FOCUSING OF WEAK SHOCK-WAVES AND THE VON-NEUMANN PARADOX OF OBLIQUE SHOCK REFLECTION

Some phenomena involving intersection of weak shock waves at small ang les are considered: the focusing of curved fronts at aretes, the trans ition 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 sho ck reflection and to the curious transition between linear and fully n onlinear focusing investigated experimentally by Sturtevant and Kulkar ny [J. Fluid Mech. 73, 651 (1976)]. This ''triple-point paradox'' is s tudied in the context of an asymptotic model, and a solution is propos ed that involves an unusual kind of singularity.