Magnetic reversals in a geodynamo model with a stably-stratified layer

TL;DR

The paper demonstrates that a stably-stratified layer beneath the core–mantle boundary strengthens the axial dipole and raises the dipolar–multipolar transition threshold, due to a skin effect that damps high-order magnetic modes. When an axisymmetric heterogeneous heat flux is imposed at the CMB, equatorial symmetry is broken, producing hemispheric dynamos or triggering polarity reversals through dipole–quadrupole interactions. Kinematic dynamo analyses reveal near-degeneracy between dipole and quadrupole growth rates in the SSL, supporting a low-dimensional mechanism for reversals and aligning with a broader class of dynamo models. These results suggest that SSLs can stabilize or enable Earth-like reversals, though the study operates at higher $E$ and $Pm$ than Earth's core, highlighting the need for further exploration toward Earth-like parameters.

Abstract

We study the process of magnetic reversals in the presence of a stably-stratified layer below the core-mantle boundary using direct numerical simulations of the incompressible magnetohydrodynamics equations under the Boussinesq approximation in a spherical shell. We show that the dipolar-multipolar transition shifts to larger Rayleigh numbers in the presence of a stably-stratified layer, and that the dipolar strength of the magnetic field at the core-mantle boundary increases due to the skin effect. By imposing an heterogeneous heat flux at the outer boundary, we break the equatorial symmetry of the flow, and show that different heat flux patterns can trigger different dynamo solutions, such as hemispheric dynamos and polarity reversals. Using kinematic dynamo simulations, we show that the stably-stratified layer leads to similar growth rates of the dipole and quadrupole components of the magnetic field, playing the role of a conducting boundary layer, favouring magnetic reversals, and a dynamics predicted by low-dimensional models.

Figures (8)

• Figure 1: Schematic picture of the static temperature gradient used to reproduce a mixed system, with a convective region and a stably-stratified layer described by \ref{['eq:static_temperature_gradient']}.
• Figure 2: (a) Time averaged dipolar strength $f_\mathrm{dip}$ as a function of the size of the stably-stratified layer $\mathcal{H}_s$ for $\mathrm{Pm}=10$ and $\mathrm{E}=10^{-3}$ for different $\mathrm{Ra}$. As the size of the layer $\mathcal{H}_s$ increases, the dipolar component of the magnetic field at the CMB increases due to the skin effect. Error bars correspond to the standard deviation. (Right panels) Visualisation for $\mathrm{Ra}=15 \mathrm{Ra}_c$ of the radial (left) velocity and (right) magnetic fields for (b) a fully convective system $\mathcal{H}_s=0$, and (c) $\mathcal{H}_s = 0.24 L$.
• Figure 3: Dipolar-multipolar transition for different sizes $\mathcal{H}_s$ of the stably-stratified layer as a function of (a) the Rayleigh number and (b) the local Rossby number for $\mathrm{E}=10^{-3}$, $\Pr=1$, and $\mathrm{Pm}=10$. Circles indicate stable solutions, while square markers indicate reversing solutions.
• Figure 4: (a) Evolution of the magnetic field at the CMB in the D-Q phase space for different amplitudes of the heterogeneous heat flux $\delta q$ for the simplest pattern $Y_1^0$. The points correspond to a portion of the time series ($50\tau_\nu$) taken from the statistically steady state of the dynamo solution. (b) Time averaged hemisphericity, defined as in Eq. \ref{['eq:hemisphericity']}, as a function of $\delta q$. All simulations correspond to $\mathrm{E}=10^{-3}$, $\Pr=1$, $\mathrm{Pm}=10$, and $\mathrm{Ra} / \mathrm{Ra}_c = 25$. Error bars indicate the standard deviation.
• Figure 5: (a) Evolution of the magnetic field at the CMB in the D-Q phase space for different amplitudes of the heterogeneous heat flux $\delta q$ for the pattern $Y_3^0$. Arrows indicate the orientation of the typical trajectories of reversals. (b) Time series of $D$ and $Q$ for the case $\delta q = 5.3\%$. All simulations correspond to $\mathrm{E}=10^{-3}$, $\Pr=1$, $\mathrm{Pm}=10$, and $\mathrm{Ra} / \mathrm{Ra}_c = 25$.