Maffei, S, Jackson, A and Livermore, PW orcid.org/0000-0001-7591-6716 (2017) Characterisation of columnar inertial modes in rapidly rotating spheres and spheroids. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2204). ISSN 1364-5021
Abstract
We consider fluid-filled spheres and spheroidal containers of eccentricity ε in rapid rotation, as a proxy for the interior dynamics of stars and planets. The fluid motion is assumed to be quasi-geostrophic (QG): horizontal motions are invariant parallel to the rotation axis z, a characteristic which is handled by use of a stream function formulation which additionally enforces mass conservation and non-penetration at the boundary. By linearising about a quiescent background state, we investigate a variety of methods to study the QG inviscid inertial wave modes which are compared with fully 3-D calculations. We consider the recently-proposed weak formulation of the inviscid system valid in spheroids of arbitrary eccentricity, to which we present novel closed-form polynomial solutions. Our modal solutions accurately represent, in both spatial structure and frequency, the most z-invariant of the inertial wave modes in a spheroid, and constitute a simple basis set for the analysis of rotationally dominated fluids. We further show that these new solutions are more accurate than those of the classical axial-vorticity equation, which is independent of ε and thus fails to properly encode the container geometry. We also consider the effects of viscosity for the cases of both no-slip and stress-free boundary conditions for a spherical container. Calculations performed under the columnar approximation are compared with 3-D solutions and excellent agreement has been found despite fundamental differences in the two formulations.
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Copyright, Publisher and Additional Information: | © 2017, Royal Society of London. This is an author produced version of a paper published in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Uploaded in accordance with the publisher's self-archiving policy. | ||||||
Keywords: | Inertial modes; Quasi-geostrophy; Earth's outer core | ||||||
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Institution: | The University of Leeds | ||||||
Academic Units: | The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) > Inst of Geophysics and Tectonics (IGT) (Leeds) | ||||||
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Depositing User: | Symplectic Publications | ||||||
Date Deposited: | 26 Jul 2017 13:30 | ||||||
Last Modified: | 09 Aug 2018 00:38 | ||||||
Status: | Published | ||||||
Publisher: | Royal Society of London | ||||||
Identification Number: | https://doi.org/10.1098/rspa.2017.0181 |