Acoustic receptivity of high-speed boundary layers on a flat plate at angles of attack

Direct numerical simulation and theoretical analysis of acoustic receptivity are performed for the boundary layer on a flat plate in Mach 6 flow at various angles of attack (AoA). Slow or fast acoustic wave passes through: a bow shock at AoA \(=-5^{\circ }\), a weak shock induced by the viscous–inviscid interaction at AoA \(=0^{\circ }\) or an expansion fan emanating from the plate leading edge at AoA \(=5^{\circ }\). The study is focused on cases where the integral amplification of unstable mode S (or Mack second mode) is sufficiently large \((N\approx 8.4)\) to be relevant to transition in low-disturbance environments. It is shown that excitation of dominant modes F and S occurs in a small vicinity of the plate leading edge. The initial disturbance propagates further downstream in accord with the two-mode approximation model accounting for the mean-flow nonparallel effects and the intermodal exchange mechanism. This computationally economical model can be useful for predictions of the second mode dominated transition onset using the physics-based amplitude method.