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Experiments on the instability of stratified shear flows: immiscible fluids

Published online by Cambridge University Press:  29 March 2006

S. A. Thorpe
S. A. Thorpe
Affiliation:
National Institute of Oceanography, Wormley, Godalming, Surrey
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Abstract

When a long rectangular tube containing two immiscible fluids is slightly tilted away from the horizontal, a uniformly accelerating flow is produced with shear at the interface. The presence of shear leads to instability, which is characterized by the spontaneous and rapid growth of almost stationary waves if the fluid depths are equal and the density difference small. The conditions for the onset of Kelvin-Helmholtz instability, taking account of the accelerating flow and the presence of a velocity transition region at the interface, are investigated theoretically and comparison made with observations. The time at which instability occurs is quite well predicted by this theory, but the wavelength of the unstable waves is rather greater than predicted in the accelerating flow. The difference between the predictions and observations may be the result of finite amplitude effects or of the development of Tollmien-Schlichting instability before Kelvin-Helmholtz.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 1 , 23 October 1969 , pp. 25 - 48
Copyright
© 1969 Cambridge University Press

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References

Abramowitz, M. & Stegun, A. 1965 Handbook of Mathematical Functions. New York: Dover.
Benjamin, T. B. 1960 J. Fluid Mech. 9, 513.
Benjamin, T. B. 1963 J. Fluid Mech. 16, 436.
Davies, J. T. & Rideal, E. K. 1963 Interfacial Phenomena, 2nd ed. New York: Academic.
Holmboe, J. 1962 Geofys. Public. 24, 67.
Kelvin, LORD 1871 Phil. Mag. 42, 368, and Mathematical and Physical Papers 4, 76.
Landahl, M. T. 1962 J. Fluid Mech. 13, 609.
Lock, R. C. 1954 Proc. Camb. Phil. Soc. 50, 105.
Sohlichting, H. 1955 Boundary Layer Theory. London: Pergamon.
Thorpe, S. A. 1968 J. Fluid Mech. 32, 693.