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Resonance in flows with vortex sheets and edges

Published online by Cambridge University Press:  20 April 2006

Paul A. Durbin
Paul A. Durbin
Affiliation:
NASA Lewis Research Center, Cleveland, Ohio 44135
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Abstract

It is shown that the vortex sheet in a slot between two semi-infinite plates does not admit incompressible resonant perturbations. The semi-infinite vortex sheet entering a duct does admit incompressible resonance. These results indicate that the vortex-sheet approximation is less useful for impinging shear flows than for non-impinging flows. They also suggest an important role of downstream vortical disturbances in resonant flows.

The general solution for perturbations to flow with a vortex sheet and edges is written in terms of a Cauchy integral. Requirements on the behaviour of this solution at edges and at downstream infinity fix the criteria for resonance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 275 - 285
Copyright
© 1984 Cambridge University Press

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References

Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261–298.Google Scholar
Crighton, D. G. & Innes, D. 1981 Analytical models for shear-layer feedback cycles. AIAA Paper 81–0061, presented at the 19th Aerospace Sciences Meeting, St. Louis, MO.Google Scholar
Durbin, P. A. 1979 Asymptotic expansion of Laplace transforms about the origin using generalized functions. J. IMA 23, 181–192.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill..
Goldstein, M. E. 1981 The coupling between flow instabilities and incident disturbances at a leading edge. J. Fluid Mech. 104, 217–246.Google Scholar
Howe, M. S. 1981a The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations. J. Fluid Mech. 109, 125–146.Google Scholar
Howe, M. S. 1981b On the theory of unsteady shearing flow over a slot. Phil. Trans. R. Soc. Lond. A 303, 151–180.Google Scholar
Lighthill, M. J. 1975 Introduction to Fourier Analysis and Generalized Functions. Cambridge University Press.
Möhring, W. 1975 On flows with vortex sheets and solid plates. J. Sound Vib. 38, 403–412.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Ann. Rev. Fluid Mech. 11, 67–94.Google Scholar
Roos, B. W. 1969 Analytic Functions and Distributions in Physics and Engineering. Wiley.
Ziada, S. & Rockwell, D. 1982 Oscillations of an unstable mixing layer impinging upon an edge. J. Fluid Mech. 124, 307–334.Google Scholar