Dynamic mode decomposition to retrieve torsional Alfv\'{e}n waves

TL;DR

This paper explores the use of dynamic mode decomposition (DMD) to identify torsional Alfvén waves in planetary interior models, demonstrating its ability to distinguish internal modes from simulation data.

Contribution

It introduces DMD as a tool for analyzing MHD simulations of planetary interiors, highlighting its effectiveness in identifying torsional Alfvén waves and their eigenmodes.

Findings

DMD can distinguish internal from boundary modes in MHD simulations.

Internal modes correspond to free torsional Alfvén waves with identifiable eigenvalues.

Further work needed on global eigenvalue problems in spherical shells.

Abstract

Dynamic mode decomposition (DMD) is utilised to identify the intrinsic signals arising from planetary interiors. Focusing on an axisymmetric quasi-geostrophic magnetohydrodynamic (MHD) wave -called torsional Alfv\'{e}n waves (TW) - we examine the utility of DMD in two types of MHD direct numerical simulations: Boussinesq magnetoconvection and anelastic convection-driven dynamos in rapidly rotating spherical shells, which model the dynamics in Earth's core and in Jupiter, respectively. We demonstrate that DMD is capable of distinguishing internal modes and boundary/interface-related modes from the timeseries of the internal velocity. Those internal modes may be realised as free TW, in terms of eigenvalues and eigenfunctions of their normal mode solutions. Meanwhile it turns out that, in order to account for the details, the global TW eigenvalue problems in spherical shells need to be further addressed.