Counterexamples to the Sonic Criterion

We consider self-similar (pseudo-steady) shock reflection at an oblique wall. There are three parameters: wall corner angle, Mach number, angle of incident shock. Ever since Ernst Mach discovered the irregular reflection named after him, researchers have sought to predict precisely for which parameters the reflection is regular. Three conflicting proposals—the detachment, sonic and von Neumann criteria—have been studied extensively without a clear result. We demonstrate that the sonic criterion is not correct. We consider polytropic potential flow and prove that there is an open nonempty set of parameters that admit a global regular reflection with a reflected shock that is transonic. We also provide a clear physical reason: the flow type (sub- or supersonic) is not decisive; instead the reflected shock type (weak or strong) determines whether structural perturbations decay towards the reflection point.