The spin-up of a linearly stratified fluid in a sliced, circular cylinder
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, s...
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Cambridge University Press
2016
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| Online Access: | https://eprints.nottingham.ac.uk/38653/ |
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| author | Munro, R.J. Foster, M.R. |
| author_facet | Munro, R.J. Foster, M.R. |
| author_sort | Munro, R.J. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:35:38Z |
| format | Article |
| id | nottingham-38653 |
| institution | University of Nottingham Malaysia Campus |
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| last_indexed | 2025-11-14T19:35:38Z |
| publishDate | 2016 |
| publisher | Cambridge University Press |
| recordtype | eprints |
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| spelling | nottingham-386532024-08-15T15:20:50Z https://eprints.nottingham.ac.uk/38653/ The spin-up of a linearly stratified fluid in a sliced, circular cylinder Munro, R.J. Foster, M.R. 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. Cambridge University Press 2016-11-30 Article PeerReviewed Munro, R.J. and Foster, M.R. (2016) The spin-up of a linearly stratified fluid in a sliced, circular cylinder. Journal of Fluid Mechanics, 806 . pp. 254-303. ISSN 1469-7645 Rotating flows Stratified flows Topographic effects 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 doi:10.1017/jfm.2016.589 doi:10.1017/jfm.2016.589 |
| spellingShingle | Rotating flows Stratified flows Topographic effects Munro, R.J. Foster, M.R. The spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| title | The spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| title_full | The spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| title_fullStr | The spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| title_full_unstemmed | The spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| title_short | The spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| title_sort | spin-up of a linearly stratified fluid in a sliced, circular cylinder |
| topic | Rotating flows Stratified flows Topographic effects |
| url | https://eprints.nottingham.ac.uk/38653/ https://eprints.nottingham.ac.uk/38653/ https://eprints.nottingham.ac.uk/38653/ |