Response and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow

Vortex-induced vibrations (VIV) of two side-by-side elastically supported circular cylinders in a uniform flow with the Reynolds number of 100 are numerically investigated by using the immersed boundary method. The cylinders are constrained to oscillate in the cross-flow direction with a center-to-center spacing ratio $T/D$ ranging from 2 to 5. The structural damping is set to zero to enable large vibration amplitudes in the range of reduced velocity $U_r=3-10$. It is found that the proximity of the cylinders does not have a significant impact to the lock-in region and cylinder responses, except at a small spacing ratio of $T/D=2$. The critical spacing ratio is determined as $T/D=4$ and beyond that the interaction between the cylinders is negligible. The following six near-wake patterns are observed; the irregular pattern, in-phase flip-flopping pattern, out-of-phase flip-flopping pattern, in-phase-synchronized pattern, antiphase-synchronized pattern and the biased antiphase-synchronized pattern. These patterns are plotted in a plane of $U_r$ and $T/D$, together with approximate borderlines to distinguish one region from the others. The time histories, spectral features and wavelet transform contours of drag and lift forces are presented to elucidate the mechanisms of the in-phase and out-of-phase flip-flopping phenomena. It is established that the in-phase flip-flopping stems from the long-short near-wake pattern and its low-frequency flip-over, whereas the out-of-phase pattern originates from the large vortex shedding from the fictitious bluff-body with an augmented characteristic length.