Perturbation Analysis of Nonlinear Stages in Hypersonic Transition

Abstract

Linear theory continues to play a critical role in extracting the underlying primary instability dynamics of boundary layer transition. However, such methods have difficulty in isolating the dynamics of secondary instabilities, which dominate the later stages of transition. A Floquet analysis can bridge this gap; however, typical matrix-based approaches can be cumbersome to implement in general compressible scenarios. We address this difficulty by developing a matrix-free perturbation technique to extract the three-dimensional linearized secondary dynamics of compressible inhomogeneous flowfields. The method can be implemented into traditional Navier-Stokes codes in a straightforward manner. It is then used to examine the transition mechanism in a hypersonic boundary layer saturated by a second-mode instability. The linear response of the time-periodic basic-state is shown to precisely identify the non-parallel amplification and breakdown of oblique modes that disintegrate the boundary layer. It also correctly predicts the fundamental resonance mechanism that leads to transition.