Three-dimensional flip-flopping flow around a pair of dual-stepped circular cylinders in a side-by-side arrangement

Three-dimensional direct numerical simulations of flow around a pair of dual-stepped circular cylinders in a side-by-side arrangement and a proximity interference region are presented. The dual-stepped cylinders consist of two coaxial cylinders with a larger-to-smaller diameter ratio of 2. The Reynolds number and the side-by-side gap ratio, based on the larger (smaller) diameter, are 200 (100) and 1 (3), respectively. Two flip-flopping flow regimes A and B are observed behind the dual-stepped cylinders, exhibiting temporal variations of hydrodynamic drag and lift force coefficients. The flow regime B is featured by the flip-flopping, higher vortex-shedding frequencies and greater flow instability than those in the flow regime A. Half-loop and direct connections of vortices take place frequently in the narrower wake, while the vortex reconnection and multiple connection predominate the wider wake. This suggests that the dual-stepped cylinder with the narrower wake behaves similarly to a single dual-stepped cylinder. The dynamic mode decomposition analysis reveals pitchfork and Hopf bifurcation (in-phase and anti-phase synchronization) modes in the larger cylinder wake, with the interaction of these bifurcations originating from the flip-flopping flow pattern. However, the pitchfork mode is not found in the smaller cylinder wake, suggesting that its flip-flopping flow behavior is not self-originated but triggered by the flip-flopping flow mechanism of the larger cylinder.