Propagation of spherical weak blast waves over rough periodic surfaces

Spherical weak blast propagation above a rough periodic surface is investigated by performing numerical simulations of the Euler equations. The study of the reflection pattern shows that waves diffracted by the surface asperities merge to form an effective reflected shock. It is initially detached from the incident shock but gradually catches up with it. If the source energy is sufficient, the reflected shock interacts with the incident one and Mach reflection occurs. Thus, the triple point has a similar trajectory to that over a smooth surface. In addition, the maximal overpressure is shown to be greater for small roughness scales in a layer near the surface. Far from the surface, it is close to that of a smooth surface for small roughness scales and to the free field for the highest ones. The increase in the maximal overpressure is related to oscillations on the waveforms that appear behind the shock. These properties are associated with the existence of a surface wave that propagates along the surface. Comparison of results in the linear regime with an analytic solution confirms this explanation.