Free hydromagnetic oscillations of the earth's core and the theory of the geomagnetic secular variation

Free hydromagnetic oscillations of a rotating spherical shell of an incompressible fluid are investigated by means of a simple theoretical model. For each spatial harmonic, rotation gives rise to two distinct modes of oscillation, ‘magnetic’ and ‘inertial’, which propagate with different velocities. As an application of the theory, it is shown that if the strength of the toroidal magnetic field in the Earth’s core is 100 Oe, then many of the properties of the observed secular changes, including the slow westward drift, of the main geomagnetic field at the Earth’s surface can be accounted for in terms of the interaction of magnetic modes in the core with the Earth’s poloidal magnetic field. Concomitant magnetic variations due to inertial modes in the core would, owing to their relatively short periods (several days), fail to penetrate to the surface of the Earth, although the eddy currents induced in the lower mantle by these modes might affect the mechanical coupling between the mantle and the core.