The strong-field regime of spherical dynamos and its relevance to magnetic field generation in Earth’s core

Planetary magnetic fields are produced by dynamo action through turbulent motions of an electrically conducting fluid within the interior of the planet. Numerical experiments of dynamo action relevant to Earth's magnetic field have produced different regime branches identified within bifurcation diagrams [1,2]. Notable are distinct branches in which the resultant magnetic field is either weak or strong (when compared with the fluid flow).  Weak-field solutions can be identified by the prominent role of viscosity and/or inertia on the motion whereas the magnetic field has a leading order effect on the flow in strong-field solutions. Bistability between branches can be found within a small window of parameter space, as long theorised [3]

One measure of the success of numerical models of the geodynamo is the ability to replicate the expected balance between forces operating within Earth's core; Coriolis (rotational) and Lorentz (magnetic) forces are predicted to be most important. The value of considering lengthscale dependent force balances [4] and ‘gradient-free’ solenoidal forces has been highlighted [5].

I will review the approach in numerically modelling spherical dynamos and the challenges in doing so. I will discuss the branches and bifurcations of dynamo action previously explored in numerical simulations.  Furthermore, in new results, I shall highlight that the expected force balance of Earth's core can be preserved in the strong-field regime as input parameters of numerical simulations are moved towards more realistic values [2].

[1] E. Dormy et al, Fluid Dynamics Res. 50, 011415 (2018) 
[2] R. J. Teed & E. Dormy, Geophys. Res. Lett. (in press) 
[3] P. Roberts, In: Cupal, I. (ed.), Proc. First Int. Workshop on Dynamo Theory and the Generation of the Earth’s Magnetic Field pp. 7–12. Czech. Geophys. Inst. Rep (1979) 
[4] T. Schwaiger et al, Geophys. J. Inter. 219, S101–S114 (2019) 
[5] R. J. Teed & E. Dormy, J. Fluid Mech. 964, A26 (2023)

Venue: Fulton G20