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On Converging Shock Waves

Schwendeman, D. W. and Whitham, G. B. (1987) On Converging Shock Waves. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 413 (1845). pp. 297-311. ISSN 1364-5021. doi:10.1098/rspa.1987.0116.

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An approximate theory of shock dynamics is used to study the behaviour of converging cylindrical shocks. For cylindrical shocks with regular polygonal-shaped cross sections, exact solutions are found, showing that an original polygonal shape repeats at successive intervals with successive contractions in scale. In this sense, these shapes are stable, and the successive Mach numbers increase according to exactly the same formula as for a circular cylindrical shock. The behaviour for initial shock shapes close to these and the general tendency of perturbed circular shapes to become polygonal, not necessarily regular, is explored numerically. Further analytical results are provided for rectangular shapes. Comments are made on the interpretation of regular reflection in this theory and on converging shocks in three dimensions.

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Additional Information:© 1987 The Royal Society. Received 6 February 1987. This research was supported by the office of Naval Research, U.S. Navy. Computations were performed on the Caltech Applied Mathematics IBM-4341 computer with time donated by the IBM corporation.
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Office of Naval Research (ONR)UNSPECIFIED
Issue or Number:1845
Record Number:CaltechAUTHORS:20150128-095641303
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Official Citation: On Converging Shock Waves D. W. Schwendeman and G. B. Whitham Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 413, No. 1845 (Oct. 8, 1987) , pp. 297-311 Published by: The Royal Society Stable URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54176
Deposited On:28 Jan 2015 20:02
Last Modified:10 Nov 2021 20:30

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