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Amedeo Marzini
The onset of the two-dimensional instability in the flow past a couple of square cylinders is investigated via linear stability analysis, to understand the influence of their mutual arrangement. The geometrical configuration is defined by the non-dimensional spacings gx and gy between their centers. The cylinders are placed side-by-side (gx = 0), in tandem (gy = 0), or in the more general staggered configuration. Three values of gy are selected, corresponding to different instabilities of the side-by-side arrangement, and gx is varied from gx=0 to gx=20. For each arrangement, the base flow is presented, the neutral curve is computed and all the unstable modes are described, with emphasis on the wavemaker region.
It is found that staggering the cylinders significantly affects the stability of the flow, leading to different scenarios. This is illustrated, for instance, by the critical Reynolds number Rec, ranging from Rec = 16.3 up to Rec = 135.4 in the side-by-side and tandem configuration respectively. The side-by-side arrangement leads to similar stability properties of two side-by-side circular cylinders. The tandem arrangement, instead, presents three different unstable modes, each promoting a distinct flow regime. The staggered arrangement is characterized by two scenarios, depending on the value of gy.