Magnetoconvection in a spherical shell: Equatorial symmetry during the transition from the weak- to the strong-field regime

Abstract

At small but supercritical Rayleigh numbers, simulations of dynamos in spherical shells often separate into two broad regimes characterised either by their relative magnetic field strength (weak/strong) or by their dominant force balance (VAC/MAC). These regimes can tend smoothly from one to the other but can also be bistable, a phenomenon which occurs particularly at large $\Pm$. We show that in either case the transition correlates with a breaking of equatorial symmetry. Nonlinear simulations of the geodynamo cannot be performed at accurate parameters and hence it is important to ensure that the correct (strong-field) branch is tracked as a distinguished limit is tracked towards a correct parametrisation from the simulations that we can perform. In order to understand the transition to strong-field dynamos, and better understand the mechanisms that occur in both branches, we report on a series of magnetoconvection simulations (that is, with the magnetic field fixed at the outer boundary) with which we bridge the gap between the strong- and weak-field regimes, and show that symmetry-breaking is triggered by the sudden growth of the magnetic field and in turn supports the dynamo in the strong-field regime.

Figures (20)

• Figure 1: Global diagnostics of hydrodynamic simulations for ${\rm Ra}'$ in the range $(1,50]$: (a) Columnarity (equation \ref{['eqn:2.columnarity']}); (b) Flow symmetry (equation \ref{['eqn:2.symmetry']}); (c) Kinetic energy components (equation \ref{['eqn:2.kineticenergy']}).
• Figure 2: The $(l,m)=(1,0)$ component of the poloidal scalar, $p_{10}$, at the outer boundary, for dynamo simulations with varied ${\rm Pm}$ and ${\rm Ra}'$ close to the onset of (hydrodynamic) convection. (This data is derived from simulations conducted by TeedDormy2025aTeedDormy2025b).
• Figure 3: $u_r/{\rm Pm}$ for dynamo simulations in the "weak-field" regime, just above the onset of dynamo action.
• Figure 4: Global diagnostics of dynamo simulations for ${\rm Pm}=5,12$ and ${\rm Ra}'\in(1,5]$ where points are coloured by $p_{10}(r=r_o)$: (a-b) Columnarity (equation \ref{['eqn:2.columnarity']}); Symmetry (equation \ref{['eqn:2.symmetry']}) of the flow (c-d) and field (e-f).
• Figure 5: Global diagnostics of magnetoconvection simulations for varied ${\rm Pm}$, $p_{10}$ and ${\rm Ra}'$ in the range $(1,5]$: (a-c) Columnarity (equation \ref{['eqn:2.columnarity']}); Symmetry (equation \ref{['eqn:2.symmetry']}) of the flow (d-f) and field (g-i); Total poloidal (unfilled diamonds) and toroidal (filled circles) of the magnetic energy (j-l) and kinetic energy (m-o). Black points refer to hydrodynamic simulations which are independent of ${\rm Pm}$, but note that the kinetic energy is rescaled by a factor of ${\rm Pm}^2$ to use strong-field non-dimensionalisation.