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Spin-up problems of stratified rotating flows inside containers

  • Peter W. Duck (a1)
Abstract

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).

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Copyright
Corresponding author
Email addresses for correspondence: duck@ma.man.ac.uk
References
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Batchelor, G. K. 1958 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177190.
Benton, E. R. & Clark, A. 1974 Spin-up. Annu. Rev. Fluid Mech. 6, 257280.
van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating laminar boundary layer. J. Comput. Phys. 38, 125140.
Duck, P. W. & Foster, M. R. 2001 Spin-up of homogeneous and stratified flows. Annu. Rev. Fluid Mech. 33, 231263.
van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Ekman, V. W. 1906 Beitäge zur theorie der Meeresströmungen. Ann. Hydrograph Mar. Met. 2, 150.
Foster, M. R. & Munro, R. J. 2012 The linear spin-up of a stratified, rotating fluid in a square cylinder. J. Fluid Mech. 712, 740.
Greenspan, H. P. & Howard, L. N. 1963 On the time dependent motion of a rotating flow. J. Fluid Mech. 17, 385404.
van Heijst, G. J. F. 1989 Spin-up phenomena in non-axisymmetric containers. J. Fluid Mech. 206, 171191.
van Heijst, G. J. F., Davies, P. A. & Davis, R. G. 1990 Spin-up in a rectangular container. Phys. Fluids A 2, 150159.
Stewartson, K. 1957 On almost rigid rotation. J. Fluid Mech. 3, 1726.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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