Sensitivity of Magneto-Coriolis modes to background flows

We investigate Magneto-Coriolis modes, which are a class of hydromagnetic modes in a rapidly rotating sphere of inviscid and electrically conducting fluid, relevant to liquid planetary cores. The modes are solutions to the linearised magnetohydrodynamic equations about a background state comprising a nearly steady magnetic field and flow. In previous studies the background flow has generally been neglected, on the assumption that its influence on wave dynamics is small. Here, we investigate this assumption by modelling modes at interannual to millennial periods and examine how they are modified by the presence of a background flow. We find that modes generally exhibit significant changes in both frequency and spatial structure at periods much longer than the period of Alfvén waves. For the Earth, with an Alfvén wave period of approximately 2 years, modes at periods shorter than about 30 years are insensitive to geophysically-plausible background flows of magnitude 10 km/yr. Consequently, models of modes with periods below 30 years can safely neglect the effect of background flows. By contrast, interdecadal modes, with periods exceeding about 30 years, may be substantially altered by Earth-like background flows, with strong alteration for periods exceeding about 100 years. Therefore, the sensitivity of interdecadal modes to a background flow provides a possible means of sounding the background state based on geomagnetic observations.