On the linear stability of boundary-layer flows induced by the translation of a wavy surface

We consider the linear stability of steady boundary-layer flows induced by the translation of a moving wavy surface. The wavy surface has a sinusoidal profile and is considered here as a model for surface roughness. Previous studies have used similar surface-roughness models when analysing roughness effects on three-dimensional axisymmetric boundary-layer flows. In these instances, surface roughness has been shown to stabilize convective modes of instability. The motivation for this study is to ascertain if qualitatively similar results are predicted for two-dimensional boundary-layer flows where Tollmien–Schlichting (TS) waves are the dominant mode of instability. Combining results from two separate numerical analyses with a large Reynolds number asymptotic analysis, we show that these types of flow configurations are indeed stabilized by the presence of surface roughness.