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Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Riols, Antoine and Rincon, François and Cossu, Carlo and Lesur, Geoffroy and Longaretti, Pierre-Yves and Ogilvie, Gordon I. and Herault, Johann Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow. (2013) Journal of Fluid Mechanics, 731. 1-45. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/jfm.2013.317


Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non-linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.

Item Type:Article
Additional Information:Thanks to Cambridge University Press. The definitive version is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8966132
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Université de Paris Diderot - Paris 7 (FRANCE)
Other partners > University of Cambridge (UNITED KINGDOM)
Other partners > Université Pierre et Marie Curie, Paris 6 - UPMC (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Ecole Normale Supérieure de Paris - ENS Paris (FRANCE)
Other partners > Université Joseph Fourier Grenoble 1 - UJF (FRANCE)
Laboratory name:
Deposited On:28 Nov 2013 09:28

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