Non-uniqueness of solutions in asymptotically self-similar shock reflections

The present study addresses the self-similar problem of unsteady shock reflection on an inclined wedge. The start-up conditions are studied by modifying the wedge corner and allowing for a finite radius of curvature. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the start-up condition, as the flow “remembers” how it was started. Substantial differences were found. For example, the type of shock reflection for an incident shock Mach number $M=6.6$ and an isentropic exponent $\gamma =1.2$ changes from regular to Mach reflection between ${44}^{\circ }$ and ${45}^{\circ }$ when a straight wedge tip is used, while the transition for an initially curved wedge occurs between ${57}^{\circ }$ and ${58}^{\circ }$.