SUMMARY
During the last decade, rapid or extreme geomagnetic field intensity variations associated with rates greater than the maximum currently observed have been inferred from archeomagnetic data in the Near-East and in Western Europe. The most extreme events, termed geomagnetic spikes, are defined as intensity peaks occurring over a short time (a few decades), and are characterized by high variation rates, up to several μT yr–1. Magnetic flux expulsion from the Earth’s outer core has been suggested as one possible explanation for these peaks but has not yet been examined in detail. In this study, we develop a 2-D kinematic model for magnetic flux expulsion whose key control parameter is the magnetic Reynolds number Rm, the ratio of magnetic diffusion time to advection time. This model enables the tracking of magnetic field lines which are distorted and folded by a fixed flow pattern. Two processes govern the magnetic evolution of the system. The first is the expulsion of magnetic flux from closed streamlines, whereby flux gradually concentrates near the boundaries of the domain, which leads to an increase of the magnetic energy of the system. If the upper boundary separates the conducting fluid from an insulating medium, a second process then takes place, that of diffusion through this interface, which we can quantify by monitoring the evolution of the vertical component of magnetic induction along this boundary. It is the conjunction of these two processes that defines our model of magnetic flux expulsion through the core–mantle boundary. We analyse several configurations with varying flow patterns and magnetic boundary conditions. We first focus on flux expulsion from a single eddy. Since this specific configuration has been widely studied, we use it to benchmark our implementation against analytic solutions and previously published numerical results. We next turn our attention to a configuration which involves two counter-rotating eddies producing an upwelling at the centre of the domain, and comprises an upper boundary with an insulating medium. We find that the characteristic rise time and maximum instantaneous variation rate of the vertical component of the magnetic field that escapes the domain scale like $\sim R_m^{0.15}$ and $\sim R_m^{0.45}$, respectively. Extrapolation of these scaling laws to the Earth’s régime is compared with various purported archeointensity highs reported in the Near-East and in Western Europe. According to our numerical experiments magnetic flux expulsion is unlikely to produce geomagnetic spikes, while intensity peaks of longer duration (one century and more) and smaller variation rates appear to be compatible with this process.
Magnetic flux expulsion in a superconducting wire
