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On the measurement of turbulent magnetic diffusivities: the three-dimensional case

  • F. Cattaneo (a1) and S. M. Tobias (a2)


It has been shown that it is possible to measure the turbulent diffusivity of a magnetic field by a method involving oscillatory sources. So far the method has only been tried in the special case of two-dimensional fields and flows. Here we extend the method to three dimensions and consider the case where the flow is thermally driven convection in a large-aspect-ratio domain. We demonstrate that if the diffusing field is horizontal the method is successful even if the underlying flow can sustain dynamo action. We show that the resulting turbulent diffusivity is comparable with, although not exactly the same as, that of a passive scalar. We were not able to measure unambiguously the diffusivity if the diffusing field is vertical, but argue that such a measurement is possible if enough resources are utilized on the problem.


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Ångström, Å, J. 1861 Neue methode, das wärmeleitungsvermögen der körper zu bestimmen. Ann. Phys. Chem. 114, 513530.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics. Springer.
Cattaneo, F. 1999 On the origin of magnetic fields in the quiet photosphere. Astrophys. J. Lett. 515, L39L42.
Cattaneo, F., Emonet, T. & Weiss, N. 2003 On the interaction between convection and magnetic fields. Astrophys. J. 588, 11831198.
Cattaneo, F. & Hughes, D. W. 2006 Dynamo action in a rotating convective layer. J. Fluid Mech. 553, 401418.
Cattaneo, F., Lenz, D. & Weiss, N. 2001 On the origin of the solar mesogranulation. Astrophys. J. Lett. 563, L91L94.
Cattaneo, F. & Vainshtein, S. I. 1991 Suppression of turbulent transport by a weak magnetic field. Astrophys. J. Lett. 376, L21L24.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford (Clarendon).
Garabedian, P. R. 1998 Partial Differential Equations. AMS Chelsea Publishing.
Krause, F. & Raedler, K.-H. 1980 Mean-field Magnetohydrodynamics and Dynamo Theory. Pergamon.
Meneguzzi, M. & Pouquet, A. 1989 Turbulent dynamos driven by convection. J. Fluid Mech. 205, 297318.
Moffatt, H. K. 1974 The mean electromotive force generated by turbulence in the limit of perfect conductivity. J. Fluid Mech. 65, 110.
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
Ogilvie, G. I. & Lesur, G. 2012 On the interaction between tides and convection. Mon. Not. R. Astron. Soc. 422, 19751987.
Parker, E. N. 1979 Cosmical Magnetic Fields: Their Origin and Their Activity. Clarendon (Oxford University Press).
Rieutord, M. & Rincon, F. 2010 The Sun’s supergranulation. Living Rev. Solar Phys. 7, 2.
Schrinner, M., Rädler, K.-H., Schmitt, D., Rheinhardt, M. & Christensen, U. 2005 Mean-field view on rotating magnetoconvection and a geodynamo model. Astron. Nachr. 326, 245249.
Tobias, S. M. & Cattaneo, F. 2013 On the measurement of the turbulent diffusivity of a large-scale magnetic field. J. Fluid Mech. 717, 347360.
Tobias, S. M., Cattaneo, F. & Brummell, N. H. 2008 Convective dynamos with penetration, rotation, and shear. Astrophys. J. 685, 596605.
Tobias, S. M., Cattaneo, F. & Brummell, N. H. 2011 On the generation of organized magnetic fields. Astrophys. J. 728, 153.
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On the measurement of turbulent magnetic diffusivities: the three-dimensional case

  • F. Cattaneo (a1) and S. M. Tobias (a2)


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