DNS study on the roughness wavelength selectivity of crossflow vortex transition due to distributed surface roughness

Abstract

This numerical study investigates the transition process in a Falkner–Skan–Cooke boundary layer on a homogeneously-roughened swept flat plate, with varying roughness wavelengths and heights. Using direct numerical simulations, we determine the onset and development of stationary crossflow vortices (CFVs) and their eventual breakdown via secondary instabilities (SIs). The results highlight the wavelength-selective nature of roughness-induced instability: roughness matching the most unstable mode for the stationary CFV triggers the earliest CFV development and collapse. In contrast, both longer and shorter wavelengths alter the growing mode, ultimately delaying the collapse of CFVs and the transition to turbulence. Through spectral and statistical analyses, we identify clear milestones—occurrences of CFVs and SIs, and collapse of CFVs—which correspond well with flow visualizations. While canonical SI types (Type-1, 2, 3) are observed on short-wavelength roughness, mid- and long-wavelength cases reveal atypical unsteady behavior lacking clear spectral peaks. The observed delay in transition due to wavelength mismatches would have practical relevance to turbulent transition control.