Waves in the Earth's core. III. A perturbative approach to quasi-free-decay modes
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Date
2023-02
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Journal Article
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yes
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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.
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published
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479 (2270)
Pages / Article No.
20220684
Publisher
Royal Society
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Subject
core dynamics; Earth’s core; geomagnetism
Organisational unit
03734 - Jackson, Andrew / Jackson, Andrew
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Funding
833848 - Unravelling Earth’s magnetic history and processes UEMHP (EC)