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The instability of a non-uniform vortex sheet

Published online by Cambridge University Press:  28 March 2006

L. M. Hocking
L. M. Hocking
Affiliation:
University College London, Gower Street, W.C. 1
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Abstract

The classical Kelvin-Helmholtz problem of the instability of the vortex sheet between two uniform streams is extended to allow for non-uniformity in the streams. A small-wavelength approximation shows that the most unstable disturbances have a growth rate proportional to the greatest discontinuity of velocity at the vortex sheet. The solution for all wavelengths is found for two cases when the variation in the stream velocity is small compared with the stream velocity itself. One of these cases indicates that a transverse variation in the stream velocity can increase the instability for long wavelengths, but only to a small extent.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 2 , February 1964 , pp. 177 - 186
Copyright
© 1964 Cambridge University Press

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References

Benjamin, T. Brooke 1963 J. Fluid Mech. 16, 436.
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Greenspan, H. P. & Benney, D. J. 1963 J. Fluid Mech. 15, 133.
Lighthill, M. J. 1958 Fourier Analysis and Generalized Functions, p. 49. Cambridge University Press.
Mangler, K. W. & Smith, J. H. B. 1959 Proc. Roy. Soc. A, 251, 200.