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On the Von Neumann Paradox of Weak Mach Reflection* |
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| Authors: | Akira Sakurai L F Henderson Kazuyoshi Takayama Zbigniew Walenta Philip Colella |
| Affiliation: | Department of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama, 350-03, Japan Department of Mechanical Engineering, University of Sydney, Australia Institute of High Speed Mechanics, Tohoku University, Sendai, 980, Japan Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw, Poland Lawrence Livermore National Laboratory, University of California, Berkeley, USA |
| Abstract: | Recent experimental and numerical studies of weak Mach reflections are examined. It is shown that the fundamental reason for the von Neumann paradox is that his theory of Mach reflection is based on the assumption that the flow downstream of the reflected wave and the Mach shock near the wave triple point is uniform. The assumption is shown to be valid for strong Mach reflection which agrees with experiment, but invalid for weak Mach reflection which does not agree with experiment. It is also shown that viscous effects are dominant when the incident shock is within about 100 mean free path lengths of the corner, but not otherwise. The analytical theory of the entire subsonic region supports these conclusions. |
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