On the synchronisation of three-dimensional shock layer and laminar separation bubble instabilities in hypersonic flow over a double wedge

Linear three-dimensional instability is studied in the shock layer and the laminar separation bubble (LSB) induced by shock-wave/boundary-layer interactions in a Mach 7 flow of nitrogen over a double wedge with a $30^{\circ }\text {--}55^{\circ }$ cross-sectional profile. At a free-stream unit Reynolds number $Re=5.2\times 10^{4}\,{\rm m}^{-1}$ this flow exhibits rarefaction effects and has shock thicknesses comparable to the thickness of the boundary layer at separation. Flow features have been fully resolved using a high-fidelity massively parallel implementation of the direct simulation Monte Carlo method that captures the flow evolution from the inception of three-dimensionality, through linear growth of instabilities, to the early stages of nonlinear saturation. It is shown that the LSB sustains self-excited, small-amplitude perturbations that originate past the primary separation line and lead to spanwise-periodic wall striations inside the bubble and downstream of the primary reattachment line, as known from earlier experiments, simulations and instability analyses. A spanwise-periodic instability, synchronised with that in the separation zone, is identified herein for the first time, which exists in the internal structure of the separation and detached shock layers, and manifests itself as spanwise-periodic cats-eyes patterns in the global mode amplitude functions. The growth rate and the spanwise-periodicity length of linear disturbances in the shock layers and the LSB are found to be identical. Linear amplification of the most unstable three-dimensional flow perturbations leads to synchronised low-frequency unsteadiness of the triple point, with a Strouhal number of $St\approx 0.028$ .