Lin, Y, Hollerbach, R orcid.org/0000-0001-8639-0967, Noir, J et al. (1 more author) (2023) Resonant and non-resonant flows in longitudinally and latitudinally librating spheres. Physics of Fluids, 35 (7). 076612. ISSN 1070-6631
Abstract
We investigate the linear response to longitudinal and latitudinal libration of a rapidly rotating fluid-filled sphere. Asymptotic methods are used to explore the structure of resonant modes in both cases, provided that the nondimensional libration frequency is in the range ω∈[0,2]. High-resolution numerics are then used to map out this entire frequency range, picking out both the resonant peaks as well as the non-resonant troughs in between. The kinetic energy is independent of the Ekman number E at the peaks and scales as E1/2 at the troughs. As the Ekman number is reduced, down to E=10−10 for longitudinal libration and E=10−9 for latitudinal libration, the frequency response also exhibits an increasingly fractal structure, with more and more peaks and troughs emerging. The spacing between peaks is seen to follow an E1/2 self-similarity factor. However, detailed examinations of some of the more prominent troughs shows that their widths follow an E∼0.23 self-similarity factor.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// creativecommons.org/licenses/by/4.0/). |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number STFC (Science and Technology Facilities Council) ST/W000873/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Apr 2023 11:18 |
Last Modified: | 26 Jul 2023 13:11 |
Status: | Published |
Publisher: | American Institute of Physics |
Identification Number: | 10.1063/5.0142705 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198228 |
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