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Interaction of a shock wave with a mixing region

Published online by Cambridge University Press:  28 March 2006

N. Riley
N. Riley
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

The interaction of a simple wave, in steady supersonic flow, with a two-dimension mixing region is treated by applying Fourier analysis to the linearized equations of motion. From asymptotic forms for the Fourier transforms of physical quantities, for large wave-number, the dominant features of the resulting flow pattern are predicted; in particular it is found that a shock wave, incident on the mixing region, is reflected as a logarithmically infinite ridge of pressure. For two particular Mach-number distributions in the undisturbed flow, numerical solutions are obtained, showing greater detail than the results predicted by the asymptotic approach. A method is given whereby the linear theory may be improved to take into account some non-linear effects; and the reflected wave, for an incident shock wave, is then seen to consist of a shock wave, gradually diminishing in strength, followed by the main expansion wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 3 , March 1960 , pp. 321 - 339
Copyright
© 1960 Cambridge University Press

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References

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