On fast dynamo action in steady chaotic flows

  • Andrew D. Gilbert
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 392)


Fluid Element Dynamo Action Magnetic Field Generation Chaotic Flow Liapunov Exponent 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arnold, V.I. & Korkina, E.I. 1983 The growth of a magnetic field in a three-dimensional steady incompressible flow, Vest. Mosk. Un. Ta. Ser. 1, Math. Mec., 3, 43–46.Google Scholar
  2. Arnold, V.I., Zeldovich, Ya. B., Ruzmaikin, A.A. & Sokoloff, D.D. 1981 A magnetic field in a stationary flow with stretching in Riemannian space, Zh. Eksp. Teor. Fiz., 81, 2052–2058 [Sov. Phys. J.E.T.P., 54, 1083-1086].Google Scholar
  3. Bayly, B.J. 1991 Infinitely conducting dynamos and other horrible eigenproblems, Proc. Workshop on Nonlinear Phenomena in Atmospheric & Oceanic Sciences, I.M.A. (Minnesota) June 1990, to appear.Google Scholar
  4. Bayly, B.J. & Childress, S. 1988 Construction of fast dynamos using unsteady flows and maps in three dimensions, Geophys. Astrophys. Fluid Dyn., 44, 211–240.Google Scholar
  5. Bayly, B.J. & Childress, S. 1989 Unsteady dynamo effects at large magnetic Reynolds number, Geophys. Astrophys. Fluid Dyn., 49, 23–43.Google Scholar
  6. Beloshapkin, V.V., Chernikov, A.A., Natenzon, M.Ya., Petrovichev, B.A., Sagdeev, R.Z. & Zaslavsky, G.M. 1989 Chaotic streamlines in pre-turbulent states, Nature, 337, 133–137.CrossRefGoogle Scholar
  7. Childress, S. & Klapper, I. 1991 On some transport properties of baker's maps, J. Stat. Phys., in press.Google Scholar
  8. Dombre, T., Frisch, U., Greene, J.M., Hénon, M., Mehr, A. & Soward, A.M. 1986 Chaotic streamlines in the ABC flows, J. Fluid Mech., 167, 353–391.Google Scholar
  9. Finn, J.M., Hanson, J.D., Kan, I. & Ott, E. 1989 Do steady fast dynamos exist? Phys. Rev. Lett., 25, 2965–2968.CrossRefGoogle Scholar
  10. Finn, J.M., Hanson, J.D., Kan, I. & Ott, E. 1990 Steady fast dynamo flows, Plasma Preprint UMLPR 90-015, University of Maryland.Google Scholar
  11. Finn, J.M. & Ott, E. 1988 Chaotic flows and fast magnetic dynamos, Phys. Fluids, 31, 2992–3011.CrossRefGoogle Scholar
  12. Finn, J.M. & Ott, E. 1990 The fast kinematic magnetic dynamo and the dissipationless limit, Phys. Fluids, B2, 916–926.Google Scholar
  13. Galloway, D. & Frisch, U. 1986 Dynamo action in a family of flows with chaotic streamlines, Geophys. Astrophys. Fluid Dyn., 36, 58–83.Google Scholar
  14. Gilbert, A.D. & Childress, S. 1990 Evidence for fast dynamo action in a chaotic web, Phys. Rev. Lett., 65, 2133–2136.CrossRefPubMedGoogle Scholar
  15. Gilbert, A.D. 1988 Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dyn., 44, 241–258.Google Scholar
  16. Gilbert, A.D. 1991 Evidence for fast dynamo action in a chaotic ABC flow, Nature, 350, 483–485.CrossRefGoogle Scholar
  17. Klapper, I. 1991 Shadowing and the role of small diffusivity in the chaotic advection of scalars, Phys. Rev. Lett., submitted.Google Scholar
  18. Moffatt, H.K. 1978 Magnetic field generation in electrically conducting fluids, Cambridge University Press.Google Scholar
  19. Moffatt, H.K. & Proctor, M.R.E. 1985 Topological constraints associated with fast dynamo action, J. Fluid Mech., 154, 493–507.Google Scholar
  20. Otani, N. 1989 E.O.S., Trans. Geophys. Union Vol. 69, No. 44, Nov. 1, Abstract No. HS51-15, p. 1366.Google Scholar
  21. Soward, A.M. 1987 Fast dynamo action in a steady flow, J. Fluid Mech., 180, 267–295.Google Scholar
  22. Vainshtein, S.I. & Zeldovich, Ya.B. 1972 Origin of magnetic fields in astrophysics, Sov. Phys. Usp., 15, 159–172.Google Scholar
  23. Vishik, M.M. 1989 Magnetic field generation by the motion of a highly conducting fluid, Geophys. Astrophys. Fluid Dyn., 48, 151–167.Google Scholar
  24. Zeldovich, Ya.B. 1957 The magnetic field in the two-dimensional motion of a conducting turbulent fluid, Sov. Phys. J.E.T.P., 4, 460–462.Google Scholar
  25. Zeldovich, Ya.B., Ruzmaikin, A.A. & Sokoloff, D.D. 1983 Magnetic fields in astrophysics, Gordon and Breach.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Andrew D. Gilbert
    • 1
  1. 1.D.A.M.T.P.CambridgeUnited Kingdom

Personalised recommendations