dorsal/arxiv
View SchemaWhy dynamos are prone to reversals
| Authors | Frank Stefani, Gunter Gerbeth, Uwe Guenther, Mingtian Xu |
|---|---|
| Categories | |
| ArXiv ID | physics/0509118 |
| URL | https://arxiv.org/abs/physics/0509118 |
| DOI | 10.1016/j.epsl.2006.01.030 |
| Journal | Earth Planet.Sci.Lett. 243 (2006) 828-840 |
Abstract
In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it was shown that a simple mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha can exhibit a number of features which are typical for Earth's magnetic field reversals. In particular, the model produces asymmetric reversals, a positive correlation of field strength and interval length, and a bimodal field distribution. All these features are attributable to the magnetic field dynamics in the vicinity of an exceptional point of the spectrum of the non-selfadjoint dynamo operator. The negative slope of the growth rate curve between the nearby local maximum and the exceptional point makes the system unstable and drives it to the exceptional point and beyond into the oscillatory branch where the sign change happens. A weakness of this reversal model is the apparent necessity to fine-tune the magnetic Reynolds number and/or the radial profile of alpha. In the present paper, it is shown that this fine-tuning is not necessary in the case of higher supercriticality of the dynamo. Numerical examples and physical arguments are compiled to show that, with increasing magnetic Reynolds number, there is strong tendency for the exceptional point and the associated local maximum to move close to the zero growth rate line. Although exemplified again by the spherically symmetric alpha^2 dynamo model, the main idea of this ''self-tuning'' mechanism of saturated dynamos into a reversal-prone state seems well transferable to other dynamos. As a consequence, reversing dynamos might be much more typical and may occur much more frequently in nature than what could be expected from a purely kinematic perspective.
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"abstract": "In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it\nwas shown that a simple mean-field dynamo model with a spherically symmetric\nhelical turbulence parameter alpha can exhibit a number of features which are\ntypical for Earth\u0027s magnetic field reversals. In particular, the model produces\nasymmetric reversals, a positive correlation of field strength and interval\nlength, and a bimodal field distribution. All these features are attributable\nto the magnetic field dynamics in the vicinity of an exceptional point of the\nspectrum of the non-selfadjoint dynamo operator. The negative slope of the\ngrowth rate curve between the nearby local maximum and the exceptional point\nmakes the system unstable and drives it to the exceptional point and beyond\ninto the oscillatory branch where the sign change happens. A weakness of this\nreversal model is the apparent necessity to fine-tune the magnetic Reynolds\nnumber and/or the radial profile of alpha. In the present paper, it is shown\nthat this fine-tuning is not necessary in the case of higher supercriticality\nof the dynamo. Numerical examples and physical arguments are compiled to show\nthat, with increasing magnetic Reynolds number, there is strong tendency for\nthe exceptional point and the associated local maximum to move close to the\nzero growth rate line. Although exemplified again by the spherically symmetric\nalpha^2 dynamo model, the main idea of this \u0027\u0027self-tuning\u0027\u0027 mechanism of\nsaturated dynamos into a reversal-prone state seems well transferable to other\ndynamos. As a consequence, reversing dynamos might be much more typical and may\noccur much more frequently in nature than what could be expected from a purely\nkinematic perspective.",
"arxiv_id": "physics/0509118",
"authors": [
"Frank Stefani",
"Gunter Gerbeth",
"Uwe Guenther",
"Mingtian Xu"
],
"categories": [
"physics.geo-ph",
"astro-ph",
"physics.flu-dyn"
],
"doi": "10.1016/j.epsl.2006.01.030",
"journal_ref": "Earth Planet.Sci.Lett. 243 (2006) 828-840",
"title": "Why dynamos are prone to reversals",
"url": "https://arxiv.org/abs/physics/0509118"
},
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