The structure of primary instability modes in the steady wake and separation bubble of a square cylinder

Flows past symmetric two-dimensional bluff bodies such as the circular cylinder, the square cylinder, and the normal flat plate produce large separation bubbles which (in the steady restriction) may become very elongated at comparatively low Reynolds numbers. The present work focuses on the steady/symmetric wake of a square cylinder at Re ⩽ 300, which loses stability to anti-symmetric two-dimensional global modes at Rec = 45. It is observed that while there is a continuous evolution in the parameters of the leading instability mode with increasing Re, a change in spatial structure of the modes begins near Re = 175, where the peak growth rate is found. At lower Re, instability modes are generally associated with the wake downstream of the separation bubble, but as Re increases the origin of the modes migrates into the separated shear layers. At the optimal Reynolds number Re = 175, the base flow streamlines around the end of the bubble are most parallel. The observed relation between structures of the bubble and global instabilities is explained on the basis of local stability analyses.