Direct stability analysis and numerical simulations have been employed to identify and characterize secondary instabilities in the wake of the flow around two identical circular cylinders in tandem arrangements. The centre-to-centre separation was varied from 1.2 to 10 cylinder diameters. Four distinct regimes were identified and salient cases chosen to represent the different scenarios observed, and for each configuration detailed results are presented and compared to those obtained for a flow around an isolated cylinder. It was observed that the early stages of the wake transition changes significantly if the separation is smaller than the drag inversion spacing. The onset of the three-dimensional instabilities were calculated and the unstable modes are fully described. In addition, we assessed the nonlinear character of the bifurcations and physical mechanisms are proposed to explain the instabilities. The dependence of the critical Reynolds number on the centre-to-centre separation is also discussed.

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The wake transition of the flow around two circular cylinders placed in staggered arrangements with fixed streamwise separation of 5D and cross stream separation varying from 0D to 3D has been studied. The wake transition is compared to that of a single isolated cylinder. Linear stability analysis utilising Floquet theory and direct numerical simulations, using the spectral/hp element method were carried out. It is found that besides modes A and B, mode C can also appear in the wake transition, depending on the relative positioning of the cylinders. The structure of mode C is analysed and the non-linear character of the bifurcation for this mode is investigated. IntroductionThe flow around circular cylinders has been extensively studied due to its practical importance in engineering and scientific relevance in fluid mechanics. On the engineering side, there are a number of applications in mechanical, civil and naval engineering that employ circular-cylindrical structures, such as heat exchangers, chimneys and off- shore platforms. In scientific terms, the flow around circular cylinders presents various important physical phenomena, such as separation, vortex shedding and transition.In the next two subsections, some of the relevant research that has been carried out on two different aspects of this flow is reviewed. These aspects are the wake transition in bluff body flows and the flow around circular cylinders in staggered arrangements, illustrated in figure 1. Wake transitionIn the last two decades, much effort has focused on the study of the three-dimensional transition that takes place in the von Kármán wake that appears in the flow downstream of a single cylinder. This line of research in its contemporary form was instigated by the seminal work of Williamson (1988), in which two distinct stages were identified in the wake transition, spanning 160 Re 300. The limits of these stages were identified by discontinuities in the curve obtained when the Strouhal number (St) was plotted against the Reynolds number (Re) and these discontinuities correspond to the manifestation of different three-dimensional structures in the wake. The first to appear is called mode A, and it has a spanwise wavelength of approximately 4 diameters. The second is called mode B, and its spanwise wavelength is close to 1 diameter. A number of papers on additional experiments and direct numerical simulations (DNS) for this Re range have Wake transition in staggered arrangements 3 been published since then with the aim of reproducing these findings, see for example Wu et al. (1994), Zhang et al. (1995) and Thompson et al. (1996). A great leap forward occurred with the work of Barkley & Henderson (1996), who performed high accuracy Floquet stability analyses of two-dimensional time periodic base flows, precisely identifying the critical Reynolds numbers and also characterising each of the modes that take part in the wake transition. Williamson (1996) presented an extensive study on the wake transition, setting the most significant results pre...

When a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. Assi, Bearman & Meneghini (J. Fluid Mech., vol. 661, 2010, pp. 365-401) concluded that the WIV excitation mechanism has its origin in the unsteady vortex-structure interaction encountered by the cylinder as it oscillates across the wake. In the present paper we investigate how the cylinder responds to that excitation, characterising the amplitude and frequency of response and its dependency on other parameters of the system. We introduce the concept of wake stiffness, a fluid dynamic effect that can be associated, to a first approximation, with a linear spring with stiffness proportional to Re and to the steady lift force occurring for staggered cylinders. By a series of experiments with a cylinder mounted on a base without springs we verify that such wake stiffness is not only strong enough to sustain oscillatory motion, but can also dominate over the structural stiffness of the system. We conclude that while unsteady vortex-structure interactions provide the energy input to sustain the vibrations, it is the wake stiffness phenomenon that defines the character of the WIV response.

The possible states in the flow around two identical circular cylinders in tandem arrangements are investigated for configurations in the vicinity of the drag inversion separation. By means of numerical simulations, the hysteresis in the transition between the shedding regimes is studied and the relationship between (three-dimensional) secondary instabilities and shedding regime determination is addressed. The differences observed in the behavior of two- and three-dimensional flows are analyzed, and the regions of bistable flow are delimited. Very good agreement is found between the proposed scenario and results available in the literature.