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

Abstract

The interaction between a forward-facing step (FFS) and single-frequency Tollmien-Schlichting (TS) waves is investigated with experiments and two-dimensional (2D) Direct Numerical Simulations (DNS). Dedicated hot-wire anemometry (HWA) and particle image velocimetry (PIV) measurements in the vicinity of the FFS provide a characterization of the perturbation field, as well as validation of the DNS results. Comparison between experiments, 2D-DNS, and Linear Parabolized Stability Equations (LPSE) confirm the two-dimensional 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. LST results suggest the presence of superimposed modes on the original TS mode in this region. Despite their decay in 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, characterized by a region of stabilization followed by destabilization further downstream. Eventually, the TS waves realign to their asymptotic (modal) behavior. Overall, the FFS destabilizes the TS wave far downstream. However, the streamwise extent and magnitude of the stabilization downstream of the FFS remain significant. The stability mechanisms identified in this work could guide future research in designing step geometries that leverage the local stabilization downstream of the step to achieve transition delay.