Back to Search
Start Over
Waves in the Earth's core. III. A perturbative approach to quasi-free-decay modes.
- Source :
-
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences . Feb2023, Vol. 479 Issue 2270, p1-19. 19p. - Publication Year :
- 2023
-
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]
Details
- Language :
- English
- ISSN :
- 13645021
- Volume :
- 479
- Issue :
- 2270
- Database :
- Academic Search Index
- Journal :
- Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 162943195
- Full Text :
- https://doi.org/10.1098/rspa.2022.0684