arXiv subjects

Christopher J. Davies

Publications and source records attributed to Christopher J. Davies.

11 recordsLinked to original sources

arXiv2026

Onset of dynamo action in planetesimals

Several meteorites have been found to carry primary remanent magnetizations imparted by fields generated within planetesimal cores during the early solar system. Thermal evolution models have shown that thermal convection likely drove the dynamo in the early evolution of these bodies. In such small cores, the magnetic Reynolds number is thought to be close to the threshold for dynamo action. However, the critical value of the magnetic Reynolds number, meaning its value at the onset, is also poorly constrained in dynamo simulations. We perform dynamo simulations to investigate the onset of the dynamo at different Ekman ($E$) and magnetic Prandtl ($Pm$) numbers, in a quasi-full sphere. Along two empirical paths in this $(E,Pm)$ space, the onset of dynamo action depends on whether the magnetic field is initially strong or weak. The onset of the dynamo occurs at larger supercriticality (ratio between the Rayleigh number ($Ra$) and its critical value ($Ra_c$)) when moving toward more realistic parameter values. Once extrapolated to planetesimal core conditions, the supercriticality for the onset of the dynamo is about $10^3$ for a strong initial magnetic field (meaning magnetic energy is of the same order of magnitude or larger than the kinetic energy). For a weak initial field, the required $Ra/Ra_c$ would be larger. Compared to previous estimates, this revised criterion facilitates dynamo activity, and so extends the lifetime of the magnetic field compared to previous models and allows the generation of a magnetic field in smaller planetesimals.

astro-ph.EP↗

arXiv2026

Paleomagnetic signatures of core-mantle interactions inferred from top-heavy thermochemical geodynamo simulations

The time-averaged geomagnetic field provides crucial insights into deep Earth dynamics and thermal core-mantle interactions. Paleomagnetic observations and numerical dynamo simulations are equivocal regarding the longitudinal structure of the time-averaged field, though the latter have often considered a generic buoyancy source, which may obscure distinct signatures of thermal and chemical buoyancy that arise near the equator and poles, respectively. In this study, we present a new suite of top-heavy geodynamo simulations, varying the relative strengths of thermal and chemical driving and comparing the resultant magnetic signatures to observational field models spanning centuries to tens of thousands of years. None of the spatially-averaged measures of field morphology and variability we tested could robustly distinguish between different levels of chemical driving or the presence of heterogeneous outer boundary heat flux. On the other hand, observational constraints requiring longitudinal variations in time-averaged inclination anomaly are readily matched by simulations with heterogeneous outer boundary thermal forcing, in contrast to those with homogeneous mantle heat flux. Longitudinal field structures are reduced, but not erased, by elevated chemical driving, which also promotes the formation and deepening of polar minima in the radial magnetic field. Our simulations indicate that both the strong heat flux heterogeneity and chemical driving in Earth's core are likely to result in small but persistent departures from the geocentric axial dipole approximation.

physics.geo-ph↗

arXiv2026

Thermochemical models of outer core convection with heterogeneous core-mantle boundary heat flux

Convection in Earth's outer core is driven by the release of heat and light elements at the inner core boundary. A key question is whether these buoyancy sources drive convection throughout the core, or whether a stable layer exists just below the core-mantle boundary (CMB). Recent simulations incorporating CMB heat flux heterogeneities propose locally stable ``regional inversion lenses'' (RILs) rather than a global layer, allowing stable and unstable regions to coexist. However, these simulations combine thermal and compositional anomalies, ignoring differences in diffusivities and boundary conditions. Here we simulate thermal, chemical, and thermochemical convection at Ekman number $E=10^{-5}$, with thermal and chemical flux Rayleigh numbers $\widetilde{Ra}_T=30-4000$ and $\widetilde{Ra}_ξ=30-100000$, and Prandtl numbers $Pr_T=1$ and $Pr_ξ=10$. Purely chemical simulations accumulate light elements below the CMB, forming locally stable regions near the poles or global layers, depending on $\widetilde{Ra}_ξ$. These chemically stratified regions persist in thermochemical simulations even when thermal forcing is destabilising. Introducing heterogeneous CMB heat flux produces thermally stratified RILs even with strongly destabilising compositional buoyancy. Our simulations reveal a diverse range of locations, properties, and morphologies of stable regions depending on $\widetilde{Ra}_T$ and $\widetilde{Ra}_ξ$, they can have a seismically detectable thickness and strength and might also have a signature in geomagnetic observations.

astro-ph.EP↗

arXiv2026

Geomagnetic signatures of the slurry F-layer inferred from dynamo simulations

Seismic observations indicate that the lowermost portion of Earth's liquid core is density stratified. The existence of this so-called F-layer challenges classical theories of core dynamics, where the geodynamo process that generates Earth's main magnetic field is assumed to be powered by heat and light element release at the inner core boundary. The seismically-inferred thickness, density, and velocity anomaly can be reproduced by a dynamical model that represents the F-layer as a two-phase two-component slurry on the liquidus, with a ``snow'' of solid iron particles falling through a quasi-static iron-oxygen liquid. Here, we present the first fluid dynamical simulations of thermochemically driven rotating convection and dynamo action that include a simple representation of the stratified slurry F-layer at the base of the spherical shell geometry. We show that the F-layer can create a barrier to columnar quasi-geostrophic flow, which is expressed near the core surface as a migration of peak radial and azimuthal flow speeds to lower latitudes as the thickness and stratification strength increase. In dynamo simulations, this effect induces polar minima in the radial magnetic field at the outer boundary ($B_r$) that strengthen and deepen with increasing stratification, and peaks in latitudinal profiles of $B_r$ moving to lower latitudes with reduced temporal variability. The geomagnetic signature of the F-layer is most prominent in time-averaged $B_r$, when resolved to at least spherical harmonic degree 5, and a trend of increasingly negative zonal degree 3 and 5 Gauss coefficients as the F-layer thickness and stratification strength increase. Our results suggest that an F-layer thickness of 600~km is incompatible with geomagnetic observations and favour weak stratification (normalised Brunt-Väisälä frequency $<1$) and a layer $<400$~km thick.

physics.geo-ph↗

arXiv2025

Accessing the dipole-multipole transition in rapidly rotating spherical shell dynamos

Polarity reversals are a key feature of Earth's magnetic field, yet the processes governing them are still poorly understood. Dipole reversals have been found in many numerical dynamo simulations and often occur close to the transition between dipolar and multipolar regimes. Simulated conditions are far from those in Earth's liquid iron core because of the long runtimes needed to capture polarity transitions. We develop a unidimensional path theory in an attempt to simplify the search for the dipole-multipole transition at increasingly realistic physical conditions. We build 3 paths, all based on a constant magnetic Reynolds number $Rm$; one aiming for Magnetic, Coriolis, and Archimedean (MAC), and 2 aiming for inertia-MAC force balance. We add inertia due to its role in simulated reversals. Results show reasonable agreement with predictions within the accessible parameter space, but deviate from predicted behaviour for certain quantities, e.g. magnetic field strength and magnetic/kinetic energy ratio. Further, simulations move into the dipolar non-reversing regime as they are advanced along the path. By increasing the buoyancy driving (via higher Rayleigh number) above the values predicted by the path theory, we are able to access the dipole-multipole transition down to an Ekman number $E\sim 10^{-6}$, comparable to the most extreme conditions reported to date. Results demonstrate that our approach is an efficient method for seeking the dipole-multipole transition at low $E$. However, the conditions under which we access the dipole-multipole transition become increasingly hard to access numerically and also increasingly unrealistic because $Rm$ rises beyond plausible bounds inferred from geophysical observations. Future work combining path theory with variations in the core buoyancy distribution, appears a promising approach to accessing the transition at extreme physical conditions.

physics.geo-ph↗

arXiv2025

Local Flow Estimation at the top of the Earth's Core using Physics Informed Neural Networks

The Earth's main geomagnetic field arises from the constant motion of the fluid outer core. By assuming that the field changes are advection-dominated, the fluid motion at the core surface can be related to the secular variation of the geomagnetic field. The majority of existing core flow models are global, showing features such as an eccentric planetary gyre, with some evidence of rapid regional changes. By construction, the flow defined at any location by such a model depends on all magnetic field variations across the entire core-mantle boundary making it challenging to interpret local structures in the flow as due to specific local changes in magnetic field. Here we present an alternative strategy in which we construct regional flow models that rely only on local secular changes. We use a novel technique based on machine learning termed Physics-Informed Neural Networks (PINNs), in which we seek a regional flow model that simultaneously fits both the local magnetic field variation and dynamical conditions assumed satisfied by the flow. Although we present results using the Tangentially Geostrophic flow constraint, we set out a modelling framework for which the physics constraint can be easily changed by altering a single line of code. After validating the PINN-based method on synthetic flows, we apply our method to the CHAOS-8.1 geomagnetic field model, itself based on data from Swarm. Constructing a global mosaic of regional flows, we reproduce the planetary gyre, providing independent evidence that the strong secular changes at high latitude and in equatorial regions are part of the same global feature. Our models also corroborate regional changes in core flows over the last decade. Furthermore, our models endorse the existence of a dynamic high latitude jet, which began accelerating around 2005 but has been weakening since 2017.

physics.geo-ph↗

arXiv2024

Unlocking planetesimal magnetic field histories: a refined, versatile model for thermal evolution and dynamo generation

The thermal and magnetic histories of planetesimals provide unique insights into the formation and evolution of Earth's building blocks. These histories can be gleaned from meteorites by using numerical models to translate measured properties into planetesimal behaviour. In this paper, we present a new 1D planetesimal thermal evolution and dynamo generation model. This magnetic field generation model is the first of a differentiated, mantled planetesimal that includes both mantle convection and non-eutectic core solidification. We have improved fundamental aspects of mantle heat transport by including a more detailed viscosity model and stagnant lid convection parametrisations consistent with internal heating. We have also added radiogenic heating from $^{60}Fe$ in the metallic Fe-FeS core. Additionally, we implement a combined thermal and compositional buoyancy flux, as well as the latest magnetic field scaling laws to predict magnetic field strengths during the planetesimal's thermal evolution until core solidification is complete. We illustrate the consequences of our model changes with an example run for a 500 km radius planetesimal. These effects include more rapid erosion of core thermal stratification and longer duration of mantle convection compared to previous studies. The additional buoyancy from core solidification has a marginal effect on dynamo strength, but for some initial core sulfur contents it can prevent cessation of the dynamo when mantle convection ends. Our model can be used to investigate the effects of individual parameters on dynamo generation and constrain properties of specific meteorite parent bodies. Combined, these updates mean this model can predict the most reliable and complete magnetic field history for a planetesimal to date, so is a valuable tool for deciphering planetesimal behaviour from meteorite properties.

astro-ph.EP↗

arXiv2020

A regime diagram for the slurry F-layer at the base of Earth's outer core

Seismic observations of a slowdown in P wave velocity at the base of Earth's outer core suggest the presence of a stably-stratified region known as the F-layer. This raises an important question: how can light elements that drive the geodynamo pass through the stably-stratified layer without disturbing it? We consider the F-layer as a slurry containing solid particles dispersed within the liquid iron alloy that snow under gravity towards the inner core. We present a regime diagram showing how the dynamics of the slurry F-layer change upon varying the key parameters: Péclet number ($Pe$), the ratio between advection and chemical diffusion; Stefan number ($St$), the ratio between sensible and latent heat; and Lewis number ($Le$), the ratio between thermal and chemical diffusivity. We obtain four regimes corresponding to stable, partially stable, unstable and no slurries. No slurry is found when the heat flow at the base of the layer exceeds the heat flow at the top, while a stably-stratified slurry arises when advection overcomes thermal diffusion ($Pe \gtrsim Le$) that exists over a wide range of parameters relevant to the Earth's core. Our results estimate that a stably-stratified F-layer gives a maximum inner-core boundary (ICB) body wave density jump of $Δρ_\textrm{bod} \leq 534 \ \mathrm{kg} \mathrm{m}^{-3}$ which is compatible with the lower end of the seismic observations where $280 \leq Δρ_\textrm{bod} \leq 1,100 \ \mathrm{kg} \mathrm{m}^{-3}$ is reported in the literature. With high thermal conductivity the model predicts an inner core age between $0.6$ and $1.2 \ \mathrm{Ga}$, which is consistent with other core evolution models. Our results suggest that a slurry model with high core conductivity predicts geophysical properties of the F-layer and core that are consistent with independent seismic and geodynamic calculations.

physics.geo-ph↗

arXiv2019

Parallel-in-time integration of Kinematic Dynamos

The precise mechanisms responsible for the natural dynamos in the Earth and Sun are still not fully understood. Numerical simulations of natural dynamos are extremely computationally intensive, and are carried out in parameter regimes many orders of magnitude away from real conditions. Parallelization in space is a common strategy to speed up simulations on high performance computers, but eventually hits a scaling limit. Additional directions of parallelization are desirable to utilise the high number of processor cores now available. Parallel-in-time methods can deliver speed up in addition to that offered by spatial partitioning but have not yet been applied to dynamo simulations. This paper investigates the feasibility of using the parallel-in-time algorithm Parareal to speed up initial value problem simulations of the kinematic dynamo, using the open source Dedalus spectral solver. Both the time independent Roberts and time dependent Galloway-Proctor 2.5D dynamos are investigated over a range of magnetic Reynolds numbers. Speed ups beyond those possible from spatial parallelization are found in both cases. Results for the Galloway-Proctor flow are promising, with Parareal efficiency found to be close to 0.3. Roberts flow results are less efficient, but Parareal still shows some speed up over spatial parallelization alone. Parallel in space and time speed ups of $\sim300$ were found for 1600 cores for the Galloway-Proctor flow, with total parallel efficiency of $\sim0.16$.

physics.comp-ph↗

arXiv2018

Penetration of boundary-driven flows into a rotating spherical thermally-stratified fluid

Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a numerical model, we explore a broad range of three key dimensionless numbers: a thermal stratification parameter (the relative size of boundary temperature gradients to imposed vertical temperature gradients), $10^{-3} \le S \le 10^{4}$, a buoyancy parameter (the strength of applied boundary heat flux anomalies), $ 10^{-3} \le B \le 10^{6}$, and the Ekman number (ratio of viscous to Coriolis forces), $10^{-6} \le E \le 10^{-4}$. We find both steady and time-dependent solutions and delineate the temporal regime boundaries. We focus on steady-state solutions, for which a clear transition is found between a low $S$ regime, in which buoyancy dominates dynamics, and a high $S$ regime, in which stratification dominates. For the latter case, the radial and horizontal velocities scale respectively as $u_r \sim S^{-1}$, $u_h \sim S^{-\frac{3}{4}}\ B^{\frac{1}{4}}$ and are confined to boundary-induced flow within a thin layer of depth $(S\ B)^{-\frac{1}{4}}$ at the outer edge of the domain. For the Earth, if lower-mantle heterogeneous structure is due principally to chemical anomalies, we estimate that the core is in the high-$S$ regime and steady flows arising from strong outer-boundary thermal anomalies cannot penetrate the stable layer. However, if the mantle heterogeneities are due to thermal anomalies and the heat-flux variation is large, the core will be in a low-$S$ regime in which the stable layer is likely penetrated by boundary-driven flows.

physics.flu-dyn↗

arXiv2017

Heat Flow and Boundary Heterogeneity in Rotating Convection

Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly influence global diagnostics of core convection when the Rayleigh number, $Ra$, is weakly supercritical; however, little is known about the strongly supercritical regime appropriate for planets. We perform numerical simulations of rapidly rotating convection in a spherical shell geometry and impose two patterns of boundary heat flow heterogeneity: a hemispherical $Y_1^1$ spherical harmonic pattern; and one derived from seismic tomography of Earth's lower mantle. We consider Ekman numbers $10^{-4} \le E \le 10^{-6}$, flux-based Rayleigh numbers up to $\sim800$ times critical, and Prandtl number unity. The amplitude of the lateral variation in heat flux is characterised by $q_{\rm L}^*=0, 2.3, 5.0$, the peak-to-peak amplitude of the outer boundary heat flux divided by its mean. We find that the Nusselt number, $Nu$, can be increased by up to $\sim25$\% relative to the equivalent homogeneous case due to boundary-induced correlations between the radial velocity and temperature anomalies near the top of the shell. The $Nu$ enhancement tends to become greater as the amplitude and length scale of the boundary heterogeneity are increased and as the system becomes more supercritical. This $Ra$ dependence can steepen the $Nu \propto Ra^γ$ scaling in the rotationally dominated regime, with $γ$ for our most extreme case approximately $20\%$ greater than the equivalent homogeneous scaling. Therefore, it may be important to consider boundary heterogeneity when extrapolating numerical results to planetary conditions.

physics.geo-ph↗