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Triple-shock entropy theorem and its consequences. (English) Zbl 0935.76036

The well-known triple shock theorem postulates that a sequence of two shocks has a lower entropy than a simple shock with the same final pressure. This theorem has important consequences for shock interactions. The intersection of three shocks, such as a Mach configuration, must have a contact. For the transition between a regular and Mach reflection, this suggests that the von Neumann criterion would be preferred based on thermodynamic stability. However, to explain the observed hysteresis of the transition, the authors propose an analogy with phase transitions in which locally stable wave patterns (regular or Mach reflection) play the role of meta-stable thermodynamic states. The transition threshold is affected by flow gradients in the neighbourhood of the shock intersection point, and the background fluctuations are due to acoustic noise. Consequently, the occurrence of hysteresis is sensitive to the experimental design, and only under special circumstances the hysteresis is observed.

MSC:

76L05 Shock waves and blast waves in fluid mechanics
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