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Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Published online by Cambridge University Press:  14 August 2013

A. Riols ,
F. Rincon ,
C. Cossu ,
G. Lesur ,
P.-Y. Longaretti ,
G. I. Ogilvie  and
J. Herault
A. Riols
Affiliation:
Université de Toulouse; UPS-OMP; IRAP; Toulouse, France CNRS; IRAP; 14 avenue Edouard Belin, F-31400 Toulouse, France
F. Rincon*
Affiliation:
Université de Toulouse; UPS-OMP; IRAP; Toulouse, France CNRS; IRAP; 14 avenue Edouard Belin, F-31400 Toulouse, France
C. Cossu
Affiliation:
CNRS-Institut de Mécanique des Fluides de Toulouse (IMFT), Allée du Professeur Camille Soula, 31400 Toulouse, France
G. Lesur
Affiliation:
UJF-Grenoble 1 / CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, Grenoble, F-38041, France
P.-Y. Longaretti
Affiliation:
UJF-Grenoble 1 / CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, Grenoble, F-38041, France
G. I. Ogilvie
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
J. Herault
Affiliation:
Laboratoire de Physique Statistique de l’Ecole Normale Supérieure, CNRS UMR 8550, 24 Rue Lhomond, 75231 Paris CEDEX 05, France
*
†Email address for correspondence: francois.rincon@irap.omp.eu
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Abstract

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional nonlinear magnetohydrodynamic process, the study of which 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 with 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 born out of saddle-node bifurcations. 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 injection of both kinetic and magnetic energy for the problem of transition to turbulence and dynamo action 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 understand better 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.

JFM classification

Nonlinear Dynamical Systems: Bifurcation MHD and Electrohydrodynamics: Dynamo theory Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 1 - 45
Copyright
©2013 Cambridge University Press 

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