Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-08T05:03:17.499Z Has data issue: false hasContentIssue false
  • English
  • Français

The transient response of a contained rotating stratified fluid to impulsively started surface forcing

Published online by Cambridge University Press:  26 April 2006

G. S. M. Spence ,
M. R. Foster  and
P. A. Davies
G. S. M. Spence
Affiliation:
Department of Civil Engineering, The University, Dundee DD1 4HN. UK Present address: Risley Nuclear Power Development Laboratories, Northern Division, UKAEA, Risley, Warrington, Cheshire, WA3 6AT, UK.
M. R. Foster
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus OH 43210-1275, USA
P. A. Davies
Affiliation:
Department of Civil Engineering, The University, Dundee DD1 4HN. UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The transient response of a contained stratified rapidly rotating fluid to an impulsive surface stress has been studied theoretically and experimentally. The analysis predicts, and the experiments confirm, that for low values of the Burger number S the initial fluid adjustment within the E−½Ω−1 timescale is characterized by a barotropic response in which the magnitude of the interior velocity is independent of depth. (Here E and Ω are the Ekman number and rotation rate respectively.) The period of the barotropic response decreases as S increases. For large S, the barotropic flow adjusts subsequently to a baroclinic flow within the E−½Ω−1 scale, and during this later stage the excess and deficit in velocity in the lower and upper parts respectively of the fluid are removed. The baroclinic flow forced by the surface stress in these cases is thereby established in a timescale which is typically less than the spin-up time for a homogeneous fluid. The agreement between theory and experiment is shown to be qualitatively good, and the quantitative discrepancies observed between the predicted and measured interior velocities are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 33 - 50
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benton, E. R. & Clark, A. 1974 Spin up. Ann. Rev. Fluid Mech. 6. 257–280.Google Scholar
Boyer, D. L. & Davies, P. A. 1982 Flow past a circular cylinder on a beta plane.. Phil. Trans. R. Soc. Lond. A 306, 533–556.Google Scholar
Buzyna, G. & Veronis, G. 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579–608.Google Scholar
Davies, P. A. 1972 Experiments on Taylor columns in rotating stratified fluids. J. Fluid Mech. 54, 691–717.Google Scholar
Davies, P. A., Davis, R. G. & Foster, M. R. 1990, Flow past a cylinder in a rotating, stratified fluid. Phil. Trans. R. Soc. Lond. A331, 245–286.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Holton, J. R. 1965 The influence of viscous boundary layers on transient motions in a stratified rotating fluid. Part I. J. Atmos. Sci. 22, 402–411.Google Scholar
Holton, J. R. 1965b The influence of viscous boundary layers on transient motions in a stratified rotating fluid. Part II. J. Atmos. Sci. 22, 535–540.Google Scholar
Honji, H., Taneda, S. & Tatsuno, A. 1980 Some practical details of the electrolytic precipitation method of flow visualisation. Res. Inst. Appl. Mech. Kyushu Univ. 28, 83–89.Google Scholar
Hyun, J. M. 1983 Axisymmetric flows in spin-up from rest of a stratified fluid in a cylinder. Geophys. Astrophys. Fluid Dyn. 23, 127–141.Google Scholar
Linden, P. F. 1977 The flow of a stratified fluid in a rotating annulus. J. Fluid Mech. 79, 435–447.Google Scholar
Pedlosky, J. 1967 The spin-up of a stratified fluid. J. Fluid Mech. 28, 463–479.Google Scholar
Pedlosky, J. 1971 Geophysical fluid dynamics. In Mathematical Problems in the Geophysical Sciences (ed. (W. H. Reid). Lectures in Applied Mathematics, vol. 13. Providence, RI: Am., Math. Soc.
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Sakurai, T. 1969 Spin down problems of rotating stratified fluid in thermally-insulated circular cylinders. J. Fluid Mech. 37, 689–699.Google Scholar
Spence, G. S. M. 1986 Studies of baroclinic flows in rotating fluids. Ph.D. dissertation, University of Dundee.
Walin, G. 1969 Some aspects of time-dependent motion of a stratified rotating fluid. J. Fluid Mech. 1936, 289–307.Google Scholar
Wedemeyer, E. H. 1964 The unsteady flow with a spinning cylinder. J. Fluid Mech. 20, 383–399.Google Scholar
Weidmann, P. D. 1976a On the spin-up and spin-down of a rotating fluid. Part 1. Extending the Wedemeyer model. J. Fluid Mech. 77, 685–708.Google Scholar
Weidmann, P. D. 1976b On the spin-up and spin-down of a rotating fluid. Part 2. Measurements and stability. 77, 709–725.Google Scholar