On Converging Shock Waves
- Creators
- Schwendeman, D. W.
- Whitham, G. B.
Abstract
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.
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.Additional details
- Eprint ID
- 54176
- DOI
- 10.1098/rspa.1987.0116
- Resolver ID
- CaltechAUTHORS:20150128-095641303
- Office of Naval Research (ONR)
- Created
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2015-01-28Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field