The spin-up of a linearly stratified fluid in a sliced, circular cylinder

Munro, R.J.; Foster, M.R.

Abstract

A linearly stratified fluid contained in a circular cylinder with a linearly-sloped base, whose axis is aligned with the rotation axis, is spun up from a rotation rate Ώ to Ώ + ΔΏ (with ΔΏ << Ώ ) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number S is not small, then that spinup looks quite different from that reported by Pedlosky & Greenspan [J. Fluid Mech., vol. 27, 1967, pp. 291–304] for S = 0. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height S−1/2 above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al. [Phys. Fluids A, vol. 2, 1990, pp. 150–159] and Munro & Foster [Phys. Fluids, vol. 26, 2014, article no. 026603], for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom S−1/2 region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with S as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large S, and vertical vortices are found to occur only for Rossby numbers comparable to E1/2, where E is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

Citation

Munro, R., & Foster, M. (2016). The spin-up of a linearly stratified fluid in a sliced, circular cylinder. Journal of Fluid Mechanics, 806, 254-303. https://doi.org/10.1017/jfm.2016.589

• Journal Article Type: Article
• Acceptance Date: Sep 1, 2016
• Online Publication Date: Sep 30, 2016
• Publication Date: Nov 30, 2016
• Deposit Date: Nov 11, 2016
• Publicly Available Date: Nov 11, 2016
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 806
• Pages: 254-303
• DOI: https://doi.org/10.1017/jfm.2016.589
• Keywords: Rotating flows, Stratified flows, Topographic effects
• Public URL: https://nottingham-repository.worktribe.com/output/826442
• Publisher URL: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/the-spin-up-of-a-linearly-stratified-fluid-in-a-sliced-circular-cylinder/7F507D1681C8D9813A2C365A1862F5DC
• Additional Information: © Cambridge University Press 2016
• Contract Date: Nov 11, 2016