Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection

Some phenomena involving intersection of weak shock waves at small angles are considered: the focusing of curved fronts at arêtes, the transition between regular and irregular reflection of oblique shock waves on rigid walls and the diffraction patterns arising behind obstacles. The intersection of three shock waves plays a central role in most of these phenomena, giving rise to the von Neumann paradox of oblique shock reflection and to the curious transition between linear and fully nonlinear focusing investigated experimentally by Sturtevant and Kulkarny [J. Fluid Mech. 73, 651 (1976)]. This ‘‘triple-point paradox’’ is studied in the context of an asymptotic model, and a solution is proposed that involves an unusual kind of singularity.