Secondary instability in the near-wake past two tandem square cylinders

Abstract

Floquet stability analysis has been carried out to detect the onset of the secondary instability in the laminar flow past two identical square cylinders in tandem. Presence of a neighbouring cylinder alters flow topology, leading to change of stability characteristics. A parametric study has been performed with the gap between the two square cylinders as the key parameter. Three distinct patterns of base flow are found depending on the gap, and distinctive modes of the secondary instability are identified for each pattern of the base flow. The modes exhibit either odd reflection-translation symmetry or even RT symmetry. The critical Reynolds number and the corresponding dominant spanwise wavelength are presented for a wide range of the gap. Temporal and spatial characteristics of the dominant Floquet modes are described in detail. A hysteresis is also noticed in a certain range of the gap. Neutral stability curves are presented for some selected values of the gap. The averaged in-plane vorticity of the dominant normalized Floquet mode is depicted as a function of the downstream distance from the rear face of the cylinder that sheds vortices. Comparison of stability characteristics is also made between the current flow and the flow past two circular cylinders in tandem arrangements.