Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Abstract

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, nonlinear magnetohydrodynamic process whose study is relevant to the understanding of accretion and magnetic field generation in astrophysics. Transition to this form of dynamo 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 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 supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. This suggests 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 conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in various 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.

43 pages, 17 figures, accepted for publication in J. Fluid Mech

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• Transition to subcritical turbulence in a tokamak plasma
• Statistical simulation of the magnetorotational dynamo
• Increasing lifetimes and the growing saddles of shear flow turbulence
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• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
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• Dissipative structures in magnetorotational turbulence
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• High-speed shear driven dynamos. Part 1. Asymptotic analysis
• Transient growth of perturbations on scales beyond the accretion disc thickness
• Shedding light on the MRI driven dynamo in a stratified shearing box
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• Supertransient Magnetohydrodynamic Turbulence in Keplerian Shear Flows: The role of the Hall Effect