Linear stability of the steady flow past rectangular cylinders

The primary instability of the flow past rectangular cylinders is studied to comprehensively describe influence aspect ratio $AR$ and rounding leading- and/or trailing-edge corners. Aspect ratios ranging between $0.25$ $30$ are considered. We show that critical Reynolds number ( $\textit {Re}_c$ ) corresponding increases with ratio, starting from {Re}_c \approx 34.8$ for $AR=0.25$ a value 140$ $AR = 30$ . unstable mode its dependence on described. find positioning small circular cylinder in modifies way strongly depending ratio. rounded corners affect depends both curvature radius. For , leading-edge has always stabilising effect, whereas destabilising, although large radii only. intermediate instead, effect limited only, while \geqslant 5$ it destabilising effect. In contrast, 2$ consistently Interestingly, when all rounded, becomes more stable, at ratios. An explanation provided.