Inertial modes of a freely rotating ellipsoidal planet and their relation to nutations. (arXiv:2004.08218v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Rekier_J/0/1/0/all/0/1">Jeremy Rekier</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Triana_S/0/1/0/all/0/1">Santiago A. Triana</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Trinh_A/0/1/0/all/0/1">Antony Trinh</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Dehant_V/0/1/0/all/0/1">Veronique Dehant</a>
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 derive
analytical formulae for the frequencies of the Free Core Nutation (FCN) and
Chandler Wobble (CW) which are valid to all orders in the core and mantle
ellipticity 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.
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 derive
analytical formulae for the frequencies of the Free Core Nutation (FCN) and
Chandler Wobble (CW) which are valid to all orders in the core and mantle
ellipticity 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.
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