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Growth of localized disturbances on a vortex sheet

Published online by Cambridge University Press:  14 November 2011

A. D. D. Craik
A. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, North Haugh, St Andrews KY16 9SS
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Synopsis

Linearized local disturbances on a vortex sheet are known to develop singularities after a finite term in some cases but not in others. A simple test for the appearance of such singularities is given in terms of the Fourier transform of the initial disturbance. Such singularities are a consequence of the artificiality of the vortex sheet model and should not be regarded as physically meaningful.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 85 - 88
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Birkhoff, G.. Helmholtz and Taylor instability. Proc. Sympos. Appl. Math. XIII, 55–76 (Providence, R.I.: Amer. Math. Soc, 1962).Google Scholar
2Craik, A. D. D.. The development of wave packets in unstable flows. Proc. Roy. Soc. London Ser. A 373 (1981), 457–476.Google Scholar
3Craik, A. D. D.. The growth of localized disturbances in unstable flows. Trans. ASME J. Appl. Mech. 49 (1982), 284–290.Google Scholar
4Drazin, P. G. and Reid, W. H.. Hydrodynamic Stability (Cambridge: Cambridge University Press, 1981).Google Scholar
5Williams, J. E. Ffowcs. Sound sources in aerodynamics: fact and fiction. Proc. AIAA 19th Aerospace Sciences Meeting, AIAA-81–0056 (1981),Google Scholar
6Howe, M. S.. Transmission of an acoustic pulse through a plane vortex sheet. J. Fluid Mech. 43 (1970), 353–367.Google Scholar
7Jones, D. S. and Morgan, J. D.. The instability of a vortex sheet on a subsonic stream under acoustic radiation. Proc. Cambridge Philos. Soc. 72 (1972), 465–488.Google Scholar
8Jones, D. S.. The reflexion of an acoustic pulse by a plane vortex sheet. Proc. Cambridge Philos. Soc. 74 (1973), 349–364.CrossRefGoogle Scholar
9Merion, D. I., Baker, G. R. and Orszag, S. A.. Analytic structure of vortex sheet dynamics. Part 1. Kelvin-Helmholtz instability. J. Fluid Mech. 114 (1982), 283–298.Google Scholar
10Moore, D. W.. The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. Roy. Soc. London Ser. A 365 (1979), 105–119.Google Scholar
11Saffman, P. G. and Baker, G. R.. Vortex interactions. Ann. Rev. Fluid Mech. 11 (1979), 95–122.CrossRefGoogle Scholar