Dynamo-based limit to the extent of a stable layer atop Earth's core (1910.05102v2)

Abstract: The existence of a stably stratified layer underneath the core-mantle boundary (CMB) has been recently revived by corroborating evidences coming from seismic studies, mineral physics and thermal evolution models. Such a layer could find its physical origination either in compositional stratification due to the accumulation of light elements at the top or the core or in thermal stratification due to the heat flux becoming locally sub-adiabatic. The exact properties of this stably-stratified layer, namely its size $\mathcal{H}_S$ and the degree of its stratification characterised by the Brunt-V\"ais\"al\"a frequency $N$, are however uncertain and highly debated. A stable layer underneath the CMB can have crucial dynamical impacts on the geodynamo. Because of the inhibition of the convective motions, a stable layer is expected to primarily act as a low-pass filter on the magnetic field, smoothing out the rapidly-varying and small-scale features by skin effect. To investigate this effect more systematically, we compute 70 global geodynamo models varying the size of the stably-stratified layer from 0 to 300~km and its amplitude from $N/\Omega = 0$ to $N/\Omega \simeq 50$, $\Omega$ being the rotation rate. We show that the penetration of the convective flow in the stably-stratified layer is controlled by the typical size of the convective eddies and by the local variations of the ratio $N/\Omega$. Using quantitative measures of the degree of morphological semblance between the magnetic field obtained in numerical models and the geomagnetic field at the CMB, we establish an upper bound for the stable layer thickness $\mathcal{H}_s < (N/\Omega)^{-1} d_c$, $d_c$ being the horizontal size of the convective flow at the base of the stable layer. This defines a strong geomagnetic constraint on the properties of a stably-stratified layer beneath the CMB.

• The paper establishes an upper bound for the stable layer thickness by quantifying convective penetration through 70 detailed geodynamo simulations.
• The study finds that high stratification (measured by N/Ω) reduces convective intrusion, leading to smoother, large-scale magnetic field features.
• The results align seismic and geomagnetic findings, constraining dynamic models of Earth's core and challenging assumptions of deep, strong stratification.

Analysis of Dynamo-based Limit to the Extent of a Stable Layer Atop Earth's Core

The paper authored by T. Gastine, J. Aubert, and A. Fournier explores the physical characteristics and implications of a stably stratified layer beneath Earth's core-mantle boundary (CMB). The stratified layer's origin could be either compositional, due to the accumulation of lighter elements, or thermal, when heat flux becomes sub-adiabatic. Despite the observational and theoretical interest, the characteristics of this layer, particularly its thickness $H$ and stratification strength characterized by the Brunt-Väisälä frequency $N$, remain a subject of debate.

The paper constructs a comprehensive set of 70 global geodynamo simulations to evaluate how variations in the size and strength of this stable layer affect Earth's magnetic field. The simulations manipulate the layer’s thickness from 0 to 300 km and its stratification from $N/\Omega = 0$ to $N/\Omega \approx 50$, where $\Omega$ denotes the planet's rotation rate. From these, an upper bound was established for the stable layer thickness, given as $H < (N/\Omega)^{-1} \mathcal{L}_s$, with $\mathcal{L}_s$ representing the horizontal scale of convective motion beneath the stable layer.

Key Findings

• Convective Penetration: The penetration of the convective flow into the stable layer is inversely proportional to the local ratio of $N/\Omega$ and dependent on the size of convective eddies. For high $N/\Omega$, simulation results suggest minimal stable stratification at the core's upper boundary.
• Geomagnetic Implications: The presence of a stable layer impacts geomagnetic field characteristics. It tends to smooth rapid and small-scale magnetic field variations via a skin effect. The simulations support scenarios with no significant stable stratification, aligning with geomagnetic observations, unless unmodeled effects like double diffusion radically alter dynamics.
• Comparison with Observations: The simulation-derived constraints closely align with certain seismic and geomagnetic estimates. A stratified layer with significant depth ($H \geq 100$ km) and strong stratification ($N_m/\Omega \approx 10$) is found incompatible with observed Earth's magnetic field scenarios, which is a crucial finding given the divergence in seismic interpretations.

Implications and Future Prospects

The paper provides stringent numerical limits that contribute to our understanding of Earth's internal structures. The results signify that any dynamic model for Earth must reconcile with these constraints to ensure consistency with observed geomagnetic properties. Furthermore, the paper suggests that while current dynamo models applied at lower Ekman numbers show reasonable agreement with geomagnetic dynamics, slight modifications in layer dynamics or additional unaccounted forces could still feasibly allow for some stratification.

Future research could further evaluate the role of inertial effects not accounted for in these models and explore double-diffusive convection effects, as these could potentially reconcile some discrepancies between simulated and observed data. Investigations into heat flux heterogeneities at the CMB and their role in thermochemical diffusion within the stable layer's context may yield more nuanced insights into Earth's geodynamical processes. As computational capabilities advance, higher-fidelity models that incorporate smaller-scale dynamics may provide an even closer approximation of Earth's core dynamics under observational constraints.