A reconsideration of the transition criterion from mach to regular reflection over cylindrical concave surfaces

Following the idea forwarded by Ben-Dor and Takayama (1985) a new propagation path was assumed for the corner generated signals. In addition to the new chosen propagation path, one of the simplified assumptions used by Ben-Dor and Takayama, namely that u+a remains constant behind the incident shock wave, was further simplified, i.e., both u and a were assumed to be constant behind the incident shock wave. This new path and the further simplified assumption led to a new transition criterion from Mach to regular reflection over a cylindrical wedge which unlike the two criteria developed in Ref. by Ben-Dor and Takayama (1985) has the ability to predict the transition wedge angle quite accurately in the entire range of the incident shock wave Mach numbers which were investigated in Ref. by Ben-Dor and Takayama(1985) and in this study.