The Earth contains a liquid iron core 2,900 km below its surface. The Earth’s magnetic field is generated by convective stirring in this electrically conducting core. Slow waves with periods of a several years can occur in the core, due to the interaction of rotational and magnetic forces. These waves can be detected in two different ways. They disturb the geomagnetic field, giving it a time-dependent character, known as the magnetic secular variation, and this variation is being monitored by geomagnetic satellites. The waves can also transport angular momentum, and as they interact with the Earth’s mantle, they lead to small but observable changes in the length of the day.
The nature of both the axisymmetric and nonaxisymmetric wave modes that can occur in the core will be discussed. Axisymmetric torsional oscillations have been found in dynamo and magnetoconvection simulations, and this has enabled us to identify the excitation mechanism generating these waves, at least in the models. The waves originate primarily from the tangent cylinder, the cylinder coaxial with the rotation axis that encloses the solid inner core. Nonaxisymmetric waves are also seen in simulations, and these can be used to suggest which parts of the secular variation are likely dominated by wave propagation. Waves can also potentially shed light on the question of whether some parts of the core are stably stratified, as has been recently suggested.