The strong-field regime of the geodynamo

Abstract

The Earth’s magnetic field is generated in the Earth’s outer core from convective motions via a dynamo mechanism. Convective flows in the Earth’s core are under the influence of magnetic forces strong enough to significantly affect their dynamics (known as being in the “strong field regime”). The aim of this PhD work is to explore the strong field regime using magnetoconvection, where a magnetic field is externally imposed on the convective system. We are studying the effect of an imposed uniform axial field on convection in a rapidlyrotating spherical shell. The numerical code Parody has been used to run simulations of thermal convection and magnetic field generation, with increasing imposed magnetic field strength B0. In the first part of this thesis, we consider the effect of the imposed field on the onset of convection, finding three regimes classified via the corresponding force balance (rotationally-dominated, magnetically-dominated, and a MAC balance, in which the Coriolis, Lorentz and buoyancy forces are the dominant terms). Critical parameters including the Rayleigh number and azimuthal wavenumber are reduced when the strength of the imposed field is of order one, which corresponds to an Elsasser number (the ratio of Lorentz and Coriolis forces) of unity. We explore the changes in the flow for more supercritical values of the Rayleigh number. We find that strong zonal flows form for intermediate values of B0 for Rayleigh numbers a few times critical, driven by magnetic and thermal winds as a result of more efficient heat transfer in the equatorial region. We also investigate the mechanisms of magnetic field generation, finding that the induced magnetic field supports the imposed field when the imposed field has strength of order one. We find that the lengthscales involved in the production of the axisymmetric field vary with the strength of the imposed field, with small scales being involved in the rotationally-dominated regime and large scales in the MAC regime. In the second part of the thesis, we study the effects of varying the magnetic Prandtl number. We first focus on the effects of the imposed field on the flow at the onset of convection. Here we find further changes in the critical parameters: magnetoconvection at low Pm require significantly stronger field strengths than at high Pm for the magnetic field to influence the onset of convection, and appears to depend on Λ0 = PmB2 0 , rather than Pm and B0 individually. The reduction of the critical Rayleigh number is more marked at high Pm, and there is also a more drastic reduction in the azimuthal wavenumber mc compared to Pm ≤ 1. For high Pm, we establish a correlation between the axial vorticity and induced axial field; for example, we find that there is a strong asymmetry between the cyclones and anticyclones at onset. When considering values of the Rayleigh number away from the onset, we find that the induced axisymmetric poloidal field opposes the imposed field at high Pm.