Oscillation or rotation: a comparison of two simple reversal models

Stefani, Frank; Xu, Mingtian; Sorriso‐Valvo, L.; Gerbeth, Günter; Günther, Uwe

doi:10.1080/03091920701523311

Cited by 23 publications

(34 citation statements)

References 50 publications

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“…Some stochastic properties of palaeomagnetic scale are obtained by dynamical systems of low dimension (Shmitt et al, 2001;Pétrélis et al, 2009;Rikitake, 1965;Melbourne et al, 2001), models of mean field with noisy α-effect (Giesecke et al, 2005;Stefani and Gerbeth, 2005;Stefani et al, 2007), and direct number simulation (Takahashi et al, 2005;Wicht, 2005;Glatzmaier and Roberts, 1995;Kutzner and Christensen, 2002).…”

Section: Discussionmentioning

confidence: 99%

Reversals in the large-scale αΩ-dynamo with memory

Feschenko

Vodinchar

2015

Nonlin. Processes Geophys.

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Abstract. Inversion of the magnetic field in a model of largescale α -dynamo with α-effect with stochastic memory is under investigation. The model allows us to reproduce the main features of the geomagnetic field reversals. It was established that the polarity intervals in the model are distributed according to the power law. Model magnetic polarity timescale is fractal. Its dimension is consistent with the dimension of the real geomagnetic polarity timescale.

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Section: Discussionmentioning

confidence: 99%

Reversals in the large-scale αΩ-dynamo with memory

Feschenko

Vodinchar

2015

Nonlin. Processes Geophys.

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“…The correlation time T c has always been set to 0.005 · T c which would correspond to 1 kyr in case that the diffusion time is set to 200 kyr. The resulting time series show reversal sequences quite similar to those of the geodynamo [23,26,29]. For the sake of simplicity, we define a reversal as the sign change of the poloidal field component s(1, τ ) at the outer radius r = 1.…”

Section: The Forward Problemmentioning

confidence: 91%

“…With increasing C, i.e. with increasing supercriticality, these oscillations become more and more anharmonic (relaxation oscillations) [26,25]. Very often, then, there is another transition value of C beyond which the (noise-free) oscillatory dynamo becomes stationary again.…”

Section: The Parameters To Be Determinedmentioning

confidence: 99%

Inferring basic parameters of the geodynamo from sequences of polarity reversals

Fischer¹,

Gerbeth²,

Giesecke³

et al. 2009

Inverse Problems

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Abstract. The asymmetric time dependence and various statistical properties of polarity reversals of the Earth's magnetic field are utilized to infer some of the most essential parameters of the geodynamo, among them the effective (turbulent) magnetic diffusivity, the degree of supercriticality, and the relative strength of the periodic forcing which is believed to result from the Milankovic cycle of the Earth's orbit eccentricity. A time-stepped spherically symmetric α 2 -dynamo model is used as the kernel of an inverse problem solver in form of a downhill simplex method which converges to solutions that yield a stunning correspondence with paleomagnetic data.

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“…Solving such inverse spectral dynamo problems by means of an evolutionary strategy it was possible to obtain such α(r) profiles that lead to oscillatory dynamo solutions [58]. This model was later used to develop simple models of geomagnetic reversals that are just based on noise triggered jumps and relaxation oscillations in the vicinity of spectral exceptional points [59,60,61]. On this basis, a first attempt was further made to infer some of the most essential parameters of the geodynamo, such as its overcriticality and the turbulent resistivity from the temporal behavior and the statistical properties of field reversals [62].…”

Section: Inverse Problems At Large Rmmentioning

confidence: 99%

Forward and inverse problems in fundamental and applied magnetohydrodynamics

Giesecke

Stefani

Wondrak

et al. 2013

Eur. Phys. J. Spec. Top.

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Abstract. This Minireview summarizes the recent efforts to solve forward and inverse problems as they occur in different branches of fundamental and applied magnetohydrodynamics. As for the forward problem, the main focus is on the numerical treatment of induction processes, including self-excitation of magnetic fields in non-spherical domains and/or under the influence of non-homogeneous material parameters. As an important application of the developed numerical schemes, the functioning of the von-Kármán-sodium (VKS) dynamo experiment is shown to depend crucially on the presence of soft-iron impellers. As for the inverse problem, the main focus is on the mathematical background and some first practical applications of the Contactless Inductive Flow Tomography (CIFT), in which flow induced magnetic field perturbations are utilized for the reconstruction of the velocity field. The promises of CIFT for flow field monitoring in the continuous casting of steel are substantiated by results obtained at a test rig with a low melting liquid metal. While CIFT is presently restricted to flows with low magnetic Reynolds numbers, some selected problems of non-linear inverse dynamo theory, with possible application to geo-and astrophysics, are also discussed.

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Oscillation or rotation: a comparison of two simple reversal models

Cited by 23 publications

References 50 publications

Reversals in the large-scale αΩ-dynamo with memory

Reversals in the large-scale αΩ-dynamo with memory

Inferring basic parameters of the geodynamo from sequences of polarity reversals

Forward and inverse problems in fundamental and applied magnetohydrodynamics

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