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
Berger, M., &; Field, G. B. (1984) The topological properties of magnetic helicity. J. Fluid Mech. 147, 133–148
Berger, M. A., & Ruzmaikin, A. (2000) Rate of helicity production by solar rotation. J. Geophys. Res. 105, 10481–10490
Blackman, E. G., & Field, G. F.(2000) Constraints on the magnitude of a in dynamo theory. Astrophys. J. 534, 984–988
Brandenburg, A. (2000) The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence, Astrophys. J., astro-ph/0006186 (B2000)
Brandenburg, A., & Subramanian, K. (2000) Large scale dynamos with ambipolar diffusion nonlinearity. Astron. Astrophys. 361, L33–L36
Brandenburg, A., Bigazzi, A., & Subramanian, K.(2000) The helicity constraint in turbulent dynamos with shear, Mon. Not. Roy. Astron. Soc., astro-ph/0011081
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
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
Krause, F., & Rädler, K.-H. (1980) Mean-Field Magnetohydrodynamics and Dynamo Theory. Pergamon Press, Oxford
Moffatt, H.K. (1978) Magnetic Field Generation in Electrically Conducting Fluids. CUP, Cambridge
Pouquet, A., Frisch, U., & Léorat, J. (1976) Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354
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
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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
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