A paradigmatic model of Earth's magnetic field reversals

Abstract

Introduction. There is an ample paleomagnetic evidence that the Earth’s magnetic field has reversed its polarity many times. The last reversal occurred approximately 780000 years ago.The mean rate of reversals varies from nearly zero during the Permian and Cretaceous superchrons to approximately 5 per Myr in the present. Some observations suggest that the decay of the dipole of one polarity might be much slower than the following recreation of the dipole with opposite polarity [1]. Observational data also indicate a possible correlation of the dipole moment with the persistence time of the field in one polarity [2]. In a recent paper, a bimodal distribution of the dipole moment has been hypothesized [3]. Although some of the above mentioned features are controversially discussed in the literature, it is worthwhile to ask if and how they could be modeled by theory. With view on the successful dynamo experiments in Riga and Karlsruhe [4], one could extend this question and ask what would be the most essential ingredient for a dynamo experiment to exhibit irregular reversals in a similar way as the Earth’s dynamo does. Thus motivated, we focus in this paper on a very generic mechanism of field reversals and study it in detail by means of an extremely simple dynamo model. It is well known that the non-self adjoint dynamo operator can provide transitions between non-oscillatory and oscillatory eigenmodes. Typically, this transition occurs at the so-called ”exceptional points” [5] of the spectrum, where the eigenvalues and the eigenfunctions of two non-oscillatory modes coalesce and continue as a pair of oscillatory modes with complex conjugate eigenvalues. It is the goal of the present paper to show that even within a very simple mean-field dynamo model the main characteristics of reversals can be attributed to the magnetic field dynamics in the vicinity of such exceptional points.