Nonlinear interaction of an acoustical wave with a counter-propagating weak shock

During its propagation, a shock wave may come across and interact with different perturbations, including acoustical waves. While this issue has been the subject of many studies, the particular acoustic-acoustic interaction between a weak shock and a sound wave has been very scarcely investigated. Here, a theory describing the encounter of those two waves is developed, up to second- and third-order. According to the incidence angle and shock strength, several regimes of acoustic transmission through the shock are identified. The generation of entropy as well as vorticity modes are determined, while the perturbation of the shock front by the acoustic wave is quantified. The theory predicts strongly different behaviors between air and water, and preliminary results are coherent with recent experimental observations in solids. It paves the way to both an acoustic monitoring of shock wave as well as a method to determine the quadratic and cubic nonlinear parameters of material.