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Stability of a Compressible Two-Dimensional Vortex Under a Three- Dimensional Perturbation

E. G. Broadbent
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 392, No. 1803 (Apr. 9, 1984), pp. 279-299
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/2397541
Page Count: 21
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Stability of a Compressible Two-Dimensional Vortex Under a Three- Dimensional Perturbation
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Abstract

Kelvin showed that a two-dimensional vortex under a two-dimensional disturbance in incompressible flow responds at a discrete set of eigenvalues, which were found by Broadbent & Moore (Phil. Trans. R. Soc. Lond. A 290, 353-371 (1979) to become unstable in a compressible fluid. It is now shown that three-dimensional perturbations are also unstable provided the wavelength is greater than some critical value that depends on the Mach number of the vortex. A critical boundary dividing stable from unstable modes is defined. Most of the results relate to a Rankine vortex, as in the previous work mentioned above, but some results are also given for a vortex with a different velocity profile within the core; qualitatively the same kind of behaviour is found.

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