Skip to main content

On fast dynamo action in steady chaotic flows

  • Conference paper
  • First Online:
Large Scale Structures in Nonlinear Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 392))

  • 128 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 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 

  • 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 

  • 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 

  • 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 

  • Bayly, B.J. & Childress, S. 1989 Unsteady dynamo effects at large magnetic Reynolds number, Geophys. Astrophys. Fluid Dyn., 49, 23–43.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Childress, S. & Klapper, I. 1991 On some transport properties of baker's maps, J. Stat. Phys., in press.

    Google Scholar 

  • 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 

  • Finn, J.M., Hanson, J.D., Kan, I. & Ott, E. 1989 Do steady fast dynamos exist? Phys. Rev. Lett., 25, 2965–2968.

    Article  Google Scholar 

  • 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 

  • Finn, J.M. & Ott, E. 1988 Chaotic flows and fast magnetic dynamos, Phys. Fluids, 31, 2992–3011.

    Article  Google Scholar 

  • Finn, J.M. & Ott, E. 1990 The fast kinematic magnetic dynamo and the dissipationless limit, Phys. Fluids, B2, 916–926.

    Google Scholar 

  • Galloway, D. & Frisch, U. 1986 Dynamo action in a family of flows with chaotic streamlines, Geophys. Astrophys. Fluid Dyn., 36, 58–83.

    Google Scholar 

  • Gilbert, A.D. & Childress, S. 1990 Evidence for fast dynamo action in a chaotic web, Phys. Rev. Lett., 65, 2133–2136.

    Article  PubMed  Google Scholar 

  • Gilbert, A.D. 1988 Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dyn., 44, 241–258.

    Google Scholar 

  • Gilbert, A.D. 1991 Evidence for fast dynamo action in a chaotic ABC flow, Nature, 350, 483–485.

    Article  Google Scholar 

  • Klapper, I. 1991 Shadowing and the role of small diffusivity in the chaotic advection of scalars, Phys. Rev. Lett., submitted.

    Google Scholar 

  • Moffatt, H.K. 1978 Magnetic field generation in electrically conducting fluids, Cambridge University Press.

    Google Scholar 

  • Moffatt, H.K. & Proctor, M.R.E. 1985 Topological constraints associated with fast dynamo action, J. Fluid Mech., 154, 493–507.

    Google Scholar 

  • Otani, N. 1989 E.O.S., Trans. Geophys. Union Vol. 69, No. 44, Nov. 1, Abstract No. HS51-15, p. 1366.

    Google Scholar 

  • Soward, A.M. 1987 Fast dynamo action in a steady flow, J. Fluid Mech., 180, 267–295.

    Google Scholar 

  • Vainshtein, S.I. & Zeldovich, Ya.B. 1972 Origin of magnetic fields in astrophysics, Sov. Phys. Usp., 15, 159–172.

    Google Scholar 

  • Vishik, M.M. 1989 Magnetic field generation by the motion of a highly conducting fluid, Geophys. Astrophys. Fluid Dyn., 48, 151–167.

    Google Scholar 

  • 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 

  • Zeldovich, Ya.B., Ruzmaikin, A.A. & Sokoloff, D.D. 1983 Magnetic fields in astrophysics, Gordon and Breach.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean-Daniel Fournier Pierre-Louis Sulem

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Gilbert, A.D. (1991). On fast dynamo action in steady chaotic flows. In: Fournier, JD., Sulem, PL. (eds) Large Scale Structures in Nonlinear Physics. Lecture Notes in Physics, vol 392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54899-8_52

Download citation

  • DOI: https://doi.org/10.1007/3-540-54899-8_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54899-7

  • Online ISBN: 978-3-540-46469-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics