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Shear flow instabilities in rotating systems

Published online by Cambridge University Press:  28 March 2006

F. H. Busse
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics University of California, Los Angeles
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Abstract

A theoretical description is given for infinitesimal non-axisymmetric disturbances of a shear flow caused by differential rotation. It is assumed that the deviations from the state of rigid rotation are small corresponding to the case of small Rossby number. The shear flow becomes unstable at a finite critical value of the Rossby number, at which the inertial forces overcome the friction in the Ekman boundary layers and the constraint imposed by the variation in depth of the container. The governing equation is closely related to the Rayleigh stability equation in the theory of hydrodynamic stability of plane parallel flow. Experimental observations by R. Hide show reasonable agreement with the theoretical predictions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 3 , 2 September 1968 , pp. 577 - 589
Copyright
© 1968 Cambridge University Press

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References

Busse, F. H. 1968 To be published.
Drazin, P. G. & Howard, L. N. 1962 J. Fluid Mech. 14, 257.
Drazin, P. G. & Howard, L. N. 1966 Adv. Appl. Mech. 9, 1.
Eckart, C. 1963 Phys. Fluids, 6, 1042.
Esch, R. E. 1957 J. Fluid Mech. 3, 289.
Faller, A. G. 1963 J. Fluid Mech. 15, 560.
Greenspan, H. P. 1965 J. Fluid Mech. 22, 449.
Hide, R. 1967 Unpublished results.
Hide, R. & Titman, C. W. 1967 J. Fluid Mech. 29, 39.
Howard, L. N. & Drazin, P. G. 1964 J. Math. Phys. 43, 83.
Kuo, H. L. 1949 J. Meteor. 6, 105.
Malkus, W. V. R. 1968 To be published.
Rayleigh, LORD 1920 Scientific Papers, 6, 447. Cambridge University Press, England.
Stewartson, K. 1957 J. Fluid Mech. 3, 17.