Robins, LJM, Kersalé, E and Jones, CA orcid.org/0000-0002-1105-3920 (2020) Viscous and inviscid strato-rotational instability. Journal of Fluid Mechanics, 894. A13. ISSN 0022-1120
Abstract
We examine the critical viscous mode of the Taylor–Couette strato-rotational instability, concentrating on cases where the buoyancy frequency N and the inner cylinder rotation rate Ωin are comparable, giving a detailed account for N = Ωin. The ratio of the outer to the inner cylinder rotation rates µ = Ωout/Ωin and the ratio of the inner to the outer cylinder radius η = rin/rout satisfy 0 < µ < 1 and 0 < η < 1. We find considerable variation in the structure of the mode, and the critical Reynolds number Rec at which the flow becomes unstable. For N = Ωin, we classify different regions of the ηµ-plane by the critical viscous mode of each region. We find that there is a triple point in the ηµ-plane where three different viscous modes all onset at the same Reynolds number. We also find a discontinuous change in Rec along a curve in the ηµ-plane, on one side of which exist closed unstable domains where the flow can restabilise when the Reynolds number is increased. A new form of viscous instability occurring for wide gaps has been detected. We show for the first time that there is a region of the parameter space for which the critical viscous mode at the onset of instability corresponds to the inviscid radiative instability of Le Dizès & Riedinger (J. Fluid Mech., vol. 660, 2010, pp. 147–161). Focusing on small-to-moderate wavenumbers, we demonstrate that the viscous and inviscid systems are not always correlated. We explore which viscous modes relate to inviscid modes and which do not. For asymptotically large vertical wavenumbers, we have extended the inviscid analysis of Park & Billant (J. Fluid Mech., vol. 725, 2013, pp. 262–280) to cover the cases where N and Ωin are comparable.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2020. Published by Cambridge University Press. This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | Taylor–Couette flow, stratified flows |
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/K000853/1 STFC (Science and Technology Facilities Council) ST/N000765/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 May 2020 12:09 |
Last Modified: | 07 May 2024 14:37 |
Status: | Published |
Publisher: | Cambridge University Press (CUP) |
Identification Number: | 10.1017/jfm.2020.245 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:161195 |
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