Convective instabilities in a laminar shock-wave/boundary-layer interaction

Linear stability analyses are performed to study the dynamics of linear convective instability mechanisms in a laminar shock-wave/boundary-layer interaction at Mach 1.7. In order to account for all two-dimensional gradients elliptically, we introduce perturbations into an initial-value problem that are found as solutions to an eigenvalue problem formulated in a moving frame of reference. We demonstrate that this methodology provides results that are independent of the numerical setup, frame speed, and type of eigensolutions used as initial conditions. The obtained time-integrated wave packets are then Fourier-transformed to recover individual-frequency amplification curves. This allows us to determine the dominant spanwise wavenumber and frequency yielding the largest amplification of perturbations in the shock-induced recirculation bubble. By decomposing the temporal wave-packet growth rate into the physical energy-production processes, we provide an in-depth characterization of the convective instability mechanisms in the shock-wave/boundary-layer interaction. For the particular case studied, the largest growth rate is achieved in the near-vicinity of the bubble apex due to the wall-normal (productive) and streamwise (destructive) Reynolds-stress energy-production terms. We also observe that the Reynolds heat-flux effects are similar but contribute to a smaller extent.