Regular Reflection in Self-Similar Potential Flow and the Sonic Criterion

Abstract

Reflection of a shock from a solid wedge is a classical problem in gas dynamics. Depending on the parameters either a regular or a irregular (Mach-type) reflection results. We construct regular reflection as an exact self-similar solution for potential flow. For some upstream Mach numbers $M_I$ and isentropic coefficients $\gamma$, a solution exists for all wedge angles $\theta$ allowed by the sonic criterion. This demonstrates that, at least for potential flow, weaker criteria are false.