Boundary Layer Flows Induced By The Motion Of Rough Surfaces

Abstract

We consider the linear stability of steady boundary layer flows induced by the translation of a moving wavy surface of infinite length. 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 stabilise 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 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 stabilised by the presence of surface roughness. We validate our numerical analyses by employing an alternative approach, where the modified mean flow is determined by solving the Reynolds-averaged boundary layer equations. Once again, our results demonstrate that these types of flow configurations are stabilised by the presence of surface roughness.