Precessing spherical shells: flows, dissipation, dynamo and the lunar core

Abstract

Precession of planets or moons affects internal liquid layers by driving flows, instabilities and possibly dynamos. The energy dissipated by these phenomena can influence orbital parameters such as the planet's spin rate. However, there is no systematic study of these flows in the spherical shell geometry relevant for planets, and the lack of scaling law prevents convincing extrapolation to celestial bodies.We have run more than 900 simulations of fluid spherical shells affected by precession, to systematically study basic flows, instabilities, turbulence, and magnetic field generation. We observe no significant effects of the inner core on the onset of the instabilities. We obtain an analytical estimate of the viscous dissipation, mostly due to boundary layer friction in our simulations. We propose theoretical onsets for hydrodynamic instabilities, and document the intensity of turbulent fluctuations.We extend previous precession dynamo studies towards lower viscosities, at the limits of today's computers. In the low viscosity regime, precession dynamos rely on the presence of large-scale vortices, and the surface magnetic fields are dominated by small scales. Interestingly, intermittent and self-killing dynamos are observed. Our results suggest that large-scale planetary magnetic fields are unlikely to be produced by a precession-driven dynamo in a spherical core. But this question remains open as planetary cores are not exactly spherical, and thus the coupling between the fluid and the boundary does not vanish in the relevant limit of small viscosity. Moreover, the fully turbulent dissipation regime has not yet been reached in simulations.Our results suggest that the melted lunar core has been in a turbulent state throughout its history. Furthermore, in the view of recent experimental results, we propose updated formulas predicting the fluid mean rotation vector and the associated dissipation in both the laminar and the turbulent regimes.

A Past Lunar Dynamo Thermally Driven by the Precession of Its Inner Core

“…Because of the sharp spatial attenuation of this field outside the core, the larger length scale part would dominate the field recorded at the lunar surface, but it may only amount to a fraction of a μT. Indeed, numerical models of dynamos generated by precession at the CMB suggest this is the case (Cébron et al, 2019). Hence, a lunar dynamo from precession at the ICB generating surface field strengths of a fraction of a μT may be compatible with the weak paleointensities recorded after 1 Ga, which would push the end of the lunar dynamo to more recently than 0.44 Ga. We hope that our results may serve as a motivation to modelers to attempt to address these questions.…”

“…A more proper evaluation of Q cmb should take into account the fact that f cmb depends on Ω o (e.g., Cébron et al, 2019). However, the dependence is weak, and since our primary objective is to derive an order of magnitude estimate of how Q cmb has evolved, we neglect this effect here.…”

Geodynamo Conductivity Limits

“…Du et al (2017) and Badro et al (2018) found exsolution of MgO in Earth's core to be possible, but it does not produce sufficient heat to replace radiogenic decay in the thermal budget of the core (Du et al, 2017), which is needed to resolve both the cooling of the mantle and the driving of the core dynamo (Driscoll & Bercovici, 2014). Tidal forcing could potentially drive core flows but they are predicted to prefer thermally stratified regions (Cebron et al, 2010); so it remains unclear whether they can power a dynamo (e.g., Cébron et al, 2019).…”

Reflection of oscillating internal shear layers: nonlinear corrections

“…Similar concentrated wave beams are also found in rotating fluids (Kerswell, 1995;Le Dizès & Le Bars, 2017). They have mainly been studied in spherical geometries (Calkins et al, 2010;Koch et al, 2013;Cébron et al, 2019;Lin & Noir, 2020) in the context of planetary applications (Le Bars et al, 2015). These wave beams are the temporal equivalent of the thin shear layers found at the periphery of Taylor-Proudman columns between differentially rotating disks or spheres (Proudman, 1956;Stewartson, 1966).…”