Scattering of Tollmien-Schlichting waves as they pass over forward-/backward-facing steps

Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes (e.g., Tollmien-Schlichting (T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward- and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step (BFS) always has a greater impact than a forward-facing step (FFS). These facts agree with most of the previous investigations. However, one numerical study (WORNER, A., RIST, U., andWAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192-197 (2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results.