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The decay of a plane shock wave

Published online by Cambridge University Press:  29 March 2006

H. Ardavan-Rhad
H. Ardavan-Rhad
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

An analytic solution of the non-isentropic equations of gas-dynamics, for the one-dimensional motion of a non-viscous and non-conductive medium, is derived in this paper for the first time. This is a particular solution which contains only one arbitrary function. On the basis of this solution, the interaction of a centred simple wave with a shock of moderate strength is analyzed; and it is shown that, for a weak shock, this analysis is compatible with Friedrichs's theory. Furthermore, in the light of this analysis, it is explained why the empirical methods employed by the shock-expansion theory, including Whitham's rule for determining the shock path, work.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 4 , 2 October 1970 , pp. 737 - 751
Copyright
© 1970 Cambridge University Press

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References

Ardavan-Rhad, H. 1969 Dynamics of cosmic explosions. Ph.D. thesis, University of Cambridge.
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. New York: Interscience.
Eggars, A. J., Savin, R. C. & Syverston, C. A. 1955 The generalized shock-expansion method and its application to bodies travelling at high supersonic air speeds. J. Aero. Sci. 22, 231.Google Scholar
Friedrichs, K. O. 1947 Formation and decay of shock waves. Institute for Mathematics and Mechanics, New York University no. 158.Google Scholar
Mahony, J. J. 1955 A critique of shock-expansion theory. J. Aero. Sci. 22, 673.Google Scholar
Stanyukovich, K. P. 1960 Unsteady Motion of Continuous Media (translated by M. Holt). Oxford: Pergamon.
Whitham, G. B. 1958 On the propagation of shock waves through zones of non-uniform area or flow. J. Fluid Mech. 4, 337.Google Scholar