The Spin-Over Mode of freely rotating planets and its relation to their Free Core Nutation

The Earth’s rotation is not perfectly steady: both its rotation rate (its spin rate) and its orientation in space change in time due to the gravitational pull of the Sun and Moon. The precession-nutation response of the Earth to this external tidal forcing depends strongly on the planet’s deep interior structure. 
In particular, the existence of the Earth’s liquid outer core is known to produce a resonance in the nutation signal at a near-diurnal frequency (as measured in the Earth-bound rotating frame). Physically, this resonance corresponds to the excitation of free mode whereby the liquid core experiences a global rotation of uniform vorticity, hence its name: Free Core Nutation (FCN). 

In parallel, experimental and theoretical studies of fluid dynamics have since long demonstrated that rotating fluids can support oscillatory motions known as inertial waves, which are due to the restoring effect of the Coriolis force. In planetary situations where the fluid domain is bounded by solid boundaries, these oscillations become global, so that they are sometimes referred to as inertial modes. The Spin-Over Mode (SOM), is the simplest of these inertial mode, with uniform vorticity. Because of this and the fact that the SOM, like the FCN, has a near-diurnal frequency, the two modes have often been identified as one and the same. In a former study, we showed that the FCN is in fact a generalization of the SOM to the case of a (non-steadily) freely rotating planet (Rekier et al 2020). 

In the present work, we analyse the relation between the SOM and the FCN in more details by showing how the two modes can, in fact, coexist together in a planet subjected to external gravitational forcing. We also show that the proximity between the frequencies of the SOM and the FCN can have a significant effect on the shape and the intensity of the FCN resonance – represented by the transfer function for nutations – when viscous and/or electromagnetic coupling is introduced at the planet’s Core-Mantle Boundary (CMB). In particular, we estimate that this can cause an increase of ∼1 day in the (retrograde) period of the resonance as measured in the inertial frame. 

We conclude with a discussion on some of the implications of our findings for the nutations of other planetary objects like Mars and the Moon.

Reference:

• Rekier, J., Trinh, A., Triana, S. A., & Dehant, V. (2020). Inertial modes of a freely rotating ellipsoidal planet and their relation to nutations. The Planetary Science Journal, 1(1), 20