Direct numerical simulation and modal analyses of spanwise-adjacent roughness elements induced transition

Direct numerical simulation has been employed to investigate the transition caused by spanwise-adjacent roughness elements within the boundary layer of a flat plate. The study elucidates the alterations of the energy-containing structures and global linear unstable modes due to variations in the roughness elements' shapes and spanwise spacing. Findings indicate that reduced spanwise spacing enhances the interaction between adjacent vortex sequences, thereby expediting transition. The ramp-induced disturbances are most effective in stimulating streamwise fluctuating vorticity. In the modal analyses, the configurations with identical roughness elements exhibit symmetrical streamwise and wall-normal fluctuating velocities, while the spanwise fluctuating velocity is antisymmetric, which is the varicose mode. The interaction between the energy-containing wavepackets gives rise to another unstable mode, which is the sinuous mode as confirmed by global stability analysis. In the case of strong ramp disturbance, the core of the leading unstable mode aligns with the energetic regions of the three fluctuating velocities. In the absence of a ramp, diminishing spanwise spacing leads to a symmetry inversion in the three velocity components, transitioning from the varicose to the sinuous mode. This change originates from alterations in the distribution of the counter-rotating vortex pairs.