Critical interaction of a shock wave with an acoustic wave

The interaction of linear waves with normal or oblique shock waves has been studied by Moore [NACA Report No. 1165 (1954)], Ribner [AIAA J. 23 (1984)], and McKenzie and Westphal [Phys. Fluids 11, 2350 (1968)] by writing the fluctuating quantities as normal modes. These different studies have shown that downstream of the shock exists a critical angle of the incident acoustic waves where the reflection coefficient is equal to 1. The purposes of this paper are first to point out that this critical angle may appear as a singularity in the linearized Euler equations, and second to show that this problem can actually be removed if the perturbation is no longer assumed to be a normal mode but has a mathematical form which is strictly deduced from the mathematical nature of the linearized Euler equations. This analysis is then applied to the shock wave oscillations occurring on a wing profile and in a nozzle. Despite many simplifications, good results are obtained in comparison with the available experimental data. (C) 2001 American Institute of Physics.