On the reflection of Alfv\'en waves and its implication for Earth's core modeling

TL;DR

This paper explores how Alfvén wave reflection properties, influenced by the magnetic Prandtl number, impact the modeling of Earth's core dynamics, especially torsional oscillations, revealing limitations in current geodynamo simulations.

Contribution

It demonstrates that the reflection of Alfvén waves at the core boundary depends on Pm and shows that typical geodynamo models cannot simulate torsional oscillation modes due to low wave reflection.

Findings

Reflection coefficient remains below 0.2 for Pm > 0.3

No-slip boundary conditions prevent torsional oscillation modes in models

Wave energy is absorbed at the boundary when Pm=1

Abstract

Alfv\'en waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case Pm=1, there is no reflection on an insulating, no-slip boundary, and the wave energy is entirely dissipated in the boundary layer. We investigate the consequences of this remarkable behaviour for the numerical modeling of torsional Alfv\'en waves (also known as torsional oscillations), which represent a special class of Alfv\'en waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm << 1, these waves are reflected at the core equator, where they are entirely absorbed for Pm=1. Our numerical calculations show that the reflection coefficient at the equator of these waves remains below 0.2 for Pm > 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal modes.