HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

On the inertial wave activity during spin-down in a rapidly rotating penny shaped cylinder: a reduced model

Abstract : In a previous paper, Oruba et al. (J. Fluid Mech., vol. 818, 2017, pp. 205-240) considered the 'primary' quasi-steady geostrophic (QG) motion of a constant density fluid of viscosity ⌫ that occurs during linear spin-down in a cylindrical container of radius r † = L and height z † = H, rotating rapidly (angular velocity ⌦) about its axis of symmetry subject to mixed rigid and stress-free boundary conditions for the case L = H. Here, Direct numerical simulation at large L = 10H and Ekman numbers E = ⌫/H 2 ⌦ in the range = 10 3-10 7 reveals inertial wave activity on the spin-down time scale E 1/2 ⌦ 1. Our analytic study, based on E ⌧ 1, builds on the results of Greenspan & Howard (J. Fluid Mech., vol. 17, 1963, pp. 385-404) for an infinite plane layer L ! 1. In addition to QG spin-down, they identify a 'secondary' set of quasi-maximum frequency ! † ! 2⌦ (MF) inertial waves, which is a manifestation of the transient Ekman layer, decaying algebraically / 1/ p t †. Here, we acknowledge that the blocking of the meridional parts of both the primary-QG and the secondary-MF spin-down flows by the lateral boundary r † = L provides a trigger for other inertial waves. As we only investigate the response to the primary QG-trigger, we call the model 'reduced' and for that only inertial waves with frequencies ! † < 2⌦ are triggered. We explain the ensuing organised inertial wave structure via an analytic study of the thin disc limit L H restricted to the region L r † = O(H) far from the axis, where we make a Cartesian approximation of the cylindrical geometry. Other than identifying a small scale fan structure emanating from the corner [r † , z † ] = [L, 0], we show that inertial waves, on the gap length scale H, radiated (wave energy flux) away from the outer boundary r † = L (but propagating with a phase velocity towards it) reach a distance determined by the mode with the fastest group velocity.
Complete list of metadata

Cited literature [31 references]  Display  Hide  Download

Contributor : Catherine Cardon Connect in order to contact the contributor
Submitted on : Friday, February 7, 2020 - 4:06:04 PM
Last modification on : Thursday, March 17, 2022 - 10:08:19 AM


Publication funded by an institution



Ludivine Oruba, A. M. Soward, E. Dormy. On the inertial wave activity during spin-down in a rapidly rotating penny shaped cylinder: a reduced model. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2020, 888 (10 April), pp.A9. ⟨10.1017/jfm.2019.1064⟩. ⟨insu-02470932⟩



Record views


Files downloads