Evidence for MAC waves at the top of Earth's core and implications for variations in length of day

Earth's liquid core hosts a diverse set of waves with periods ranging from days to thousands of years. One class of waves with periods of several decades is known to arise from an interplay between magnetic, Archimedes and Coriolis forces. These so-called MAC waves are thought to be relevant for interpreting historical fluctuations in the geomagnetic field. In this study, we show that MAC waves provide a good description of time-dependent zonal flow at the top of the core. The same collection of waves also offers a simple explanation for observed fluctuations in the dipole field. Both of these predictions require a stratified layer at the top of the core with a thickness of 130-140 km and a buoyancy frequency comparable to Earth's rotation rate. We extend these predictions to include changes in the length of day (LOD) and find that MAC waves can account for about half of the observed fluctuation at decadal periods. Larger fluctuations are possible when electromagnetic stresses couple MAC waves to flow in the interior of the core. In fact, an idealized model for the coupled motion overestimates the LOD fluctuations, probably reflecting limitations in this idealized model. Our results offer support for stable stratification at the top of the core and suggest a common origin for decadal fluctuations in the geomagnetic field and the LOD.