Shock propagation in granular flow subjected to an external impact.

We analyze a recent experiment [Boudet, Cassagne, and Kellay, Phys. Rev. Lett. 103, 224501 (2009)] in which the shock created by the impact of a steel ball on a flowing monolayer of glass beads is studied quantitatively. We argue that radial momentum is conserved in the process and hence show that in two dimensions the shock radius increases in time t as a power law t{1/3}. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction and are shown to compare well at intermediate times. At long times the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to the accumulation of particles at the shock front and propose a simple hard sphere model that incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.