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

Abstract

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.