Three-dimensional instability in flow past a rectangular cylinder ranging from a normal flat plate to a square cylinder

Floquet stability analysis has been carried out to detect the onset of the three-dimensional (3D) instability in flow past a rectangular cylinder ranging from a normal flat plate to a square cylinder with various aspect ratios (AR). The conventional modes A, B, and QP vanish as AR decreases towards a thin normal flat plate, whereas new modes A2 and QP2 emerge. For “thin” rectangular cylinders, mode QP2 becomes unstable first with increasing Reynolds number (Re). In a certain range of AR, mode A becomes unstable and then stable again as Re increases, resulting in a closed curve on the neutral stability diagram. For validation, 3D simulations were also performed.