Modal and non-modal transition scenarios of compression ramp flows at a range of Reynolds numbers*

Transition to turbulence of laminar compressible flow over a compression ramp has been addressed using modal and non-modal stability analysis. The importance of highly accurate base states has been identified leading us to analyse steady base states obtained by high-order temporal and spatial discretization schemes. These steady states have been compared with theoretical solutions of the triple-deck equations and excellent agreement has been shown. Modal analysis was employed to obtain the neutral loop pertaining to the leading stationary, three-dimensional global flow eigenmode. Globally stable eigenmodes in the spectrum were found to correspond to Mack mode, also seen in experiments. An impedance well between the wall and separation shock is also presented which has the ability to sustain and trap thermoacoustic waves downstream of separation. Non-modal global stability analysis performed demonstrated that large transient energy growth of linear perturbations can lead to transition substantially earlier than the time needed for modally unstable perturbations to grow (exponentially) to nonlinear levels.