Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T12:43:06.582Z Has data issue: false hasContentIssue false

Spin-up phenomena in non-axisymmetric containers

Published online by Cambridge University Press:  26 April 2006

G. J. F. Van Heijst
Affiliation:
Institute of Meteorology and Oceanography, University of Utrecht, Princetonplein 5, Utrecht, The Netherlands

Abstract

The spin-up from rest of a contained homogeneous free-surface fluid has been examined in the laboratory for a variety of non-axisymmetric containers. It was found that in the spin-up process three stages can be distinguished before the fluid reaches the ultimate state of rigid-body rotation. When the container starts spinning, the non-axisymmetric lateral tank boundaries induce horizontal pressure gradients, and as a result relative flows arise instantaneously after the start of the experiment. The absolute vorticity of the starting flow is zero, and a description can be given in terms of potential theory. Theoretical solutions have been derived for a number of geometries, and comparison with experimentally observed streamline patterns shows good agreement. In the next stage, flow separation sets in, in most cases leading to locally intense three-dimensional turbulent flows. The basic rotation causes a transition from three-dimensional to two-dimensional motion, and a subsequent organization of the relative flow into a number of cells is observed. During the final stage, the flow in these cells gradually decays owing to the spin-up/spin-down mechanism provided by the Ekman layer at the bottom of each cell, until eventually the fluid is in solid-body rotation.

Type
Research Article
Copyright
© 1989 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

Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12, (Suppl. II), 233240.Google Scholar
Benton, E. R. & Clark, A. 1974 Spin-up. Ann. Rev. Fluid Mech. 6, 257280.Google Scholar
Buzyna, G. & Veronis, G. 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579608.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385404.Google Scholar
Heijst, G. J. F. Van, Davies, P. A. & Davis, R. G. 1989 Spin-up in a rectangular container. Phys. Fluids. (submitted).Google Scholar
Holton, J. R. 1965 The influence of viscous boundary layers on transient motions in a stratified rotating fluid. Part 1. J. Atmos. Sci. 22, 402411.Google Scholar
Linden, P. F. & Heijst, G. J. F. Van 1984 Two-layer spin-up and frontogenesis. J. Fluid Mech. 143, 6994.Google Scholar
Pedlosky, J. 1967 The spin-up of a stratified fluid. J. Fluid Mech. 28, 463480.Google Scholar
Walin, G. 1969 Some aspects of time-dependent motion of a stratified rotating fluid. J. Fluid Mech. 36, 289307.Google Scholar