Giant and anomalous Doppler effect, negative transmission and meta-like interaction between an acoustical wave and a weak shock.

The interaction of a weak shock wave in a fluid with an incident sound wave is investigated, either in the counter- or co-propagating cases. This last situation is possible because the shock wave moves supersonically and overcomes the sonic sound wave. For a sustained shock, the problem can be solved analytically by introducing a transmitted sound wave, a vorticity mode and an entropy mode in the post-shock region, and a perturbation of the shock front. Due to the relative motions of the shock and the incident wave, a Doppler effect occurs. The analysis of the eight possible regimes of interaction outlines the influence of the shock strength. For an intermediate range of angles, transmitted waves are observed. For the highest incidence angles in the co-propagating case, the transmitted wave is propagative again but exhibits meta-like properties similar to those searched for in artificial meta-materials. These properties are negative transmission, or reversal of the direction of the transmitted wave along the shock front, and anomalous Doppler effect (Doppler ratio smaller than unity).