Axial invariance of rapidly varying diffusionless motions in the Earth's core interior

TL;DR

This paper demonstrates that certain rapidly varying, axially invariant motions in Earth's core, driven by magnetic and rotational forces, are largely unaffected by magnetic diffusivity, revealing fundamental invariance properties.

Contribution

It introduces the concept of axial invariance in rapidly varying core motions and shows their independence from magnetic diffusivity, supported by numerical and theoretical analysis.

Findings

Geostrophic Alfvén waves are axially invariant.

Fast motions are independent of magnetic diffusivity.

Extension to non-axisymmetric motions supported by dynamo studies.

Abstract

Geostrophic jets propagating as Alfv\'en waves are shown to arise ina rapidly rotating spherical shell permeated by a magnetic field among the transient motions set up by an impulsive rotation of the inner core. These axially invariant motions evolve on a time-scale which is short compared to the magnetic diffusion time. The numerical study is taken as illustrative of a more general point: on such a fast time-scale the dimensionless number appropriate to compare the rotation and magnetic forces is independent of the magnetic diffusivity in contrast with the often used Elsasser number. Extension of the analysis to non-axisymmetrical motions is supported by published studies of dynamo models and magnetic instabilities.