Spin-up of stratified rotating flows at large Schmidt number: experiment and theory

Hewitt, R.E. and Davies, P.A. and Duck, P.W. and Foster, M.R. (1999) Spin-up of stratified rotating flows at large Schmidt number: experiment and theory. Journal of Fluid Mechanics, 389. pp. 169-207. ISSN 1469-7645

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Abstract

We consider the nonlinear spin-up/down of a rotating stratified fluid in a coni- cal container. An analysis of axisymmetric similarity-type solutions to the relevant boundary-layer problem, Duck, Foster & Hewitt (1997), has revealed three types of behaviour for this geometry. In general, the boundary layer evolves to either a steady state, or a gradually thickening boundary layer, or a finite-time singularity depending on the Schmidt number, the ratio of initial to final rotation rates, and the relative importance of rotation and stratification. In this paper we emphasize the experimental aspects of an investigation into the initial readjustment process. We make comparisons with the previously presented boundary-layer theory, showing good quantitative agreement for positive changes in the rotation rate of the container (relative to the initial rotation sense). The boundary-layer analysis is shown to be less successful in predicting the flow evolution for nonlinear decelerations of the container. We discuss the qualitative features of the spin-down experiments, which, in general, are dominated by non-axisymmetric effects. The experiments are conducted using salt-stratified solutions, which have a Schmidt number of approximately 700. The latter sections of the paper present some stability results for the steady boundary-layer states. A high degree of non-uniqueness is possible for the system of steady governing equations; however the experimental results are repeatable and stability calculations suggest that �higher branch� solutions are, in general, unstable. The eigenvalue spectrum arising from the linear stability analysis is shown to have both continuous and discrete components. Some analytical results concerning the continuous spectrum are presented in an appendix. A brief appendix completes the previous analysis of Duck, Foster & Hewitt (1997), presenting numerical evidence of a different form of finite-time singularity available for a more general boundary-layer problem.

Item Type:	Article
Additional Information:	© 1999 Cambridge University Press
Uncontrolled Keywords:	Spin-up Ekman layer rotating flow
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics
Depositing User:	Dr Richard E. Hewitt
Date Deposited:	14 Nov 2013
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2053

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