We numerically study the flow past an azimuthally oscillating cylinder at Reynolds number Re=250 to analyse the three-dimensionalities observed in the recent experiments of Bhattacharyya et al. (J. Fluid Mech. , vol. 950, 2022, p. A10). Specifically, we focus on the two newly discovered three-dimensional instability modes, referred to as modes Z and Y in the experiments, by suitably varying the cylinder oscillation amplitude and forcing frequency. Our direct numerical simulations (DNS) visually confirm the unique honeycomb-like structure of mode Y, also matching its spanwise wavelength, while mode Z, also referred to as mode D elsewhere, is not found at the expected parametric space but at an oscillation amplitude three times higher. Spectral proper orthogonal decomposition modes extracted from the DNS data reveal the near-wake dynamics of mode Y to be modulated by the forcing frequency and its subharmonics. Mode D/Z is found to be strongly correlated with a two-dimensional modal regime, especially at the forcing frequency, its subharmonic and higher harmonics. Mode Y does not show significant correlations with this two-dimensional flow except at a low frequency and only at its far wake. The honeycomb nature of mode Y is a result of its relatively higher forcing frequency causing multiple vortex sheddings over a rather compact space. Higher cylinder oscillation amplitude increases the overall drag, with the two-dimensional flow regimes generally yielding lower drag and lift. The results here suggest mode Y to be a unique three-dimensional mode of azimuthally oscillating cylinders and mode D/Z to be merely an intermediate state with the cylinder wake transitioning from the classical three-dimensional mode B to a two-dimensional state.
Boral et al. (Mon,) studied this question.