Wake stability features behind a square cylinder: Focus on small incidence angles

The stability of the flow behind a cylinder with a square cross-section is investigated with a focus on small incidence angles 0°≤α≤12°. The first-occurring Mode A instability is found to be completely suppressed as the incidence angle is increased through α≈10.5°. The critical Reynolds number curve for the quasi-periodic mode is found to smoothly join the transition curve for the subharmonic mode. The switch from quasi-periodic to subharmonic properties occurs as α is increased from 2° to 3°, with no appreciable change in the structure of the leading eigenmode. Changes in the gradient of the critical Reynolds number curve with α, the gradient of the instability growth rate with Reynolds number, and the dominant spanwise wavelength demonstrate that the switch from quasi-periodic to subharmonic eigenvalues brings about subtle changes in the stability of the flow. The Reynolds number-incidence angle regimes for linear stability have been comprehensively mapped.