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On the origin of the flip–flop instability of two side-by-side cylinder wakes

Published online by Cambridge University Press:  21 February 2014

M. Carini ,
F. Giannetti  and
F. Auteri
M. Carini
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
F. Giannetti
Affiliation:
Dipartimento di Ingegneria Industriale, Università degli studi di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy
F. Auteri*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: franco.auteri@polimi.it
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Abstract

In this work the flip–flop instability occurring in the flow past two side-by-side circular cylinders is numerically investigated within the range of non-dimensional gap spacing $0.6<g<1.4$ and Reynolds number $50<Re\leq 90$. The inherent two-dimensional flow pattern is characterized by an asymmetric unsteady wake (with respect to the horizontal axis of symmetry) with the gap flow being deflected alternatively toward one of the cylinders. Such behaviour has been ascribed by other authors to a bistability of the flow, and therefore termed flip–flop. In contrast, the simulations performed herein provide new evidence that at low Reynolds numbers the flip–flopping state develops through an instability of the in-phase synchronized vortex shedding between the two cylinder wakes. This new scenario is confirmed and explained by means of a linear global stability investigation of the in-phase periodic base flow. The Floquet analysis reveals indeed that a pair of complex-conjugate multipliers becomes unstable having the same low frequency as the gap flow flip-over. The neutral curve of this secondary instability is tracked within the above range of gap spacing. The spatiotemporal shape of the unstable Floquet mode is then analysed and its structural sensitivity is considered in order to identify the ‘core’ region of the flip–flop instability mechanism.

JFM classification

Instability: Instability Wakes/Jets: Wakes/Jets Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 552 - 576
Copyright
© 2014 Cambridge University Press 

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