The refraction of shock pairs

We study shock refractions at the interface between two materials with convex equations of state involving only two shocks, which we refer to as shock pairs or shock pair systems. We present experimental and computational evidence for the existence of both regular and irregular shock pair systems in gases and develop a von Neumann type theory for regular systems that one can use to predict the angle of incidence at which a regular shock pair will occur. We show regular shock pair refractions obey the Principle of Shock Reciprocity; i.e., if the two materials are exchanged there is no effect on the polar diagram of the regular shock pair system, the angle between the two shocks in the pair or the streamline deflection angle. We also study regular and irregular shock pair systems in gases numerically and compare the numerical results with experimental data and our theory.