Flow past a transversely oscillating cylinder at lock-on region and three-dimensional Floquet stability analysis of its wake

Abstract

A numerical investigation is conducted on the flow past a transversely oscillating square cylinder at various amplitudes with a Reynolds number of 200 in the “lock-on” region. Floquet stability analysis was then applied to study the three-dimensional instability of its wake. The results show that mean recirculating region sizes decrease and force coefficients increase as the oscillating amplitude increases. The dynamic mode decomposition analysis reveals that although oscillating amplitude changes the topology of high order harmonic modes, the primary modes share similar features, which result in the classical “2S” mode at various amplitudes. The distinct high-order-harmonic modes lead to the difference of the flow pattern at various amplitudes. For the three-dimensional instability, the oscillating amplitudes can be divided into three stages, I (0 ≤ A/D < 0. 3), II (0.3 ≤ A/D < 0.4), and III (0.4 ≤ A/D < 0.7). In region I, the dominant Floquet mode is Mode-A corresponding to a long wavelength λz/D ≈ 3.49. As the oscillating amplitude increases to region III, the wavelength of the dominant mode abruptly changes to a much shorter wavelength λz/D ≈1.14 (a new mode called Mode-SA). Mode-SA shows similar features to Mode-A, except that this mode dissipates rapidly in the wake. Region II is the transitional region.