Parameterization of Boundary-Layer Transition Induced by Isolated Roughness Elements

The laminar-to-turbulent transition of boundary layers induced by isolated three-dimensional 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. It is found 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 which 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 supercritical flow cases. On the other hand, the sinuous mode appears to dominate the evolution of marginally subcritical cases, which feature quasi-steady momentum streaks.