Secondary Instability of the Flow Past Two Side-By-side Cylinders

In this work the flip-flop instability occurring in the flow past two sideby- side circular cylinders is numerically investigated at a fixed nondimensional gap spacing of g = 0.7 and within the range of Reynolds numbers 60 < Re ≤ 90. The inherent two-dimensional flow pattern is characterized by an asymmetric unsteady wake (with respect to the horizontal axis of symmetry) and the gap flow is deflected alternatively toward one of the cylinders. Such behaviour has been ascribed by other authors to a bi-stability of the flow, and therefore termed flip-flop. On the contrary, the simulations performed herein provide new evidence that at low Reynolds numbers the flip-flopping state develops through an instability of the in-phase synchronized vortex shedding between the two cylinder wakes. This new scenario is confirmed and explained by means of a global linear stability investigation of the in-phase periodic base flow. The Floquet analysis reveals indeed that a pair of complex-conjugate multipliers becomes unstable above the critical threshold of Re = 61.74 having the same low frequency as the gap flow flip-over.