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The linear spin-up of a stratified, rotating fluid in a square cylinder

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

Authors

M.R. Foster

Richard J. Munro

Abstract

Here we present experimental and theoretical results for how a stratified fluid, initially rotating as a solid body with constant angular velocity, , within a closed cylinder of square cross-section, is spun up when subject to a small, impulsive increase, , in the cylinder’s rotation rate. The fluid’s adjustment to the new state of solid rotation can be characterized by: (a) an inviscid, horizontal starting flow which conserves the vorticity of the initial condition; (b) the eruption of Ekman layer fluid from the perimeter region of the cylinder’s base and lid; (c) horizontal-velocity Rayleigh layers that grow into the interior from the container’s sidewalls; and (d) the formation and decay of columnar vortices in the vertical corner regions. Asymptotic results describe the inviscid starting flow, and the subsequent interior spin-up that occurs due to the combined effects of Ekman suction through the base and lid Ekman layers, and the growth of the sidewall Rayleigh layers. Attention is focused on the flow development over the spin-up time scale , where is the Ekman number. (The spin-up process over the much longer diffusive time scale, , is not considered here.) Experiments were performed using particle imaging velocimetry (PIV) to measure horizontal velocity components at fixed heights within the flow interior and at regular stages during the spin-up period. The velocity data obtained are shown to be in excellent agreement with the asymptotic theory.

Journal Article Type Article
Publication Date Dec 1, 2012
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 712
Institution Citation Foster, M., & Munro, R. J. (2012). The linear spin-up of a stratified, rotating fluid in a square cylinder. Journal of Fluid Mechanics, 712, doi:10.1017/jfm.2012.402
DOI https://doi.org/10.1017/jfm.2012.402
Keywords boundary layer structure; rotating flows; stratified flows
Publisher URL http://dx.doi.org/10.1017/jfm.2012.402
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information ©2012 Cambridge University Press

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf




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