Optimal growth in a high-speed Görtler vortex flow

Optimal growth in Görtler vortex flow over a concave wall at Mach 6 is investigated via well-established parabolized governing equations (PSE3D-APSE3D). The influence of parameters, i.e., the initial/final positions and the frequency, is studied, and the physical mechanism of optimal growth is explored. The optimal growth consists of an algebraic growth stage near the initial location and a subsequent quasi-exponential growth stage. The algebraic growth is dominated by a combination of the lift-up effect and the Orr mechanism. High-frequency disturbances initially tilt against the flow direction and amplify via the Orr mechanism during downstream rotation. The quasi-exponential growth of optimal disturbances is governed by the modal instability mechanisms. Energy analysis results indicate that both the spanwise and wall-normal components of the optimal antisymmetric disturbance are relatively important downstream. For the optimal antisymmetric disturbance, the wall-normal component consistently dominates throughout the growth evolution. Optimal growth gains energy from the strong wall-normal and spanwise shear.