A weakly nonlinear analysis of transition in a hypersonic flow

We study responses of compressible Navier-Stokes equations to unsteady exogenous disturbances in a hypersonic flow over a double-wedge geometry. Our analysis of the laminar shock-boundary layer interaction reveals strong amplification of upstream disturbances with non-zero temporal frequency. We utilize a weakly nonlinear framework to investigate the early stages of transition to turbulence in the presence of such unsteady disturbances. We demonstrate that quadratic interactions of harmonic perturbations induce steady three-dimensional spanwise-periodic streaks. These streaks are amplified by the flow separation and serve as a precursor to transition further downstream. Our examination of the spatial structure of the streaks demonstrates that they can be reliably reproduced via a reduced-order dynamical representation. The low-dimensional models, such as those discovered in the present study, are critically important for the development of control-oriented models for transition to turbulence in hypersonic flows.