Compressible boundary layer transition induced by isolated roughness elements

The laminar-to-turbulent transition of boundary layers induced by isolated threedimensional roughness elements is analyzed by mining a direct numerical simulation database, which covers the variation of many physical parameters, including Mach and Reynolds numbers, and obstacle shape and size. We find that the transition process is approximately controlled by a Reynolds number based on the momentum deficit past the obstacle, which is proportional to the classical roughness Reynolds number, and that approximately incorporates the effects of the roughness element shape. The analysis of the perturbation energy past the obstacle shows that the varicose mode of instability is always dominant in the close proximity of the obstacle, and it promotes transition in super-critical flow cases. On the other hand, the sinuous mode appears to dominate the evolution of marginally sub-critical cases, which feature quasi-steady momentum streaks.