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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
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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

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References

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