Inertial modes of a freely rotating ellipsoidal planet and their relation to nutations

Abstract

We compute the inertial modes of a freely rotating two-layer planetary model with an ellipsoidal inviscid fluid core and a perfectly rigid mantle. We present a method to derive analytical formulae for the frequencies of the Free Core Nutation (FCN) and Chandler Wobble (CW) which are valid to all orders of the dynamical flattening of the core and mantle, and we show how the FCN and CW are the direct generalisation of the purely fluid Spin-Over mode (SO) and of the Eulerian Wobble (EW) to the case where the mantle can oscillate freely around a state of steady rotation. Through a numerical computation for an axisymmetric (oblate spheroidal) planet, we demonstrate that all other inertial modes of the steadily rotating fluid core are also free modes of the freely rotating two-layer planet.

arXiv comment19 pages, 4 figures, accepted for publication in Planetary Science Journal (AAS)

References in corpus (7)

• Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
• Completeness of Inertial Modes of an Incompressible Non-Viscous Fluid in a Corotating Ellipsoid
• The radioscience LaRa instrument onboard ExoMars 2020 to investigate the rotation and interior of Mars
• The coupling between inertial and rotational eigenmodes in planets with liquid cores
• Inertial Modes in Near-Spherical Geometries
• Formulation of a Triaxial Three-Layered Earth Rotation: I. Theory and Rotational Normal Mode Solutions
• Tilt-over mode in a precessing triaxial ellipsoid

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