An investigation of the role of buoyancy in magnetic polarity transitions in rapidly rotating dynamos

Abstract

The dynamo operating within the Earth’s outer core generates a predominantly north-south dipolar magnetic field. Occasionally, the magnetic dipole axis flips its orientation and retains its approximate alignment with the Earth’s rotation axis – a phenomenon known as a geomagnetic reversal. The first part of this thesis investigates the dipole–multipole transition in rapidly rotating dynamos by analysing forced magnetohydrodynamic waves in an unstably stratified fluid. It is demonstrated that, with progressively increasing buoyant forcing, slow magnetic–Archimedean–Coriolis (MAC) waves are suppressed, resulting in polarity transitions in low-inertia spherical dynamos. At the polarity transition, a local Rayleigh number based on the mean wavenumber of energy-containing scales exhibits a linear relationship with the square of the peak magnetic field measured at the transition point. This self-similarity of the dipole–multipole transition can place a constraint on the Rayleigh number for polarity reversals within Earth’s core. The second part of the thesis investigates convection within the tangent cylinder (TC) in rapidly rotating dynamos through the analysis of forced magnetic waves. Spherical shell dynamo simulations show that isolated upwellings within the TC originate from the localised excitation of slow MAC waves at the peak magnetic field locations, in turn producing strong anticyclonic polar vortices in the dipole-dominated regime. It is further shown that, in order to reproduce the observed maximum drift rates of the polar vortex, the Rayleigh number in the core must be approximately 1e3 times the critical value for the onset of nonmagnetic convection. With a further increase in buoyant forcing, polarity reversals are triggered, the magnetic field within the TC diminishes, and the polar circulation becomes significantly weaker. In the final part of the thesis, the mantle’s influence on magnetic polarity transitions is investigated. Mantle convection generates a laterally heterogeneous heat flux at the core–mantle boundary (CMB), which evolves over geological time scales. In an unstably stratified fluid, the frequencies associated with vertical (radial) and horizontal (lateral) buoyancy complement each other, such that an equatorially anti-symmetric heat flux heterogeneity at the boundary can induce magnetic polarity transitions by suppressing slow MAC waves, even under relatively small vertical buoyant forcing. In contrast, an equatorially symmetric heat flux heterogeneity does not induce polarity transitions. This study further shows that a composite heat flux heterogeneity, comprising equatorially symmetric and anti-symmetric components of comparable magnitude, as well as a heat flux pattern derived from a seismic shear-wave tomographic model, induce polarity transitions at a horizontal buoyancy of the same order as that for a purely anti-symmetric pattern. The findings suggest that extended periods in Earth’s history without magnetic reversals (geomagnetic superchrons) may arise when the symmetric part of heat flux variation at the CMB is dominant. Additionally, it is shown that in two-species convection, where compositional buoyancy is significantly stronger than thermal buoyancy, the geodynamo can operate under a large lower-mantle heat flux heterogeneity of O(10) times the mean heat flux at the core–mantle boundary.