Global instability of long separation bubbles in a laminar boundary layer

This work aims to numerically investigate the linear global instability of long separation bubbles origin from the changes in the adverse pressure gradient inside a laminar flat plate boundary layer disturbed by placing a bluff body with small clearances. The boundary layer starts at $Re_{\delta^\ast}$=121.7 and is steady in the computational extent after being disturbed by a NACA 4415 airfoil and a cylinder with clearance $h\leqslant 0.2$, respectively. It is found that the dominant stability is associated with two- and three-dimensional stationary eigenmodes. There is a less damped oscillation mode at a small wavenumbers range. The strong effect of three-dimensionality is further confirmed in a non-modal analysis framework. Transient growth analysis shows that the most strongest optimal perturbation is three-dimensional in the range of parameters studied. The modal analysis reveals that the instability grows with reducing the clearance, while the optimal perturbations grow with increasing the clearance. It is found that the separated boundary layer stability analysis is less dependent on the bluff body geometries.