Motions of the inner core and mantle coupled via mutual gravitation: regular precessional modes

Abstract

Abstract According to a model of the Earth's interior where the inner core symmetry axis is allowed to deviate from the mantle symmetry axis, motions of the inner core and of the mantle are coupled predominantly via a mutual gravitational torque. Solutions corresponding to regular precession have been studied in detail in this paper in order to produce predictions that may, in principle, be observationally tested. In particular, the Chandler wobble frequency is expected to be split by the presence of the inner core, giving rise to two frequencies on either side. The inner core is found to exhibit a differential rotation at the inner core surface of the order of 1 m s −1 , which corresponds to a period of ∼ 90 days. According to conventional wisdom, which assumes that the inner core co-rotates passively with the rest of the Earth, this value represents an unacceptably fast shear at the inner core-outer core boundary. These two predictions are provisional, however, in the sense that several refinements alluded to in this paper are yet to be undertaken.