Page:Threeshockwaves.pdf/11

Mach reflection occurring on the "unstable" branch of the regular reflection may indeed be realized under suitable circumstances. If we should accept this, the question as to what happens when the angle of incidence of a relatively weak shock be gradually increased raises some peculiarly delicate considerations. Specifically, what may be expected to happen if a shock of intensity $\zeta =1.111$ be allowed to be incident on rigid surface at an angle of $47.5^{\circ }$. Will a stable reflection with $\alpha '\simeq 47.5^{\circ }$ or the unstable reflection with $\alpha '\simeq 84^{\circ }$ or a Mach effect with $\alpha '\simeq 96.5^{\circ }$ occur? The situation corresponding to the first and the last of the three alternatives enumerated can apparently be realized under suitable circumstances. This places the so called "unstable" reflections in a very peculiar position. It is not impossible that laboratory experiments may settle these questions more effectively than theoretical discussions.

Finally in Fig. * we have an intermediate case. Here we have considered three shock solutions for an incident shock with $\zeta =2$. For this case the stationary Mach reflection also occurs on the unstable branch of the regular reflection but in this case the two solutions for the reflection doe not differ very appreciably.

S. Chandrasekhar