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The turbulent dynamo as an instability in a noisy medium

  • Hydrodynamics
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Abstract.

We study an example of instability in presence of a multiplicative noise, namely the spontaneous generation of a magnetic field in a turbulent medium. This so-called turbulent dynamo problem remains challenging, experimentally and theoretically. In this field, the prevailing theory is the Mean-Field Dynamo [1] where the dynamo effect is monitored by the mean magnetic field. In recent years, it has been shown on stochastic oscillators that this type of approach could be misleading. In this paper, we develop a stochastic description of the turbulent dynamo effect which enables us to define unambiguously a threshold for the dynamo effect, namely by globally analyzing the probability density function of the magnetic field instead of a given moment.

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References

  • F. Krause, K.-H. Rädler, Mean field MHD and dynamo theory (Pergamon Press, 1980)

  • R. Bourret, U. Frisch, A. Pouquet, Physica 65, 303 (1973); R. Graham, A. Schenzle, Phys. Rev. A 26, 1676 (1982); M. Lücke, F. Schank, Phys. Rev. Lett. 54, 1465 (1985)

    Article  Google Scholar 

  • K. Mallick, P. Marcq, Eur. Phys. J. B 36, 119 (2003); K. Mallick, P. Marcq, Eur. Phys. J. B 38, 99 (2004)

    CAS  Google Scholar 

  • S. Residori, R. Berthet, B. Roman, S. Fauve, Phys. Rev. Lett. 88, 024502 (2002); R. Berthet et al., Physica D 174, 84 (2003)

    Article  CAS  PubMed  Google Scholar 

  • R.L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, 1967)

  • D. Sweet et al., Phys. Rev. E 63, 066211 (2001)

    Article  Google Scholar 

  • A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); R. Stieglitz, U. Müller, Phys. Fluids 13, 561 (2001)

    Article  PubMed  Google Scholar 

  • N.L. Peffley, A.B. Cawthorne, D.P. Lathrop, Phys. Rev. E 61, 5287 (2000); M. Bourgoin et al., Phys. Fluids 14, 3046 (2002)

    Article  CAS  Google Scholar 

  • L. Marié et al., Eur. Phys. J. B 33, 469 (2003); F. Ravelet, A. Chiffaudel, F. Daviaud, J. Léorat, submitted to Phys. Fluids

    Google Scholar 

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

    Google Scholar 

  • E.N. Parker, Astrophys. J. 162, 665 (1970)

    Article  Google Scholar 

  • R.H. Kraichnan, S. Nagarajan, Phys. Fluids 10, 859 (1967)

    Article  CAS  Google Scholar 

  • Ya.B. Zel’dovich, A.A. Ruzmaikin, S.A. Molchanov, D.D. Sokolov, J. Fluid Mech. 144, 1 (1984)

    Google Scholar 

  • G. Falkovich, K. Gawedzki, M. Vergassola, Rev. Mod. Phys. 73, 913 (2001)

    Google Scholar 

  • S. Boldyrev, Astrophys. J. 562, 1081 (2001)

    Article  Google Scholar 

  • F. Pétrélis, Ph.D. Thesis, Paris VI, (2002); S. Fauve, F. Petrelis, The dynamo effect, in Peyresq Lectures on Nonlinear Phenomena (World Scientific, 2003)

  • S. Pavel, S. Berloff, J.C. McWilliams, J. Phys. Oceanogr. 32, 797 (2002)

    Google Scholar 

  • J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford, 2002)

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

  • N. Leprovost, Ph.D. Thesis, Paris VI (2004)

  • M. Chertkov, G. Falkovich, I. Kolokolov, M. Vergassola, Phys. Rev. Lett. 83, 4065 (1999)

    Article  CAS  Google Scholar 

  • G. Backus, Ann. Phys. 4, 372 (1958)

    Article  Google Scholar 

  • T. Antonov, S. Lozkhin, P. Frick, D. Sokoloff, Magnetohydrodynamics 37, 87 (2001)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Groupe Instabilité et Turbulence, CEA/DSM/DRECAM/SPEC and CNRS, URA 2464, 91191, Gif-sur-Yvette Cedex, France

    N. Leprovost & B. Dubrulle

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  1. N. Leprovost
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  2. B. Dubrulle
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Correspondence to N. Leprovost.

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Leprovost, N., Dubrulle, B. The turbulent dynamo as an instability in a noisy medium. Eur. Phys. J. B 44, 395–400 (2005). https://doi.org/10.1140/epjb/e2005-00138-y

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  • DOI: https://doi.org/10.1140/epjb/e2005-00138-y

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