Imprint of magnetic flux expulsion at the core–mantle boundary on geomagnetic field intensity variations

Abstract

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 boundary layers in numerical dynamos with heterogeneous outer boundary heat flux

“…6), i.e. stronger flow advects the magnetic boundary layer closer to the outer boundary (Bloxham, 1986;Troyano et al, 2020). Extrapolation and interpolation to Earth's core conditions using Rm = 1000 and Rm pol = 100 − 300 (Amit and Olson, 2004;Huguet et al, 2018) give < L r > ≈220 km and ≈260 − 330 km, respectively, in general agreement with the recent < L r > estimates (Terra-Nova et al, 2016;Gillet et al, 2019;Metman et al, 2019).…”

“…For both Rm and Rm pol the fitted slopes are negative, i.e. the faster the flow the thinner the magnetic boundary layer, as expected (Bloxham, 1986;Troyano et al, 2020). Extrapolation to Rm = 1000 gives < L r > ≈ 220 km (Fig.…”

“…The latter is advantageous because the magnetic boundary layers are formed by upwellings (Bloxham, 1986;Troyano et al, 2020) whose amplitudes are represented by the poloidal flow. On the other hand, application to Earth's core is more straightforward with (17) because the magnitude of the total core flow is rather well known from the geomagnetic SV (Finlay and Amit 2011;Holme 2015) whereas the poloidal flow magnitude is highly debated (see Huguet et al, 2018;Olson et al, 2018, and references therein).…”

“…Recently the magnetic flux expulsion model of Bloxham (1986) was revisited by Troyano et al (2020). They examined various magnetic boundary conditions and flow patterns.…”

“…where U is a typical velocity scale, D is a typical length scale and η is the magnetic diffusivity. Focusing on the enigmatic observation of archeomagnetic spikes (Ben-Yosef et al, 2009;Shaar et al, 2011Shaar et al, , 2016, Troyano et al (2020) developed scaling laws for the maximum magentic energy of the system and for the maximum radial field on the outer boundary, both as functions of Rm. Applying their scaling laws to Earth's core, they concluded that magnetic flux expulsion cannot explain the observed archeomagnetic spikes.…”