Abstract

Abstract In a recent paper [F. Stefani, G. Gerbeth. Asymmetric polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model. Phys. Rev. Lett. 94 (2005) 184506] it was shown that a simple mean-field dynamo model with a spherically symmetric helical turbulence parameter α can exhibit a number of features which are typical for Earth's magnetic field reversals. In particular, the model produces asymmetric reversals (with a slow decay of the dipole of one polarity and a fast recreation of the dipole with opposite polarity), 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 where two real eigenvalues coalesce and continue as a complex conjugated pair of eigenvalues. Usually, this exceptional point is associated with a nearby local maximum of the growth rate dependence on the magnetic Reynolds number. The negative slope of this curve between the 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 α in order to adjust the operator spectrum in an appropriate way. 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 where the indicated reversal scenario can be actualized. Although exemplified again by the spherically symmetric α 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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