Regimes of thermo-compositional convection and related dynamos in rotating spherical shells

Abstract

Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electricallyconducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva, Mather and Simitev, Geophys. Astrophys. Fluid Dyn. 2019, 113, 377) are found to persist significantly beyond the onset of instability while their regime transitions remain abrupt. In the semi-convecting and the fingering regimes characteristic flow velocities are small compared to those in the thermally-and compositionally-dominated overturning regimes, while zonal flows remain weak in all regimes apart from the thermally-dominated one. Compositionally-dominated overturning convection exhibits significantly narrower azimuthal structures compared to all other regimes while differential rotation becomes the dominant flow component in the thermally-dominated case as driving is increased. Dynamo action occurs in all regimes apart from the regime of fingering convection. While dynamos persist in the semi-convective regime they are very much impaired by small flow intensities and very weak differential rotation in this regime which makes poloidal to toroidal field conversion problematic. The dynamos in the thermally-dominated regime include oscillating dipolar, quadrupolar and multipolar cases similar to the ones known from earlier parameter studies. Dynamos in the compositionally-dominated regime exhibit subdued temporal variation and remain predominantly dipolar due to weak zonal flow in this regime. These results significantly enhance our understanding of the primary drivers of planetary core flows and magnetic fields.

Effects of Shell Thickness on Cross-Helicity Generation in Convection-Driven Spherical Dynamos

“…This is a standard formulation of the spherical convection-driven dynamo problem [13,[36][37][38] for which an extensive collection of results already exists [24,34,39,40]. The results reported below are not strongly model dependent as confirmed by simulations of convection driven by differential heating [41], for cases with no-slip conditions at the inner boundary and an electrical conductivity of the exterior equal to that of the fluid [25,42], and for thermo-compositional driving [35]. Thus, aiming to retain a general physical perspective, we intentionally use here a generic model formulation with a minimal number of physical parameters including only those of first-order importance for stellar and planetary applications.…”

“…A set of transformations used to recast the problem in a scalar stream-function form and a pseudo-spectral algorithm used for the numerical solution of the equations is presented. The exposition in this section is standard and follows our previous articles, for example, [34,35]. This section also serves as an introduction and a review of the typical approach to the formulation and solution of this important problem.…”

Effects of shell thickness on cross-helicity generation in convection-driven spherical dynamos

“…The exposition in this section is standard and follows our previous articles, e.g. [34,35]. This section also serves as an introduction and a review of the typical approach to the formulation and solution of this important problem.…”

Thermo-Chemical Dynamics in Earth's Core Arising from Interactions with the Mantle

“…It is well known from oceanography and astrophysics (Turner, 1973;Garaud, 2018) that stable systems where thermal and compositional fields have different diffusivities and adverse gradients are prone to instabilities that can drastically change their behaviour. These "double-diffusive" instabilities have recently begun to receive substantial attention in the planetary core context (Monville et al, 2019;Bouffard et al, 2020;Mather and Simitev, 2020).…”

“…The simulations are extremely challenging because the value of Le ∼ 1000 in Earth's core (Pozzo et al, 2013), which induces a large scale disparity between thermal and compositional fields. This difficulty has also prompted workers to invoke further simplifications, such as omitting the magnetic field (Monville et al, 2019) or imposing double diffusive conditions throughout the core (rather than just near the CMB) (Mather and Simitev, 2020). Finally, all current simulations are far from the rapidly rotating and low viscosity conditions of the core and robust scaling relationships of the kind that have recently been devised for the single-component system (Aubert et al, 2017;Wicht and Sanchez, 2019) have not yet been produced…”