Influence of background magnetic fields on the excitation of Magneto-Coriolis modes inside the Earth's core

Magneto-Coriolis (QG-MC) waves are considered an important part of the rapid dynamics of the Earth's outer core.
The detailed characteristics of these waves are however still under scrutiny.
In this study we explore the sensitivity of the QG-MC waves to the background magnetic field over which they propagate and the frequency of a periodic perturbation that we impose.
We retrieve QG-MC modes by analysing the velocity fields, where they are most easily observed.
Concentrations of QG-MC waves in the magnetic field at the core surface in our model are reminiscent of recently observed geomagnetic jerks.
The QG-MC waves are weakly sensitive to the details of the background magnetic field during their travel in the bulk and their frequency at the core surface remains close to that of the initial perturbation.
This is a potential asset for the prediction of their evolution.
Moreover, the waves in the system exhibit a complex relation with the initial perturbation: when the frequency of the initial pulsation is greater than a threshold -- depending on the Alfvén speed of the medium -- inward QG-Alfvén waves are recovered at the core mantle boundary instead of QG-MC waves, and we find that the waves evolve from QG-MC to QG-Alfvén waves depending on the input frequency.

Thus, gradually increasing the input frequency in the system, we retrieve the dispersion relation for QG-MC waves with an evolution from a k_s^4 slope to a k_s^1 slope, where k_s is the cylindrical radial wavenumber, as waves transition from QG-MC to QG-Alfvén waves.
We actually recover all the components of the dispersion relation from QG-MC waves at low pulsation \omega to QG-Alfvén and inertial waves at high pulsation \omega.
Applying our results to the Earth's core, we expect to be able to recover QG-MC waves with confidence in the Earth core with periods between 57y and 2.8y.