Consideration of von Neumann Reflection and Mach Reflection for Strong Shock Waves

  • S. Kobayashi
  • T. Adachi


Oblique shock reflection phenomena have been long considered to preserve selfsimilarity. However, the authors’ investigation of von Neumann reflection [1] was a turning point that cast doubt on self-similarity. The von Neumann reflection is a new type of oblique reflection first referred to by Colella and Henderson [2]. This reflection is geometrically characteristic in that a Mach stem is tangentially connected with an incident shock at a triple point. Furthermore, its reflected wave is very weak and a slipstream is barely optically observable (Fig. 1 (a)), and stands in contrast to ordinary Mach reflection (Fig. 1 (b)). This reflection takes place when the incident shock Mach number M i and/or the reflecting wedge angle θ w are small. According to Colella and Henderson [2], von Neumann reflection exhibits the von Neumann paradox. For weak shock waves, Kobayashi et al. [1, 3] found that, as the incident shock proceeds, the wave angles vary along a trivial solution curve of von Neumann’s three-shock theory, while the triple point moves along a straight line passing through the wedge apex as if self-similarity holds. Further investigations [4] revealed experimentally that oblique shock reflection in a shock tube is generally non-self-similar, even though the triple-point trajectory is linear. This non-selfsimilarity is a new idea requring reconsideration of the von Neumann paradox.


Shock Wave Triple Point Shock Tube Incident Shock Wedge Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kobayashi, S., Adachi, T., Satoh, M., Suzuki, T.: On the Formation Mechanism of von Neumann Reflection. In: Proc. Int. Shock Wave Symp., vol. 21, pp. 881–885 (1997)Google Scholar
  2. 2.
    Colella, P., Henderson, L.F.: The von Neumann Paradox for the Diffraction of Weak Shock Waves. J. Fluid. Mech. 213, 71–94 (1990)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Kobayashi, S., Adachi, T., Suzuki, T.: Non-self-similar Behavior of the von Neumann Reflection. Phys. Fluids 12(7), 1869–1877 (2000)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kobayashi, S., Adachi, T., Suzuki, T.: Non-self-similar Characteristics of Weak Mach Reflection: the von Neumann Paradox. Fluid. Dyn. Res. 35, 275–286 (2004)zbMATHCrossRefGoogle Scholar
  5. 5.
    Sasoh, A., Takayama, K., Saito, T.: A Weak Shock Reflection over Wedges. Shock Waves 2(4), 277–281 (1992)CrossRefGoogle Scholar
  6. 6.
    Sasoh, A., Takayama, K.: Characterization of Disturbance Propagation in Weak Shock-wave Reflection. J. Fluid. Mech. 277, 331–345 (1994)CrossRefGoogle Scholar
  7. 7.
    Itabashi, S., Henderson, L.F., Crutchfield, W.Y., Takayama, K.: Effetcs of Viscous and Thermal Dissipation on the Eruption of Mach Reflection on Rigid Steel Ramps. In: Proc. Int. Shock Wave Symp., vol. 21, pp. 887–891 (1997)Google Scholar
  8. 8.
    Kobayashi, S., Adachi, T.: Unsteady Behavior in the Transition Phenomenon of Shock Reflection Nagare. J. Japan Society Fluid. Mechanics 18, 387–390 (1999) (in Japanese)Google Scholar
  9. 9.
    Kobayashi, S., Adachi, T., Suzuki, T.: On the Unsteady Transition Phenomenon of Weak Shock Waves. Theoret. Appl. Mech. 49, 271–278 (2000)Google Scholar
  10. 10.
    Kobayashi, S., Adachi, T., Suzuki, T.: The von Neumann Paradox for Strong Shock Waves. In: Proc. Int. Shock Wave Symp., vol. 27, pp. 1539–1542 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • S. Kobayashi
    • 1
  • T. Adachi
    • 1
  1. 1.Department of Mechanical EngineeringSaitama Institute of TechnologyFusaijiJapan

Personalised recommendations