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Spin-up problems of stratified rotating flows inside containers

Published online by Cambridge University Press:  28 November 2012

Peter W. Duck
Peter W. Duck*
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK
*
†Email addresses for correspondence: [email protected]
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Abstract

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Rotating, stratified flows are important in a wide variety of both geophysical and engineering applications. Whilst ‘steady state’ flows of this type are generally very simple (in effect, rigid body rotation), the effect of abruptly altering (even a little) the rotation rate can induce significant temporal flow disruptions, made all the more complicated when the fluid is bounded inside a closed finite container, a problem studied both experimentally and theoretically by Foster & Munro (J. Fluid Mech., this issue, vol. 712, 2012, pp. 7–40).

JFM classification

Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Stratified flows
Type
Focus on Fluids
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 3 - 6
Copyright
©2012 Cambridge University Press 

References

Batchelor, G. K. 1958 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.Google Scholar
Benton, E. R. & Clark, A. 1974 Spin-up. Annu. Rev. Fluid Mech. 6, 257–280.Google Scholar
van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating laminar boundary layer. J. Comput. Phys. 38, 125–140.CrossRefGoogle Scholar
Duck, P. W. & Foster, M. R. 2001 Spin-up of homogeneous and stratified flows. Annu. Rev. Fluid Mech. 33, 231–263.Google Scholar
van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. Academic.Google Scholar
Ekman, V. W. 1906 Beitäge zur theorie der Meeresströmungen. Ann. Hydrograph Mar. Met. 2, 1–50.Google Scholar
Foster, M. R. & Munro, R. J. 2012 The linear spin-up of a stratified, rotating fluid in a square cylinder. J. Fluid Mech. 712, 7–40.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On the time dependent motion of a rotating flow. J. Fluid Mech. 17, 385–404.Google Scholar
van Heijst, G. J. F. 1989 Spin-up phenomena in non-axisymmetric containers. J. Fluid Mech. 206, 171–191.Google Scholar
van Heijst, G. J. F., Davies, P. A. & Davis, R. G. 1990 Spin-up in a rectangular container. Phys. Fluids A 2, 150–159.Google Scholar
Stewartson, K. 1957 On almost rigid rotation. J. Fluid Mech. 3, 17–26.Google Scholar