Characterisation of hydromagnetic waves propagating over a steady, non-axisymmetric background magnetic field

Abstract

Motivated by recent observations of rapid (interannual) signals in the geomagnetic data, and by advances in numerical simulations approaching the Earth's outer core conditions, we present a study on the dynamics of hydromagnetic waves evolving over a static base state. Under the assumption of timescales separation between the rapid waves and the slow convection, we linearise the classical magneto-hydrodynamics equations over a steady non-axisymmetric background magnetic field and a zero velocity field. The initial perturbation is a super-rotating pulse of the inner core, which sets the amplitude and length-scales of the waves in the system. The initial pulse triggers axisymmetric, outward propagating torsional Alfv\'en waves, with characteristic thickness scaling with the magnetic Ekman number as $Ek_M^{1/4}$. Because the background state is non-axisymmetric, the pulse also triggers non-axisymmetric, quasi-geostrophic Alfv\'en waves. As these latter waves propagate outwards, they turn into quasi-geostrophic, magneto-Coriolis waves (QG-MC) as the Coriolis force supersedes inertia in the force balance. The period of the initial wave packet is preserved across the shell but the QG-MC wave front disperses and a westward drift is observed after this transformation. Upon reaching the core surface, the westward drift of the QG-MC waves presents an estimated phase speed of about $1100\,km/y$. This analysis confirms the QG-MC nature of the rapid magnetic signals observed in geomagnetic field models near the equator.