Flow regimes in the wake of a forced transversely oscillating circular cylinder

Two-dimensional direct numerical simulations of a circular cylinder undergoing forced transverse oscillations in laminar fluid flow were conducted over ranges of 0.1 ≤ A/D ≤ 0.6 and 0.50 ≤ fe/fs ≤ 2.50 at a constant Reynolds number Re = 150, where A and D are the oscillatory amplitude and the diameter of the circular cylinder, fe and fs are the forced oscillation frequency and the vortex shedding frequency for the stationary circular cylinder at Re = 150. This work focuses on identifying different flow regimes and exploring the potential physics behind these flow regimes based on the phase dynamics. Three major flow regimes, namely synchronous, quasi-periodic, and chaotic flows, including total 21 subclasses, are identified and mapped out in the parameter spaces of A/D and fe/fs, by means of the spectra of the lift coefficients, Lissajous phase diagrams in terms of the transverse displacement vs the lift coefficient, flow visualizations, and Poincaré maps. The synchronous flow regime contains various synchronization modes, depending on the indicator of p/q, where p and q are integers. Each p/q mode is characterized by the fact that the vortex shedding frequency fv synchronizes with (p/q)fe and the lift fluctuations present exact repeatable patterns, namely, the periodicity of the lift fluctuations corresponds precisely to q cycles of the forced cylinder oscillations. Specially, the 1/1 mode is referred to as the primary synchronization or lock-on, which has been the topic of many investigations in the past decades. It is found that the synchronous mode favors odd-number denominator (q) rather than an even number, resulting from a stable state with spatial-temporal symmetry wake similar to that of the Kármán vortex street. The phase dynamic analysis indicates that all the synchronization modes (p/q) hold the phase locking, i.e., the phase difference between the displacement of the oscillating cylinder and the lift fluctuations remains constant. While the quasi-periodic flows correspond to the phase trapping, i.e., the aforementioned phase difference oscillates around a constant value. Two physical mechanisms responsible for phase trapping are identified: (1) interactions between the shear layers that resulting from flow over a fixed cylinder and a forced transversely oscillating cylinder; (2) the influence of wake vortices, which play a significant role through their interaction with the shear layers. The competition between the above two shear layer instabilities and wake vortices is identified as the primary mechanism leading to the second type of quasi-periodic flow characteristics.