On the Generation of Organized Magnetic Fields

Tobias, Steven M.; Cattaneo, Fausto; Brummell, Nicholas H.

doi:10.1088/0004-637x/728/2/153

Cited by 25 publications

(32 citation statements)

References 35 publications

(35 reference statements)

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“…It is possible that large-scale dynamos are "essentially nonlinear" rather than "essentially kinematic" and a major revision of the theory might be in order. It is also possible that the whole categorisation of dynamos into large and small-scale is misleading and that it is more useful to seek "system-scale" dynamo solutions to the MHD equations (Tobias et al 2010). In general, the lack of reflectional symmetry in astrophysical turbulence owes its origins to the presence of rotation.…”

Section: Discussionmentioning

confidence: 99%

MHD Dynamos and Turbulence

Tobias

Cattaneo

Boldyrev

2012

Ten Chapters in Turbulence

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Section: Discussionmentioning

confidence: 99%

MHD Dynamos and Turbulence

Tobias

Cattaneo

Boldyrev

2012

Ten Chapters in Turbulence

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“…Gallet et al 2012;Gissinger 2012) and there have actually been reports of heteroclinic dynamo orbits in the VKS experiment (Monchaux et al 2009). A compelling observation very likely related to the occurrence of such bifurcations is the remarkable dynamical complexity offered by the MRI dynamo and other instability-driven dynamos (Cline et al 2003;Tobias et al 2011) even in fairly low-resolution three-dimensional numerical experiments. Not only are fully three-dimensional, large-scale (comparable to the size of the domain) MRI dynamo cycles easy to excite, the problem also contains all the germs of chaotic dynamo action, a hallmark of many astrophysical dynamos.…”

Section: Connections With Dynamo Theory and Experimentsmentioning

confidence: 98%

“…This is the dynamo equivalent of the nonlinear self-advection of streamwise-dependent unstable perturbations feeding back on streamwise vortices in the hydrodynamic problem. This scenario may also be relevant to dynamos involving other MHD instabilities (Rincon et al 2008), such as the kink instability (Spruit 2002), magnetic buoyancy coupled to Kelvin-Helmholtz instability (Cline et al 2003;Davies & Hughes 2011;Tobias et al 2011), and magnetoshear instabilities (Miesch et al 2007).…”

Section: Omega Effectmentioning

confidence: 99%

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

et al. 2013

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Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, nonlinear 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. †

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“…It is not even completely clear whether the solar dynamo is driven by convective motions or by magnetic instabilities (Brandenburg 1998; Tobias et al 2011), and whether meridional circulation plays an important role for causing the equatorward migration of the Sunʼs magnetic field (Choudhuri et al 1995;Hazra et al 2014). Furthermore, we are facing even more fundamental challenges, for example, the question of catastrophic quenching, the dependence of mean field strength on magnetic Reynolds number, and the morphology of the field in the form of tubes on the one hand, and the question of magnetic buoyancy, flux tube storage, and sunspot formation on the other.…”

Section: Introductionmentioning

confidence: 99%

Is the Small-Scale Magnetic Field Correlated With the Dynamo Cycle?

Karak

Brandenburg

2015

ApJ

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The small-scale magnetic field is ubiquitous at the solar surface-even at high latitudes. From observations we know that this field is uncorrelated (or perhaps even weakly anticorrelated) with the global sunspot cycle. Our aim is to explore the origin, and particularly the cycle dependence, of such a phenomenon using three-dimensional dynamo simulations. We adopt a simple model of a turbulent dynamo in a shearing box driven by helically forced turbulence. Depending on the dynamo parameters, large-scale (global) and small-scale (local) dynamos can be excited independently in this model. Based on simulations in different parameter regimes, we find that, when only the large-scale dynamo is operating in the system, the small-scale magnetic field generated through shredding and tangling of the large-scale magnetic field is positively correlated with the global magnetic cycle. However, when both dynamos are operating, the small-scale field is produced from both the small-scale dynamo and the tangling of the large-scale field. In this situation, when the large-scale field is weaker than the equipartition value of the turbulence, the small-scale field is almost uncorrelated with the large-scale magnetic cycle. On the other hand, when the large-scale field is stronger than the equipartition value, we observe an anticorrelation between the smallscale field and the large-scale magnetic cycle. This anticorrelation can be interpreted as a suppression of the smallscale dynamo. Based on our studies we conclude that the observed small-scale magnetic field in the Sun is generated by the combined mechanisms of a small-scale dynamo and tangling of the large-scale field.

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On the Generation of Organized Magnetic Fields

Cited by 25 publications

References 35 publications

MHD Dynamos and Turbulence

MHD Dynamos and Turbulence

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Is the Small-Scale Magnetic Field Correlated With the Dynamo Cycle?

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