Experimental demonstration of a homogeneous two-scale dynamo

Stieglitz, Robert; Müller, Ulrich

doi:10.1063/1.1331315

Cited by 374 publications

(315 citation statements)

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“…Experimental evidence for mean-field EMFs (such as the α-effect) in turbulent flows has been scarce. Three experiments, relying on a laminar α-effect, have generated an EMF [8] and dynamo action [9,10], but heavilyconstrained flow geometries were used to produce the needed helicity; the role of turbulence was ambiguous. Experiments with unconstrained flows have provided evidence for turbulent EMFs, though not the turbulent α- effect.…”

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confidence: 99%

Observation of a Turbulence-Induced Large Scale Magnetic Field

et al. 2006

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An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also observed is the production of toroidal magnetic field from applied poloidal magnetic field (the ω-effect). Its potential role in the production of the induced dipole is discussed. Many stars and planets generate their own nearlyaxisymmetric magnetic fields. Understanding the mechanism by which these fields are generated is a problem of fundamental importance to astrophysics. These dynamos are sometimes modeled using two components: a process which generates toroidal magnetic field from poloidal field and a feedback mechanism which reinforces the poloidal field [1]. The first process is easily modeled in an axisymmetric system: toroidal differential rotation of a highly-conducting fluid sweeps the pre-existing poloidal field in the toroidal direction creating toroidal field. This phenomenon, known as the ω-effect, is efficient at producing magnetic field and has been observed experimentally [2,3,4]. The second ingredient to the model is more subtle, as toroidal currents must be generated to reinforce the original axisymmetric poloidal field. Cowling's theorem [5] excludes the possibility of an axisymmetric flow generating such currents so some symmetry-breaking mechanism is required.The usual mechanism invoked [6] is a turbulent electromotive force (EMF), E = ṽ ×b , whereby small scale fluctuations in the velocity and magnetic fields break the symmetry and interact coherently to generate the large scale magnetic field. This EMF is sometimes expanded [7] in terms of transport coefficients about the mean magnetic field: E = αB + β∇ × B + γ × B; α is characterized by helicity in the turbulence, β by enhanced diffusion and γ by a gradient in the intensity of the turbulence. α is of particular interest as it results in current flowing parallel to a magnetic field, and when coupled with the ω-effect can generate the toroidal currents needed to reinforce the poloidal field. Experimental evidence for mean-field EMFs (such as the α-effect) in turbulent flows has been scarce. Three experiments, relying on a laminar α-effect, have generated an EMF [8] and dynamo action [9,10], but heavilyconstrained flow geometries were used to produce the needed helicity; the role of turbulence was ambiguous. Experiments with unconstrained flows have provided evidence for turbulent EMFs, though not the turbulent α- effect. Reighard and Brown [11] have attributed a measured reduction in the conductivity of a turbulent flow of sodium to the β-effect. Pétrélis et al. have observed [12] distortion of a magnetic field similar to an α-effect (currents generated in the direction of an applied magnetic field) and postulate that turbulence may be responsible for...

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Observation of a Turbulence-Induced Large Scale Magnetic Field

et al. 2006

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“…Although laboratory experiments cannot reach the kinetic Reynolds numbers Re of the Sun or even Earth, they provide useful information about the effect of turbulence on the dynamo process. The first experimental fluid dynamos have generated either stationary or oscillatory magnetic fields [3]. Recently, the VKS experiment [4] has shown a variety of dynamical behaviors.…”

Section: Chaotic Dynamos Generated By a Turbulent Flow Of Liquid Sodiummentioning

confidence: 99%

Chaotic Dynamos Generated by a Turbulent Flow of Liquid Sodium

et al. 2008

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“…So far, dynamo experiments based on a flow of a conducting fluid have been successfully conducted in Riga [2], Karlsruhe [3], and Cadarache [4]. The first two facilities made use of a more or less predetermined fluid flow essentially fixed by the forcing and the shape of the internal tubes.…”

Section: Introductionmentioning

confidence: 99%

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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Experimental demonstration of a homogeneous two-scale dynamo

Cited by 374 publications

References 10 publications

Observation of a Turbulence-Induced Large Scale Magnetic Field

Observation of a Turbulence-Induced Large Scale Magnetic Field

Chaotic Dynamos Generated by a Turbulent Flow of Liquid Sodium

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

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