No abstract

Laminar-to-turbulent transition in a swept flat-plate boundary layer is caused by the breakdown of the crossflow vortex via high-frequency secondary instability and is promoted by the wall-surface roughness and the freestream turbulence (FST). Although the FST is characterized by its intensity and wavelength, it is not clear how the wavelength affects turbulent transitions and interacts with the roughness-induced transition. The wavelength of the FST depends on the wind tunnel or in-flight conditions, and its arbitrary control is practically difficult in experiments. By means of direct numerical simulation, we performed a parametric study on the interaction between the roughness-induced disturbance and FST in the Falkner–Skan–Cooke boundary layer. One of our aims is to determine the critical roughness height and its dependence on the turbulent intensity and peak wavelength of FST. We found a suppression and promotion in the transition process as a result of the interaction. In particular, the immediate transition behind the roughness was delayed by the long-wavelength FST, where the presence of FST suppressed the high-frequency disturbance emanating from the roughness edge. Even below the criticality, the short-wavelength FST promoted a secondary instability in the form of the hairpin vortex and triggered an early transition before the crossflow-vortex breakdown with the finger vortex. Thresholds for the FST wavelengths that promote or suppress the early transition were also discussed to provide a practically important indicator in the prediction and control of turbulent transitions due to FST and/or roughness on the swept wing.