Three-dimensional wake transitions of a square cylinder in sinusoidal oscillatory flows

The three-dimensional wake transition of a square cylinder in a streamwise sinusoidal oscillatory flow with non-zero mean velocity is investigated numerically using direct numerical simulations and Floquet stability analysis. Sinusoidal flows with different oscillation amplitudes a and frequencies f, namely (a=0.1, f=0.15), (a=0.2, f=0.15), and (a=0.1, f=0.3), are compared with steady smooth flows (a=0, f=0) to examine the influence of sinusoidal fluctuations. The imposed sinusoidal oscillations modulate the topology of the two-dimensional base flow and force the wake to shed vortices at either the oscillation frequency or its subharmonic within a finite Reynolds number (Re) range. At large oscillation amplitudes, the flow becomes asymmetric and the onset of three-dimensionality occurs earlier, with a critical transition at Re > 139.9. In contrast, the high-frequency sinusoidal oscillations stabilize the wake and significantly suppress the development of three-dimensional instabilities, delaying the critical transition to Re > 210.4 and narrowing the unstable range of spanwise wavelength. Compared with the temporally periodic instabilities observed in smooth flows, i.e., mode A and mode B instabilities, the double-period instability mode (mode C) emerges in the low-frequency sinusoidal flows, and the quasi-periodic instability mode (mode QP) arises under high-frequency oscillations. The odd and even reflection–translation symmetries of Floquet modes in smooth flows are broken when sinusoidal oscillation is applied. Furthermore, the imposed sinusoidal oscillations lead to supercritical or subcritical three-dimensional wake transitions, depending on the oscillation parameters.