Self-excited instability and transition to turbulence in laminar separation bubbles induced by surface waviness

The instability characteristics and laminar–turbulent transition of a series of laminar separation bubbles (LSBs) formed due to a single sinusoidal surface waviness are investigated in the absence of external disturbances or forcing. A scaling based on the geometrical parameters of the waviness and flow Reynolds number is found that enables the prediction of flow separation on the wall leeward side. The analysis of three-dimensional instabilities of two-dimensional base flows reveals a relation between the number of changes in the curvature sign of the recirculating streamlines and the number of unstable centrifugal modes that coexist for the same flow. When multiple curvature changes occur, in addition to the usual steady mode reported for two-dimensional recirculation bubbles, a new self-excited mode with a higher growth rate emerges, localised near the highest streamline curvature, close to the reattachment point. A detailed analysis of the mode growth and saturation using DNS reveals that the localised mode only disturbs the LSB locally, while the usual one leads to a global distortion of the bubble in the spanwise direction; this has a distinctive impact on the self-excited secondary instabilities. Then, the complete transition scenario is studied for two selected LSB cases. The first one only presents an unstable eigenmode, namely the usual centrifugal mode in recirculating flows. The second case presents three unstable eigenmodes: two centrifugal eigenmodes (the usual and the localised ones) and a two-dimensional eigenmode associated with the self-sustained Kelvin–Helmholtz waves. These results show how completely different transition scenarios can emerge from subtle changes in the LSB characteristics.