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Dynamo mechanism: Effects of correlations and viscosities

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Abstract.

We analyze the effects of the background velocity and the initial magnetic field correlations, and viscosities on the turbulent dynamo and the \(\alpha\)-effect. We calculate the \(\alpha\)-coefficients for arbitrary magnetic and fluid viscosities, background velocity and the initial magnetic field correlations. We explicitly demonstrate that the general features of the initial growth and late-time saturation of the magnetic fields due to the non-linear feedback are qualitatively independent of these correlations. We also examine the hydrodynamic limit of the magnetic field growth in a renormalization group framework and discuss the possibilities of suppression of the dynamo growth below a critical rotation. We demonstrate that for Kolmogorov-(K41) type of spectra the Ekman number \(M \gtrsim 1/2\) for dynamo growth to occur.

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References

  1. H.K. Moffatt, Magnetic Field Generation in Elctrically Conducting Fluids (Cambridge University Press, Cambridge, 1978)

  2. P.P. Kronberg, Rep. Prog. Phys. 57, 325 (1994); R. Beck, A. Brandenburg, D. Moss, A. Shokorov, D. Sokoloff, Ann. Rev. Astronomy Astrophysics 34, 155 (1996); K. Enqvist, Int. J. Mod. Phys. D 7, 331 (1998)

    Article  Google Scholar 

  3. A. Basu, Phys. Rev. E 56, 2869 (1997)

    Article  MathSciNet  Google Scholar 

  4. A. Pouquet, U. Frisch, J. Léorat, J. Fluid Mech. 77, 321 (1976)

    MATH  Google Scholar 

  5. H.K. Moffatt, J. Fluid Mech. 53, 385 (1972)

    MATH  Google Scholar 

  6. S.L. Vainshtein, F. Cattaneo, Astrophysical J. 393, 165 (1992)

    Article  Google Scholar 

  7. G.B. Field, E.G. Blackman, H. Chou, ApJ 513, 638 (1999)

    Article  Google Scholar 

  8. I. Rogachevskii, N. Kleeorin, Phys. Rev. E 64, 056307 (2001)

    Article  Google Scholar 

  9. A. Brandenburg, ApJ 550, 824 (2001)

    Article  Google Scholar 

  10. A. Bhattacharjee, Y. Yuan, ApJ, 449, 739 (1995)

  11. R.H. Kraichnan, Phys. Fluids 11, 945 (1968)

    MATH  Google Scholar 

  12. A.P. Kazantsev, Sov. Phys. JETP 26, 1031 (1968)

    Google Scholar 

  13. M. Vargassola, Phys. Rev. E 53, R3021 (1996)

  14. D. Vincenzi, J. Stat. Phys. 106, 1073 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. R. Arlt, A. Brandenburg, A&A. 376, 713 (2001)

    Google Scholar 

  16. A. Basu, A. Sain, S.K. Dhar, R. Pandit, Phys. Rev. Lett. 81, 2687 (1998)

    Article  Google Scholar 

  17. See also: E.G. Blackman, A. Brandenburg, ApJ 579, 359 (2002)

    Article  Google Scholar 

  18. P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)

    Article  Google Scholar 

  19. D. Forster, D.R. Nelson, M.J. Stephen, Phys. Rev. A 16, 732 (1977)

    Article  Google Scholar 

  20. L.W. Lee, Ann. Phys. 32, 292 (1965)

    MATH  Google Scholar 

  21. A. Basu, J.K. Bhattacharjee, Europhys. Lett. 46, 183 (1997)

    Article  MATH  Google Scholar 

  22. J.D. Jackson, Classical Electrodynamics, 2nd edn. (Wiley Eastern, New Delhi, 1975)

  23. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995)

  24. V. Yakhot, S.A. Orzag, J. Sci. Comput. 1, 1 (1986)

    Google Scholar 

  25. V.S. L’vov, I. Procaccia, Phys. Rev. Lett. 69, 3543 (1992)

    Article  Google Scholar 

  26. A. Raichudhuri, The Physics of Fluids and Plasmas (Cambridge University Press, Cambridge, 1998)

  27. J.-D. Fournier, P.-L. Sulem, A. Pouquet, J. Phys. A 15, 1393 (1982); A. Pouquet, J.-D. Fournier, P.-L. Sulem, J. Phys. Lett. 39, L199 (1978); L.L. Kichatinov, Magnetohydrodynamics 21, 105 (1985); R.G. Kleva, Phys. Fluid 29, 2882 (1986); Y. Zhou, G. Vahala, J. Plasma Phys. 39, 511 (1988); D.W. Longcope, R.N. Sudan, Phys. Fluid B 3, 1945 (1991)

    Article  MATH  Google Scholar 

  28. A. Basu, J.K. Bhattacharjee, S. Ramaswamy, Eur. Phys. J. B 9, 425 (1999)

    Google Scholar 

  29. M.K. Verma, Phys. Plasma 6, 1455 (1999)

    Article  MathSciNet  Google Scholar 

  30. A. Basu, Phys. Rev. E, 61, 1407 (2000)

    Google Scholar 

  31. S. Kida, S. Yanase, J. Mizushima, Phys. Fluids A 3, 457 (1991)

    Article  Google Scholar 

  32. H.K. Moffatt, Rep. Prog. Phys. 46, 621 (1983)

    Article  Google Scholar 

  33. A. Basu, Europhys. Lett. 65, 505 (2004)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Abteilung Theorie, Hahn-Meitner-Institut, Glienicker Strasse 100, 14109, Berlin, Germany

    A. Basu

  2. Poornaprajna Institute of Scientific Research, Bangalore, India

    A. Basu

Authors
  1. A. Basu
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Correspondence to A. Basu.

Additional information

Received: 14 November 2003, Published online: 20 April 2004

PACS:

47.65. + a Magnetohydrodynamics and electrohydrodynamics - 91.25.Cw Origins and models of the magnetic field; dynamo theories

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Basu, A. Dynamo mechanism: Effects of correlations and viscosities. Eur. Phys. J. B 38, 117–126 (2004). https://doi.org/10.1140/epjb/e2004-00107-0

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  • DOI: https://doi.org/10.1140/epjb/e2004-00107-0

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