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Dynamo properties of the turbulent velocity field of a saturated dynamo



In order better to understand how dynamo systems saturate, we study the kinematic dynamo properties of velocity fields that arise from nonlinearly saturated dynamos. The technique is implemented by solving concurrently, in addition to the momentum equation, two induction equations, one for the actual magnetic field and one for an independent passive vector field. We apply this technique to two illustrative examples: convectively driven turbulence and turbulence represented by a shell model. In all cases we find that the velocity remains an efficient kinematic dynamo even after nonlinear saturation occurs. We discuss the implications to the process of dynamo saturation.


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Boldyrev, S. & Cattaneo, F. 2004 Magnetic-field generation in Kolmogorov turbulence. Phys. Rev. Lett. 92 (14), 144501.
Brummell, N. H., Cattaneo, F. & Tobias, S. M. 2001 Linear and nonlinear dynamo properties of time-dependent ABC flows. Fluid Dyn. Res. 28, 237265.
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. & Hughes, D. W. 2008 Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers. Mon. Not. Roy. Ast. Soc. submitted.
Cattaneo, F., Hughes, D. W. & Kim, E. 1996 Suppression of chaos in a simplified nonlinear dynamo model. Phys. Rev. Lett. 76, 20572060.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Frick, P. 1983 Hierarchical models of two-dimensional turbulence. Magnitnaia Gidrodinarnika 19, 6066.
Frick, P. & Sokoloff, D. 1998 Cascade and dynamo action in a shell model of magnetohydrodynamic turbulence. Phys. Rev. emphE 57, 41554164.
Gledzer, E. B. 1973 System of hydrodynamic type admitting two quadratic integrals of motion. Sov. Phys. Dok. 18, 216217.
Kazantsev, A. P. 1968 Enhancement of a Magnetic Field by a Conducting Fluid. Sov. J. Exp. Theoret. Phys. 26, 10311034.
Klapper, I. & Young, L. S. 1995 Rigorous bounds on the fast dynamo growth-rate involving topological entropy. Comm. Math. Phys. 175, 623646.
Kraichnan, R. H. & Nagarajan, S. 1967 Growth of turbulent magnetic fields. Phys. Fluids 10, 859870.
Plunian, F. & Stepanov, R. 2007 A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence. New J. Phys. 9, 296319.
Schekochihin, A. A., Cowley, S. C., Maron, J. L. & McWilliams, J. C. 2004 Critical magnetic Prandtl number for small-scale dynamo. Phys. Rev. Lett. 92 (5), 054502.
Stellmach, S. & Hansen, U. 2004 Cartesian convection driven dynamos at low Ekman number. Phys. Rev. E 70 (5), 056312.
Vainshtein, S. I. & Cattaneo, F. 1992 Nonlinear restrictions on dynamo action. Astrophys. J. 393, 165171.
Vainshtein, S. I. & Kichatinov, L. L. 1986 The dynamics of magnetic fields in a highly conducting turbulent medium and the generalized Kolmogorov–Fokker–Planck equations. J. Fluid Mech. 168, 7387.
Vishik, M. M. 1989 Magnetic field generation by the motion of a highly conducting fluid. Geophys. Astrophys. Fluid Dyn. 48, 151167.
Yamada, M. & Ohkitani, K. 1987 Lyapunov spectrum of a chaotic model of three-dimensional turbulence. J. Phys. Soc. Jpn 56, 42104213.
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Dynamo properties of the turbulent velocity field of a saturated dynamo



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