Spin-up in a semicircular cylinder

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

Abstract

We report experimental and theoretical results on how a fluid (homogeneous or continuously stratified) is spun up in a closed, semicircular cylinder. Experiments were performed for Rossby numbers, 0.2 and 1 (the latter corresponding to the limiting case of spin-up from rest), with the Ekman number, and the Burger number varied between 0 and 10. There are two key processes: Ekman pumping that drives the core flow; and the formation and breakdown of the vertical-wall boundary layers, with respective characteristic time scales and. When these time scales are comparable, the observed flow is dominated by the gradual spin-up of the initial anticyclone that forms when the rotation rate is increased, which fills the container's interior; vorticity generated adjacent to the vertical walls throughout remains confined to the neighbourhood of the container's walls and corners. Conversely, when, the vertical-wall boundary layers rapidly break down, resulting in the formation of cyclonic vortices in the container's vertical corners, which grow and interact with the initial anticyclone, leading to the formation of a three-cell flow pattern. For, our theoretical description of the flow generally agrees well with experiments, and the computation of the eruption times for the unsteady boundary layers is consistent with the observations for both and.

Citation

Munro, R., & Foster, M. (2022). Spin-up in a semicircular cylinder. Journal of Fluid Mechanics, 938, Article A15. https://doi.org/10.1017/jfm.2022.150

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2022
• Online Publication Date: Mar 14, 2022
• Publication Date: May 10, 2022
• Deposit Date: Mar 16, 2022
• Publicly Available Date: Mar 16, 2022
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press (CUP)
• Peer Reviewed: Peer Reviewed
• Volume: 938
• Article Number: A15
• DOI: https://doi.org/10.1017/jfm.2022.150
• Keywords: Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/7607127
• Publisher URL: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/spinup-in-a-semicircular-cylinder/0BA205B10EF2A704647A407DDD8AE19E