Description:
<jats:p>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.</jats:p>