Numerous experimental investigations on the reflection of plane shock waves over
straight wedges indicated that there is a domain, frequently referred to as the weak shock wave
domain, inside which the resulted wave configurations resemble the wave configuration of a Mach
reflection although the classical three-shock theory does not provide an analytical solution. This
paradox is known in the literature as the von Neumann paradox.
While numerically investigating this paradox Colella & Henderson [1] suggested that the
observed reflections were not Mach reflections but another reflection, in which the reflected wave
at the triple point was not a shock wave but a compression wave. They termed them it von Neumann
reflection. Consequently, based on their study there was no paradox since the three-shock theory
never aimed at predicting this wave configuration.
Vasilev & Kraiko [2] who numerically investigated the same phenomenon a decade later
concluded that the wave configuration, inside the questionable domain, includes in addition to the
three shock waves a very tiny Prandtl-Meyer expansion fan centered at the triple point. This wave
configuration, which was first predicted by Guderley [3], was recently observed experimentally by
Skews & Ashworth [4] who named it Guderley reflection.
The entire phenomenon was re-investigated by us analytically. It has been found that there are in
fact three different reflection configurations inside the weak reflection domain:
• A von Neumann reflection – vNR,
• A yet not named reflection – ?R,
• A Guderley reflection – GR.
The transition boundaries between MR, vNR, ?R and GR and their domains have been
determined analytically.
The reported study presents for the first time a full solution of the weak shock wave domain,
which has been puzzling the scientific community for a few decades.
Although the present study has been conducted in a perfect gas, it is believed that the reported
various wave configurations, namely, vNR, ?R and GR, exist also in the reflection of shock waves
in condensed matter.
Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection
