Time scales separation for dynamo action

Dormy, Emmanuel; Gérard-Varet, David

doi:10.1209/0295-5075/81/64002

Cited by 30 publications

(5 citation statements)

References 19 publications

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“…A similar behavior has also been found previously in an ideal two-dimensional model by the authors of Ref. [26], who examined the induction action of a uniform shear flow perturbed by an periodic variation on intermediate time scales. The authors found a perpetual amplification even for very small perturbation amplitudes and concluded that tiny distortions ∼ Rm −1 can be sufficient to alter the ability of a flow to provide for dynamo action.…”

Section: Introductionsupporting

confidence: 83%

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Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

2012

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We present numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von Kármán-like flow subject to time-dependent nonaxisymmetric velocity perturbations. The numerical model is based on the setup of the French von Kármán-sodium dynamo (VKS) and on the flow measurements from a water experiment conducted at the University of Navarra in Pamplona, Spain. The principal experimental observations that are modeled in our simulations are nonaxisymmetric vortexlike structures which perform an azimuthal drift motion in the equatorial plane. Our simulations show that the interactions of these periodic flow perturbations with the fundamental drift of the magnetic eigenmode (including the special case of nondrifting fields) essentially determine the temporal behavior of the dynamo state. We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an (m = 2) vortexlike flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth rates and a drift of the magnetic eigenmode that is synchronized with the perturbation drift. The resonance-like enhancement of the growth rates takes place when the vortex drift frequency roughly equals the drift frequency of the magnetic eigenmode in the unperturbed system. Outside of this small window, the field generation is hampered compared to the unperturbed case, and the field amplitude of the magnetic eigenmode is modulated with approximately twice the vortex drift frequency. The abrupt transition between the resonant regime and the modulated regime is identified as a spectral exceptional point where eigenvalues (growth rates and frequencies) and eigenfunctions of two previously independent modes collapse. In the actual configuration the drift frequencies of the velocity perturbations that are observed in the water experiment are much larger than the fundamental drift frequency of the magnetic eigenmode that is obtained from our numerical simulations. Hence, we conclude that the fulfillment of the resonance condition might be unlikely in present day dynamo experiments. However, a possibility to increase the dynamo efficiency in the VKS experiment might be realized by an application of holes or fingers on the outer boundary in the equatorial plane. These mechanical distortions provoke an anchorage of the vortices at fixed positions thus allowing an adjustment of the temporal behavior of the nonaxisymmetric flow perturbations.

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Section: Introductionsupporting

confidence: 83%

“…The exclusive occurrence of dynamo action with a time-dependent flow was interpreted as dynamo action based on non-normal growth originally described in Refs. [26,27]. Looking at the details, a number of differences become visible between the study of Ref.…”

Section: Discussionmentioning

confidence: 99%

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

2012

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“…This shows that the magnetic mode amplified by the mean flow can be strongly inhibited by turbulent fluctuations that favour another magnetic mode at the dynamo threshold. However, we also know examples of dynamos generated by a time-dependent velocity field whereas the same velocity field frozen at any particular time is not a dynamo (Dormy & Gerard-Varet 2008; Tilgner 2008). Finally, in the context of mean-field magnetohydrodynamics, examples of dynamos generated only by fluctuations without any mean velocity are well known.…”

Section: Effect Of Fluctuations On the Dynamo Thresholdmentioning

confidence: 99%

Effect of fluctuations on mean-field dynamos

et al. 2018

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We discuss the effect of different types of fluctuations on dynamos generated in the limit of scale separation. We first recall that the magnetic field observed in the VKS (von Karman flow of liquid sodium) experiment is not the one that would be generated by the mean flow alone and that smaller scale turbulent fluctuations therefore play an important role. We then consider how velocity fluctuations affect the dynamo threshold in the framework of mean-field magnetohydrodynamics. We show that the detrimental effect of turbulent fluctuations observed with many flows disappears in the case of helical flows with scale separation. We also find that fluctuations of the electrical conductivity of the fluid, for instance related to temperature fluctuations in convective flows, provide an efficient mechanism for dynamo action. Finally, we conclude by describing an experimental configuration that could be used to test the validity of mean-field magnetohydrodynamics in strongly turbulent flows.

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“…This scaling, Pm c ∼ E 3/4 , has, as far a we are aware, not yet been interpreted. We propose here an interpretation in term of exponential amplification by a time dependent shear (Dormy and Gérard-Varet [24]). We know (Morin [25], Morin and Dormy, in preparation) that the minimum value of Pm for dynamo action does not correspond to an instability of the hydrodynamic solution to a magnetic perturbation, but instead to a detached dynamo branch.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

“…These scalings are all expressed using the viscous timescale as unit of time. Following Dormy and Gérard-Varet [24], we note that dynamo action through a rotating shear requires τ β < τ η (where τ η = L 2 /η and τ β is the typical timescale of rotation or oscillation of the shear, here a rotation). We then get (with this unit of time) the necessary condition for this dynamo mechanism (based on timescale separation) to occur, Pm > E 2/3 (because Pm measures τ η in the τ ν timescale).…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Geomagnetism and the dynamo: where do we stand?

Dormy

Mouël

2008

Comptes Rendus. Physique

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We review recent developments both in the observation of the Earth's magnetic field (from the short, human life timescale, to the long, geological timescale) and in the modelling of its origin (using the numerical or the experimental approach). We attempt a confrontation of these results, coming from very different fields, and show how, when combined, they can yield a better understanding of the Earth's core dynamics. We assume prior knowledge of dynamo theory, but not of geophysics. To cite this article: E.

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Time scales separation for dynamo action

Cited by 30 publications

References 19 publications

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

Effect of fluctuations on mean-field dynamos

Geomagnetism and the dynamo: where do we stand?

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