Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T07:30:05.803Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of the Stewartson layer

Published online by Cambridge University Press:  11 April 2006

Kiyoshi Hashimoto
Kiyoshi Hashimoto
Affiliation:
Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of the Stewartson layer in a rotating incompressible fluid is investigated within the framework of a linear theory. The boundary-layer structure of the shear layer is correctly taken into account and the effect of viscous dissipation on the disturbance is included in the governing equations. The growth rate ωi of the disturbance is given as a function of the unified parameter mRo/(γ½), where m, an integer, is the azimuthal component of the wavenumber vector, γ the radius of the layer, Ro the Rossby number and E the Ekman number. Instability occurs when m Ro/(γ½) > 9·5. The time evolution of a growing disturbance is given schematically. Comparison of our results with the experiments by Hide & Titman shows good agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 2 , 28 July 1976 , pp. 289 - 306
Copyright
© 1976 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

Busse, F. H. 1968 Shear flow instabilities in rotating systems. J. Fluid Mech. 33, 577.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hashimoto, K. 1975 A source-sink flow of an incompressible rotating fluid. J. Phys. Soc. Japan. 38, 1508.Google Scholar
Hide, R. & Titman, C. W. 1967 Detached shear layers in a rotating fluid. J. Fluid Mech. 29, 39.Google Scholar
Hunter, C. 1967 The axisymmetric flow in a rotating annulus due to a horizontally applied temperature gradient. J. Fluid Mech. 27, 753.Google Scholar
Siegmann, W. L. 1974 Evolution of unstable shear layers in a rotating fluid. J. Fluid Mech. 64, 289.Google Scholar
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17.Google Scholar