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Lookup NU author(s): Emeritus Professor Andrew Soward
This is the authors' accepted manuscript of an article that has been published in its final definitive form by Cambridge University Press, 2021.
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In an earlier paper, Oruba et al. (J. Fluid Mech., vol. 818, 2017, pp. 205–240) consideredthe primary quasi-steady geostrophic (QG) motion of a constant density fluid of viscosityν that occurs during linear spin-down in a cylindrical container of radius L and height H,rotating rapidly (angular velocity Ω) about its axis of symmetry subject to mixed rigid andstress-free boundary conditions for the case L = H. Direct numerical simulation (DNS)of the linear system at large L = 10H and Ekman number E ν/H 2 Ω = 10 −3 by Orubaet al. (J. Fluid Mech., vol. 888, 2020, p. 44) reveals significant inertial wave activity on thespin-down time scale. That analytic study, for E 1, builds on the results of Greenspan& Howard (J. Fluid Mech., vol. 17, 1963, pp. 385–404) for an infinite plane layer L → ∞.At large but finite distance from the symmetry axis, the meridional (QG-)flow, thatcauses the QG-spin-down, is blocked by the lateral boundary, which provides the primaryQG-trigger for inertial wave generation. For the laterally unbounded layer, Greenspanand Howard identified, in addition to the QG-flow, inertial waves of maximum frequency(MF) 2Ω, which are a manifestation of the transient Ekman layer. The blocking of theseadditional MF-waves by the lateral boundary provides an extra trigger that complementsthe QG-triggered inertial waves. Here we obtain analytic results for the full wave activitycaused by the combined trigger (QG + MF) that faithfully capture their true character.
Author(s): Oruba L, Soward AM, Dormy E
Publication type: Article
Publication status: Published
Journal: Journal of Fluid Mechanics
Year: 2021
Volume: 915
Pages: 1-39
Print publication date: 25/05/2021
Online publication date: 15/03/2021
Acceptance date: 15/12/2020
Date deposited: 15/03/2021
ISSN (print): 0022-1120
ISSN (electronic): 1469-7645
Publisher: Cambridge University Press
URL: https://doi.org/https://doi.org/10.1017/jfm.2020.1183
DOI: 10.1017/jfm.2020.1183
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