Shock leakage through an unsteady vortex-laden mixing layer: application to jet screech

In an under-expanded supersonic jet, the interaction between shock-cell structure and vortices in a mixing layer generates intense tonal noise, called jet screech. This noise generation can be explained as a shock-leakage process through an unsteady vortex-laden mixing layer. This paper studies the shock-leakage mechanism based on a geometrical theory and direct numerical simulation (DNS) in two dimensions. In the limit of weak shocks, the analysis becomes analogous to geometrical acoustics: the eikonal equation demonstrates that shock waves tend to leak near the saddle points between vortices. Analysing the wavenumber vector, it is shown that the local vorticity behaves as a barrier against shocks. Using the unsteady DNS data, trajectories of the shock fronts are computed with the time dependent eikonal equation. Furthermore, the interaction between unsteady vortices and a compression wave is solved using DNS. The geometrical theory shows good agreement with DNS for shock-front evolution, but the amplitude of the leaked waves agrees only qualitatively. This study also investigates the effects of a temperature difference across the mixing layer. The analysis based on total internal reflection and the numerical results of both geometrical acoustics and DNS indicate that the direction of the radiated shock noise tends to rotate downstream as the jet temperature increases.