On the evolution of thermally stratified layers at the top of Earth's core

Abstract

Stable stratification at the top of the Earth's outer core has been suggested based upon seismic and geomagnetic observations, however, the origin of the layer is still unknown. In this paper we focus on a thermal origin for the layer and conduct a systematic study on the thermal evolution of the core. We develop a new numerical code to model the growth of thermally stable layers beneath the CMB, integrated into a thermodynamic model for the long term evolution of the core. We conduct a systematic study on plausible thermal histories using a range of core properties and, combining thickness and stratification strength constraints, investigate the limits upon the present day structure of the thermal layer. We find that whilst there are a number of scenarios for the history of the CMB heat flow, Q c , that give rise to thermal stratification, many of them are inconsistent with previously published exponential trends in Q c from mantle evolution models. Layers formed due to an exponentially decaying Q c are limited to 250-400 km thick and have maximum present-day Brunt-Väisälä periods, T BV = 8 − 24 hrs. When entrainment of the lowermost region of the layer is included in our model, the upper limit of the layer size is reduced and can fully inhibit the growth of any layer if our non-dimensional measure of entrainment, E > 0.2. The period T BV is insensitive to the evolution and so our estimates remain distinct from estimates arising from a chemical origin. Therefore, T BV should be able to discern between thermal and chemical mechanisms as improved seismic constraints are obtained.

Influence of Thermal Stratification on the Structure and Evolution of the Martian Core

“…Dynamo action is inferred when becomes larger than 1 MW , which occurs close to the condition (see Text S1 in Supporting Information for further details on the entropy budget). Whilst our model for the core can account for solidification of either a solid inner core or iron snow (Davies & Pommier, 2018; Greenwood et al., 2021), we do not find scenarios where any core fluid freezes and so do not include their associated terms in Equation .…”

“…Dynamo action is inferred when 𝐴𝐴 𝐴𝐴J becomes larger than 1 MW 𝐴𝐴 K −1 , which occurs close to the condition 𝐴𝐴 𝐴𝐴c > 𝐴𝐴a (see Text S1 in Supporting Information S1 for further details on the entropy budget). Whilst our model for the core can account for solidification of either a solid inner core or iron snow (Davies & Pommier, 2018;Greenwood et al, 2021), we do not find scenarios where any core fluid freezes and so do not include their associated terms in Equation 2. About 8 wt% nickel is expected in the Martian core (Wänke & Dreibus, 1994), along with 10-20 wt% sulfur (Khan et al, 2018;Rivoldini et al, 2011;Wänke & Dreibus, 1994) and as such we assumed an Fe-Ni-S core.…”

“…The core is assumed to be initially well mixed with an adiabatic temperature profile. When 𝐴𝐴 𝐴𝐴c becomes sub-isentropic, a stratified layer grows beneath the CMB with a conductive temperature profile, implemented following Greenwood et al (2021). An entropy balance is then used to estimate the Ohmic dissipation produced by magnetic field generation, 𝐴𝐴 𝐴𝐴J (Greenwood et al, 2021;Gubbins et al, 2003;Williams & Nimmo, 2004):…”

“…When becomes sub‐isentropic, a stratified layer grows beneath the CMB with a conductive temperature profile, implemented following Greenwood et al. (2021). An entropy balance is then used to estimate the Ohmic dissipation produced by magnetic field generation, (Greenwood et al., 2021; Gubbins et al., 2003; Williams & Nimmo, 2004): where , , and refer to the changes in entropy arising from thermal conduction, secular cooling, and Ohmic dissipation within the core, respectively.…”

“…These previous models (Breuer & Spohn, 2006; Hemingway & Driscoll, 2021; Williams & Nimmo, 2004) predict that the Martian core was heavily sub‐isentropic () for a significant part of its history, including at present. When sub‐isentropic, the thermal state of the core deviates away from a convective state toward a conductive one, resulting in a stable, thermally stratified layer that grows from the top of the core downwards, as investigated for Earth’s core (Greenwood et al., 2021; Labrosse et al., 1997; Nimmo, 2015). This approach assumes that chemical convection is not present or that it is insufficient to destabilize the thermal layer.…”