Counterexamples to the sonic criterion

TL;DR

This paper challenges the sonic criterion for shock reflection, showing that regular reflection can occur with transonic shocks and that shock strength, not flow type, determines stability.

Contribution

It proves that the sonic criterion is incorrect by demonstrating the existence of regular reflections with transonic shocks in polytropic potential flow.

Findings

Existence of open parameter sets with transonic regular reflection

Reflected shock strength, not flow type, influences stability

Sonic criterion does not accurately predict shock reflection types

Abstract

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, it has been an open problem to predict precisely for what 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 \emph{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.