Hu, W., Hickel, S., van Oudheusden, B.W. (2019) *Phys. Rev. Fluids* 4, 103904. doi: 10.1103/PhysRevFluids.4.103904

The transition mechanism and unsteady behavior behind a backward-facing step (BFS) in the supersonic regime at Ma = 1.7 and Re_{δ} = 13718 is investigated using large-eddy simulation (LES). The visualization of the flow field shows that the transition process behind the step is initiated by a Kelvin-Helmholtz (K-H) instability of the separated shear layer, followed by secondary modal instabilities of the K-H vortices, leading to lambda-shaped vortices, hair-pin vortices and finally to a fully turbulent state.

The separation system features a broadband low-frequency dynamics in the range of f δ_{0}/u_{∞} = 0.003 ... 0.20 as concluded from the spectral and statistical analysis. Dynamic mode decomposition suggests that the medium frequency motions centered around f δ_{0}/u_{∞} = 0.06 are related to the interactions between reattaching and the shedding of large coherent shear vortices, while the lower (f δ_{0}/u_{∞} = 0.01) and higher (f δ_{0}/u_{∞} = 0.1) frequency unsteadiness are associated with the periodical expansion and shrinking of the separation system and the convection of upstream K-H vortices, respectively. All these three unsteady mechanisms are coupled to the laminar-to-turbulent transition process in the different stages.