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2 results on '"Luo, Jiawen"'

1. Waves in the Earth's core. I. Mildly diffusive torsional oscillations

Author

Luo, Jiawen and Jackson, Andrew

Subjects
torsional oscillations, quality factor, normal mode
Abstract

Axisymmetric oscillations of fluid in a rapidly rotating whole sphere immersed in a magnetic field can be supported by the elastic tension of the magnetic field lines. This special class of Alfven waves is largely geostrophic (invariant along the rotation axis) and describes a set of normal modes that has been extensively studied in the ideal, lossless case, a limit in which regular solutions do not exist when the background magnetic field is axisymmetric. We study the geophysically relevant limit with parameters such that magnetic diffusion plays a realistic role appropriate to the Earth's core, by choosing a Lundquist number Lu appropriately. We demonstrate for the first time the existence of normal modes in the presence of an axisymmetric background field, and obtain eigenfrequencies and decay rates that lead us to deduce quality factors Q for these modes for two simple background fields of dipole and quadrupole parity. Two scaling behaviours of Q are seen depending on the background field and normal modes' frequency, one scaling as Lu-1/2 and another as Lu, so that likely Q > 10 in the core of the Earth. A one-dimensional theory is presented that is able to capture the frequencies of oscillation quite accurately., Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 (2259), ISSN:1364-5021, ISSN:1471-2946, ISSN:0080-4630, ISSN:0950-1207

Published
2022

2. Waves in the Earth's core. III. A perturbative approach to quasi-free-decay modes.

Author

Maitra, Matthew, Luo, Jiawen, and Jackson, Andrew

Subjects
*EARTH'S core, *NON-degenerate perturbation theory, *DEGENERATE perturbation theory, *QUALITY factor, *CORIOLIS force, *PERTURBATION theory
Abstract

We consider the canonical problem of magnetic field decay in an electrically conducting fluid ball. The problem is closely allied to the problem of the decay modes of a rigid ball, and the spatial form of the eigenmodes survives largely intact. The decaying but oscillatory behaviour of the new fluid eigenmodes first discovered by Schmitt a decade ago (and named quasi-free-decay (QFD) modes) is deduced by application of perturbation methods to the case of rapid rotation and a static applied background magnetic field that is uniform and axial. Some, but not all, of the rigid-case poloidal eigenmodes share decay rates with other toroidal modes, necessitating the use of both degenerate and non-degenerate perturbation theory within this paper. The perturbation theory is developed in terms of the Elsasser number Λ (measuring the competition between Coriolis and Lorentz forces), and the analytic results are in striking accord with numerical calculations even when Λ is of O(1). We find linear scaling of the QFD eigenfrequency with Λ and small changes in the decay rate that scale with Λ2. Although the modes are overdamped (quality factor Q<1), they are not strongly overdamped when the applied field is strong Λ∼1. [ABSTRACT FROM AUTHOR]

Published
2023
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