A state-of-the-knowledge review on pseudo-steady shock-wave reflections and their transition criteria

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The distinguished philosopher Ernst Mach published the first known paper on the phenomenon of planar shock-wave reflections over straight wedges over 125 years ago in 1878. In his publication he presented two wave configurations that could result from this reflection process, a regular reflection (RR) and a configuration that was later named after him and called Mach reflection (MR) in the early 1940s. In 1945, Smith reported on an additional wave configuration, which had a reflected shock wave that was slightly different from that of the just-mentioned Mach reflection. Smith (OSRD Rep. 6271, Off. Sci. Res. Dev., 1945) did not ascribe any special importance to the wave configuration that he observed. The wave configuration that was observed and reported by Smith (OSRD Rep. 6271, Off. Sci. Res. Dev., 1945) was recognized as an independent one only about 5 years later when White (Tech. Rep. II-10, Princeton Univ. Dept. Phys., 1951) reported on the discovery of a new wave configuration that was named double-Mach reflections (DMR) because it had similar features to that of the Mach reflection wave configuration but all the features were doubled. For this reason the Mach reflection wave configuration has been re-named single-Mach reflection (SMR). (Until the late 1970s it was called simple-Mach reflection although nothing is simple about it.). The discovery of the double-Mach reflection revealed that the wave configuration that was first observed by Smith was an intermediate wave configuration between the SMR and the DMR wave configurations. For this reason it was named transitional-Mach reflection (TMR) (Until the early 1980s it was called complex-Mach reflection although it is not the most complex one.). Since the discovery of the DMR many investigations were aimed at elucidating the exact transition criteria between the above-mentioned four different wave configurations as well as some additional configurations and sub-configurations that were discovered later. In 1991 Ben-Dor published a monograph, entitled "Shock Wave Reflection Phenomena", that was, in fact, a state-of-the-knowledge review of the phenomena. This state-of-the-knowledge will be referred to in the followings as the "old"-state-of-the-knowledge (This state-of-the-knowledge existed until the mid 1990s. A few years later Li and Ben-Dor (Shock Wave 5(1/2), 59-73, 1995) modified the analytical approach for evaluating the transition criteria from the single-Mach to the transitional- Mach reflection (SMR ⇄ TMR) and from the transitional-Mach to the double-Mach reflection (TMR ⇄ DMR) and presented some modified and new criteria for the formation and termination of both the TMR and DMR wave configurations. Experimental results from various sources revealed that the transition boundaries between the SMR, TMR and DMR wave configurations that were based on the modified analytical approach were better than those of the "old" state-of-the-knowledge that as mentioned earlier was summarized in Ben-Dor's (Shock Wave Reflection Phenomena, Springer, 1991) monograph. Unfortunately, however, the results of Li and Ben-Dor's (Shock Wave 5(1/2), 59-73, 1995) modified analytical approach have not been internalized, and publications by various scientists in the past decade neglected the revised and better transition criteria and kept on referring to the old and wrong criteria that appeared in Ben-Dor's (Shock Wave Reflection Phenomena, Springer, 1991) monograph. For this reason, a state-of-the-knowledge review that is based on the above-mentioned 10-year-old findings of Li and Ben-Dor (Shock Wave 5(1/2), 59-73, 1995) is presented herein. At the first step, the "old" state-of-the-knowledge is presented.

Original languageEnglish
Pages (from-to)277-294
Number of pages18
JournalShock Waves
Issue number3-4
StatePublished - 1 Jul 2006


  • Shock wave diffractions
  • Shock-wave reflections
  • Transition criteria

ASJC Scopus subject areas

  • Mechanical Engineering
  • General Physics and Astronomy


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