Magnetically-Forced Axisymmetric Zonal Accelerations in Earth's Outer Core

Abstract

Azimuthal accelerations of cylindrical surfaces co-axial with the rotation axis have been inferred to exist in Earth's fluid core on the basis of magnetic field observations and changes in the length-of-day. These accelerations have a typical timescale of decades. However, the physical mechanism causing the accelerations is not well understood. Scaling arguments suggest that the leading order torque averaged over cylindrical surfaces should arise from the Lorentz force. Decadal fluctuations in the magnetic field inside the core, driven by convective flows, could then force decadal changes in the Lorentz torque and generate zonal accelerations. This hypothesis is tested by constructing a quasi-geostrophic model of magnetoconvection, with thermally-driven flows perturbing a steady, imposed background magnetic field. It is found that when the Alfvén number is similar to that estimated for Earth's fluid core, temporal fluctuations in the torque balance are dominated by the Lorentz torque, with the latter generating mean zonal accelerations. The model reproduces both fast, free Alfvén waves and slow, forced accelerations, with ratios of relative strength and relative timescale similar to those inferred for the Earth's core. The temporal changes in the magnetic field which drive the time-varying Lorentz torque are produced by the underlying convective flows, which shear and advect the magnetic field on timescales associated with convective eddies. These results support the hypothesis that temporal changes in the magnetic field deep inside Earth's fluid core drive the observed decadal zonal accelerations of cylindrical surfaces through the Lorentz torque.