The effect of a forward-facing step on Tollmien–Schlichting waves

The interaction between a forward-facing step (FFS) and single-frequency Tollmien–Schlichting (TS) waves is investigated with experiments and two-dimensional (2-D) direct numerical simulations (DNS). Dedicated hot-wire anemometry and particle image velocimetry measurements in the vicinity of the FFS provide characterisation of the perturbation field, as well as validation of the DNS results. Comparison between experiments, 2-D DNS, and linear parabolised stability equations confirm the 2-D nature of the flow and the linearity of the instability mechanisms around the FFS. Upstream of the step, TS waves are gradually amplified by the increasing adverse pressure gradient. In the step vicinity, both mean flow and perturbation field exhibit abrupt distortion, with decoupling of the base flow-oriented growth rate components indicating significant non-modal evolution. Downstream of the step, the mean flow recovers to baseline conditions, but the perturbation field remains highly distorted. Linear stability theory results suggest the presence of superimposed modes on the original TS mode in this region. Despite their decay in the streamwise direction, their presence imprints modifications in the TS wave growth and shape, manifested as the tilting of the perturbation structure in and against the mean flow shear direction. This initiates a reversed Orr mechanism, characterised by a region of stabilisation followed by destabilisation further downstream. Eventually, the TS waves realign to their asymptotic (modal) behaviour. Overall, the FFS destabilises the TS wave far downstream. However, the streamwise extent and magnitude of the stabilisation downstream of the FFS remain significant.