Influence of liquid core dynamics on rotational modes

Abstract

SUMMARY We investigate the influence of the structure and dynamics of the liquid outer core on the Earth’s rotational modes through the squared Brunt–V¨¨¨ frequency N 2 . The frequencies of the rotational modes are embedded into the continuous spectrum of inertia-gravity modes, which is governed in the complex domain by N 2 and the Earth’s rotation speed. By solving the equations for the normal modes of a rotating ellipsoidal elastic earth model and varying the N 2 parameter, we show interactions between pseudo-modes of the liquid core and three rotational modes: the Chandler Wobble (CW), Free Inner Core Nutation (FICN) and Free Core Nutation (FCN). The interaction between pseudo-modes of the outer core and the CW gives rise to avoided crossings, which result in two modes sharing similar displacements, that is, an almost rigid wobble of the mantle and oscillations in the outer core having roughly the same amplitude. The corresponding eigenperiods in a corotating frame of reference are separated by a few days. Avoided crossings are also the only kind of interaction that occurs between core pseudo-modes and the FICN. The coupling is stronger than for the CW, the eigenperiods being a few hundred days apart in an inertial frame of reference. The eigenfunctions are mixed in such a way that the amplitude of the nutation of the inner core is an order of magnitude bigger than the oscillations in the outer core. The FCN shows weaker interactions with the pseudomodes of the core. However, the shift of its nutation period can reach up to 15 d. Consequently, our results show that the angular momentum approach through Liouville’s equations is not sufficient to describe fully the nutational modes.