Earth's rotational variations and their connection to core flows

Changes in the Earth's rotation originate mostly from torques by the atmosphere and oceans, with a relatively small contribution from the Earth's core. The angular momentum exchange between core and mantle is however a long-standing problem. In this talk I will describe some of the mechanisms potentially at play and how they can be used to infer key properties of the core-mantle boundary. I will focus in particular on torsional Alfvén eigenmodes. The energy in these modes is equal parts magnetic and kinetic, and their motion is mostly columnar. The latter property has been used in the past to build approximate inviscid 1-D models. We have built a 3-D numerical model including viscosity, an electrically conductive inner core, and a thin, electrically conductive layer at the bottom of the mantle allowing the outer core to exchange angular momentum with the solid inner core and the mantle. I will present a systematic study the most relevant properties of these modes, particularly their columnarity, their torques, and their lifetimes as functions of the magnetic diffusivity and viscosity of the outer core, as well as functions of the electrical conductance of the bottom of the mantle.