Effect of roughness element on the stability of boundary layers

The instability of flows around hump and dip imperfections is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for viscous/inviscid interaction and separation bubbles. Then, the two-dimensional linear instability of this flow is analyzed, and the amplification factors are computed. Results are obtained for several height/width ratios and locations. The theoretical results have been used to correlate the experimental results of Greening and Walker. The observed transition locations are found to correspond to amplification factors varying between 7.4 and 10, consistent with previous results for flat plates. The method accounts for Tollmien-Schlichting waves, the shear layer instability, and their interaction. Separation is found to increase significantly the amplification factor.