Three-dimensional wake dynamics of a square cylinder in oscillatory flows at low Reynolds numbers

AbstractThe three-dimensional (3D) wake dynamics of a square cylinder subjected to streamwise sinusoidal inflow with a non-zero mean velocity are investigated using direct numerical simulations (DNS). The 3D wake transition process in sinusoidal flows with different oscillation amplitudes a (normalized values a = 0.1 and 0.2) and frequencies f (normalized values f = 0.15 and 0.3) is compared with that in smooth inflow (a = 0 and f = 0). The critical Reynolds numbers and spanwise wavelengths of the 3D unstable modes are predicted using an improved DNS-based method, agreeing closely with those from Floquet stability analysis. The imposed sinusoidal oscillations substantially modify the 3D wake transition process in real 3D flows. In particular, the oscillatory forcing significantly suppresses the occurrence of vortex dislocations in the 3D flow structures, especially for the 3D unstable mode in high-frequency oscillatory inflow. Despite the differences among the transition scenarios under various inflow conditions, the overall evolution exhibits a consistent trend: the wake is initially dominated by ordered large-scale structures, which then become finer scaled and increasingly chaotic as the Reynolds number increases. Synchronization between the natural vortex-shedding frequency and a subharmonic of imposed oscillatory frequency stabilizes the wake and weakens its three-dimensionality, leading to more regular temporal variations in the hydrodynamic forces. Relative to smooth inflow, the sinusoidal inflow also shortens the vortex formation length and increases the mean drag coefficients of the square cylinder.