Liquid core dynamical stability and the Earth's rotational modes

The Earth's interior, especially the mantle (MT), is believed to deviate from the state of hydrostatic equilibrium. This is mainly because the customary approaches in computing the period of the free-core nutation (FCN) for Earth models in hydrostatic equilibrium yield predicted values larger than the observed value by an average of about 30 sidereal days (sd). However, results from alternative computational approaches yield predicted periods of this mode that are close to the observed value. This suggests that the Earth's interior maybe closer to hydrostatic equilibrium than previously envisioned. In this work I study the dynamics of a compressible liquid core (LC) model, bounded by the rigid MT, and vary the square of the Brunt Väsälä frequency, within its known limits, such that the LC density profile is stably, neutrally, and unstably stratified, and compute the periods of the CW and FCN. I show that the period of the CW is unaffected, as expected, by the variations of the Brunt Väsälä frequency. Unless the LC is moderately unstably stratified, for which the computed period of this mode does not converge to a single value, the period of the FCN is also not significantly affected by these variations except for a small range of Brunt Väsälä frequency for which the core is unstably stratified. I conclude that either the LC is moderately-unstably stratified, or the discrepancy between the observed and computed period of the FCN, once the effects of the viscous and electromagnetic torques on the inner-core boundary (ICB) and core-mantle boundary (CMB) are considered, may be in the theoretical/computational treatment of the dynamics of the elastic MT.