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Part of the book series: NATO Science Series ((NAII,volume 26))

Abstract

The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the α-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field strength.

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References

  1. Berger, M., &; Field, G. B. (1984) The topological properties of magnetic helicity. J. Fluid Mech. 147, 133–148

    Article  MathSciNet  ADS  Google Scholar 

  2. Berger, M. A., & Ruzmaikin, A. (2000) Rate of helicity production by solar rotation. J. Geophys. Res. 105, 10481–10490

    Article  ADS  Google Scholar 

  3. Blackman, E. G., & Field, G. F.(2000) Constraints on the magnitude of a in dynamo theory. Astrophys. J. 534, 984–988

    Article  ADS  Google Scholar 

  4. Brandenburg, A. (2000) The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence, Astrophys. J., astro-ph/0006186 (B2000)

    Google Scholar 

  5. Brandenburg, A., & Subramanian, K. (2000) Large scale dynamos with ambipolar diffusion nonlinearity. Astron. Astrophys. 361, L33–L36

    ADS  Google Scholar 

  6. Brandenburg, A., Bigazzi, A., & Subramanian, K.(2000) The helicity constraint in turbulent dynamos with shear, Mon. Not. Roy. Astron. Soc., astro-ph/0011081

    Google Scholar 

  7. Frisch, U., Pouquet, A., Léorat, J., Mazure, A. (1975) Possibility of an inverse cascade of magnetic helicity in hydrodynamic turbulence. J. Fluid Mech. 68, 769–778

    Article  ADS  MATH  Google Scholar 

  8. Kleeorin, N. I, Moss, D., Rogachevskii, I., & Sokoloff, D. (2000) Helicity balance and steady-state strength of the dynamo generated galactic magnetic field. Astron. Astrophys. 361, L5–L8

    ADS  Google Scholar 

  9. Krause, F., & Rädler, K.-H. (1980) Mean-Field Magnetohydrodynamics and Dynamo Theory. Pergamon Press, Oxford

    MATH  Google Scholar 

  10. Moffatt, H.K. (1978) Magnetic Field Generation in Electrically Conducting Fluids. CUP, Cambridge

    Google Scholar 

  11. Pouquet, A., Frisch, U., & Léorat, J. (1976) Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354

    Article  ADS  MATH  Google Scholar 

  12. Steenbeck, M., Krause, F., & Rädler, K.-H. (1966) Berechnung der mittleren Lorentz-Feldstärke v x B für ein elektrisch leitendendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung. Z. Naturforsch. 21a, 369–376 See also the translation in Roberts & Stix (1971) The turbulent dynamo, Tech. Note 60, NCAR, Boulder, Colorado

    ADS  Google Scholar 

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© 2001 Springer Science+Business Media Dordrecht

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Brandenburg, A. (2001). The Inverse Cascade in Turbulent Dynamos. In: Chossat, P., Ambruster, D., Oprea, I. (eds) Dynamo and Dynamics, a Mathematical Challenge. NATO Science Series, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0788-7_15

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  • DOI: https://doi.org/10.1007/978-94-010-0788-7_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7070-3

  • Online ISBN: 978-94-010-0788-7

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