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Inertial wave activity during spin-down in a rapidly rotating penny shaped cylinder

Published online by Cambridge University Press:  15 March 2021

L. Oruba Open the ORCID record for L. Oruba [Opens in a new window] ,
A.M. Soward Open the ORCID record for A.M. Soward [Opens in a new window]  and
E. Dormy Open the ORCID record for E. Dormy [Opens in a new window]
L. Oruba*
Affiliation:
Laboratoire Atmosphères Milieux Observations Spatiales (LATMOS/IPSL), Sorbonne Université, UVSQ, CNRS, Paris, France
A.M. Soward*
Affiliation:
School of Mathematics and Statistics, Newcastle University, Newcastle upon TyneNE1 7RU, UK
E. Dormy*
Affiliation:
Département de Mathématiques et Applications, UMR-8553, École Normale Supérieure, CNRS, PSL University, 75005Paris, France
*
†Email addresses for correspondence: ludivine.oruba@latmos.ipsl.fr, andrew.soward@ncl.ac.uk, emmanuel.dormy@ens.fr
†Email addresses for correspondence: ludivine.oruba@latmos.ipsl.fr, andrew.soward@ncl.ac.uk, emmanuel.dormy@ens.fr
†Email addresses for correspondence: ludivine.oruba@latmos.ipsl.fr, andrew.soward@ncl.ac.uk, emmanuel.dormy@ens.fr
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Abstract

In an earlier 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 $\nu$ that occurs during linear spin-down in a cylindrical container of radius $L$ and height $H$, rotating rapidly (angular velocity $\varOmega$) about its axis of symmetry subject to mixed rigid and stress-free boundary conditions for the case $L=H$. Direct numerical simulation (DNS) of the linear system at large $L= 10 H$ and Ekman number $E\leqslant \nu /H^2\varOmega =10^{-3}$ by Oruba et al. (J. Fluid Mech., vol. 888, 2020, p. 44) reveals significant inertial wave activity on the spin-down time scale. That analytic study, for $E\ll 1$, builds on the results of Greenspan & Howard (J. Fluid Mech., vol. 17, 1963, pp. 385–404) for an infinite plane layer $L\to \infty$. At large but finite distance from the symmetry axis, the meridional (QG-)flow, that causes the QG-spin-down, is blocked by the lateral boundary, which provides the primary QG-trigger for inertial wave generation. For the laterally unbounded layer, Greenspan and Howard identified, in addition to the QG-flow, inertial waves of maximum frequency (MF) $2\varOmega$, which are a manifestation of the transient Ekman layer. The blocking of these additional MF-waves by the lateral boundary provides an extra trigger that complements the QG-triggered inertial waves. Here we obtain analytic results for the full wave activity caused by the combined trigger ($\text {QG}+\text {MF}$) that faithfully capture their true character.

JFM classification

Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A53
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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