Transitional hysteresis loop and coexistence of synchronized shedding in coupled wakes

Abstract

Hysteretic in-phase ↔ anti-phase exchange of vortex shedding and co-existence of reverse-synchronized bistable wake structures past two side-by-side elliptic/circular cylinders are examined through extensive numerical simulations and bifurcation analysis. Wake characteristics and synchronizations past two side-by-side cylinders have often been demarcated in terms of the gap-ratio “G” and the Reynolds number “Re.” The focus here is the “in-phase ↔ anti-phase” two-way transition of oppositely synchronized bistable shedding states. In a remarkable parallel to discontinuous shifts of Strouhal frequency (prompting growth of two distinct instability modes past a single cylinder), the present work reveals interesting in-phase ↔anti-phase transitional switching of vortex shedding past two side-by-side symmetric cylinders, as facilitated by “discontinuous jumps of combined lift-force CL,1+2,” and preceding bistable wake evolution via both of these two reverse-synchronized phases. The hysteresis loops are demarcated (for cylinders of different aspect-ratios A) through extended computations of two anti-synchronized solution branches by slowly increasing/decreasing the Re at fixed gap-ratio (G) and increasing/decreasing G minutely at a constant Re, thereby facilitating transitions and using the computed discontinuous jumps of CL,1+2. Simulations conducted with various A (0.5 ≤ A ≤ 2.0) exhibit, both in-phase and anti-phase shedding co-exist over significantly wide ranges of G-space/Re-space, and the exchange of vortex synchronization at the ends of hysteresis loop occurs through discontinuous variation of the CL,1+2. The “gap-biased” anti-phase → in-phase transition gets gradually delayed, as the cylinder aspect-ratio A is decreased. However, the “Re-biased” in-phase → anti-phase transition is advanced with the decrease of A. The tolerance width “HW” of gap-biased hysteresis loop increases fairly linearly, as A decreased over the range 1.0 ≤ A ≤ 2.0.