Free Core Nutation and Its Relation to the Spin-over Mode

Abstract

The time-varying response of Earth’s and other planets’ rotation to external gravitational torques depends strongly on their internal structure. In particular, the existence of the mode known as the free core nutation in the fluid core is known to amplify the forced nutations in the near-diurnal retrograde frequency band (as measured in the planetary frame of reference). Due to their proximity in shape and frequency, this mode is sometimes equated with the so-called spin-over mode, which denotes the free oscillation of a steadily rotating ellipsoidal fluid core. Through a careful study of the freely rotating two-layer planetary model with a rigid mantle and an inviscid fluid core, we show that the spin-over mode frequency corresponds to that where the sum of the external and internal torques on the mantle is balanced, causing it to rotate steadily. The presence of dissipation at the core−mantle boundary causes the free core nutation to become damped and slightly offsets its resonance frequency. We show that this offset, which is ≈−1 day for Earth, can be interpreted as the result of the proximity of the free core nutation frequency to that of the spin-over mode, which now corresponds to a minimum in the magnitude of the transfer function for nutations. We also show how this proximity leads to a slightly lower quality factor for the resonance than that computed from the usual formula. We conclude by discussing possible implications of this mechanism for Mars, the Moon, and the long-term evolution of Earth.

Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation

“…7c has a flow vorticity that is uniform in the frame of the mode and points in a direction perpendicular to the solar rotation axis. This particular mode is often called the "spin-over inertial mode" (e.g., Greenspan et al 1968) and has been extensively studied in the context of planetary cores (e.g., Triana et al 2012;Rekier 2022).…”

Effects of the Librationally Induced Flow in Mercury’s Fluid Core with an Outer Stably Stratified Layer

“…Its vorticity is uniform and parallel to the equatorial plane and precesses around the rotation axis at a near-diurnal frequencyhence its name-and produces no torque along the rotation axis. It is therefore irrelevant to libration but has relevance to precession-nutation (Triana et al 2019;Rekier 2022). The other mode has a vorticity parallel to the rotation axis and an exactly zero frequency.…”

Theory of solar oscillations in the inertial frequency range

“…4.8c has a flow vorticity that is uniform in the frame of the mode and points in a direction perpendicular to the solar rotation axis. This particular mode is often called the "spin-over inertial mode" (e.g., Greenspan et al 1968) and has been extensively studied in the context of planetary cores (e.g., Triana et al 2012, Rekier 2022.…”