It is well known that the classical three-shock theory of von Neumann (1943) does not adequately describe the configuration of the shocks close to the triple-point of a Mach reflection of an incident shock with a Mach number less than about 1.5. The assumptions on which the three-shock theory is based have been examined and several of them are shown to be invalid. The assumption that may be of most significance is that the normal components of the flows behind the reflected and the Mach stem shocks are parallel. Dropping this assumption removes an essential equation in the three-shock solution. An alternative assumption, based on experimental observation, is that there is an approximate linear relationship between the pressure behind the reflected shock and the triple-point trajectory angle. This assumption permits a revised three-shock solution which gives results that are in agreement with experimental observations of reflections of incident shocks with Mach numbers between 1.1 and 1.5.
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Olim, M., Dewey, J.M. A revised three-shock solution for the Mach reflection of weak shocks (1.1<M i<1.5). Shock Waves 2, 167–176 (1992). https://doi.org/10.1007/BF01414639
- Mach reflection
- von Neumann paradox