics book series (LNP, volume 511)


In this paper we review results on the fast kinematic dynamo problem, emphasizing the recent realization that Lagrangian chaos of the underlying flow is the key element for understanding of the problem. We also discuss the generic tendency for fractal magnetic field distributions with extreme cancellation properties. The relation of ergodic properties of the chaotic flow to properties of the dynamo (e.g., growth rate, fractal dimension) are also reviewed.


Magnetic Field Fractal Dimension Field Line Topological Entropy Ideal Equation 
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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  1. 1.
    Vainshtein S. I., Zeldovich Ya. B. (1972): Sov. Phys. Usp. 15, 159CrossRefADSGoogle Scholar
  2. 2.
    Arnold V. I., Zeldovich Ya. B., Ruzmaikin A. A., Sokolov D. D. (1981): Sov. Phys. JETP 54, 1083Google Scholar
  3. 3.
    Bayly B. J., Childress S. (1989): Geophys. Astrophys. Fluid Dyn. 44, 211 (1988); ibid. 49, 23zbMATHADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Finn J. M., Ott, E. (1988): Phys. Fluids 31, 2992zbMATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Bayly B. J., Childress S. (1988): Geophys. Astrophys. Fluid Dyn. 44, 211zbMATHADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Finn J., Hanson J., Kan I., Ott E (1989): Phys. Rev. Lett. 62, 2965zbMATHCrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Vishik M. M. (1989): Geophys. Astrophys. Fluid Dyn. 48, 151zbMATHADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Ott E., Antonsen T. M. (1989): Phys. Rev. A 39, 3660CrossRefADSGoogle Scholar
  9. 9.
    Finn J., Ott E. (1990): Phys. Fluids B 2, 916CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Finn J., Hanson J., Kan I., Ott E. (1991): Phys. Fluids B 3, 1250CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Galloway D. J., Proctor M. R. E. (1992): Nature 356, 691CrossRefADSGoogle Scholar
  12. 12.
    Gilbert A. D., Bayly B. J. (1992): J. Fluid Mech. 241, 199zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Gilbert A. D. (1992): Philos. Trans. R. Soc. London Ser. A 339, 627ADSCrossRefGoogle Scholar
  14. 14.
    Ott E., Du Y., Sreenivasan K. R., Juneja A., Suri A. K. (1992): Phys. Rev. Lett. 69, 2654CrossRefADSGoogle Scholar
  15. 15.
    Du Y., Ott E. (1993): Physica D 67, 387zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Du Y., Ott E. (1993): J. Fluid Mech. 257, 265zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Lau Y.-T., Finn J. (1993): Phys. Fluids B 5, 365CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Soward A. (1993): Geophys. Astrophys. Fluid Dyn. 73, 179ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Gilbert A. D., Otani N. F., Childress S. (1993): in Theory of Solar and Planetary Dynamics, edited by M. R. E. Proctor, P. C. Matthews, and A. M. Rucklidge (Cambridge University Press, New York,), 129–136Google Scholar
  20. 20.
    Otani N. F. (1993): J. Fluid Mech. 253, 327zbMATHCrossRefADSGoogle Scholar
  21. 21.
    Ponty Y., Pouquet A., Sulem P. L. (1995): Geophys. Astrophys. Fluid Dyn. 79, 239ADSCrossRefGoogle Scholar
  22. 22.
    Cattaneo F., Kim E., Proctor M., Tao L. (1995): Phys. Rev. Lett. 75, 1522CrossRefADSGoogle Scholar
  23. 23.
    Klapper I., Young, L. S. (1995): Comm. Math. Phys. 173, 623zbMATHCrossRefADSMathSciNetGoogle Scholar
  24. 24.
    Reyl C., Ott E., Antonsen T. M. (1996): Phys. Plasmas 3, 2564CrossRefADSGoogle Scholar
  25. 25.
    Childress S., Gilbert A. D. (1995): Stretch, Twist, Fold: The Fast Dynamo, (Springer-Verlag, New York)zbMATHGoogle Scholar
  26. 26.
    Galloway D., Frisch U. (1986): Geophys. Astrophys. Fluid Dyn. 36, 53 (1986); V. I. Arnold and E. I. Korkiina, Vestn. Mosk. Univ. Mat. Mekh. 3, 43 (in Russian)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Grassberger P., Procaccia I. (1983): Physica D 9, 189zbMATHCrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Ott E. (1994): Chaos in Dynamical Systems (Cambridge University Press), 78–85Google Scholar
  29. 29.
    Farmer J. D., Ott E., Yorke J. A. (1983): Physica D 7, 153CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Edward Ott
    • 1
    • 2
  1. 1.Institute for Plasma ResearchUniversity of MarylandCollege Park
  2. 2.Department of Physics, Department of Electrical EngineeringInstitute for Systems ResearchUSA

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