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Bistabilities in two parallel Kármán wakes

Published online by Cambridge University Press:  19 October 2021

Chengjiao Ren
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, PR China School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
Liang Cheng*
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, PR China School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
Chengwang Xiong
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, PR China School of Engineering, Ocean University of China, Qingdao 266100, PR China
Feifei Tong
Affiliation:
School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
Tingguo Chen
Affiliation:
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, PR China
*
Email address for correspondence: liang.cheng@uwa.edu.au

Abstract

Bistabilities of two equilibrium states discovered in the coupled side-by-side Kármán wakes are investigated through Floquet analysis and direct numerical simulation (DNS) with different initial conditions over a range of gap-to-diameter ratio ($g^*= 0.2\text {--}3.5$) and Reynolds number ($Re = 47\text {--}100$). Two bistabilities are found in the transitional $g^*-Re$ regions from in-phase (IP) to anti-phase (AP) vortex shedding states. By initialising the flow in DNS with zero initial conditions, the flow in the first bistable region (i.e. bistable IP/FF$_C$ at $g^*= 1.4 \text {--} 2.0$, where FF$_C$ denotes the conditional flip-flop flow) attains flip-flop (FF) flow, it settles into the IP state by initialising the flow with an IP flow. The second bistability is observed between cylinder-scale IP and AP states at large $g^*$ ($=$ 2.0–3.5). The transition from the FF$_C$ to IP is dependent on initial conditions and irreversible over the parameter space, meaning that the flow cannot revert back to the FF$_C$ state once it jumps to the IP state irrespective of the direction of $Re$ variations. Its counterpart for the bistable IP/AP state is reversible. We also found that the FF$_C$ flow in the first bistable region is primarily bifurcated from synchronised AP with cluster-scale features, possibly because the cluster-scale AP flow is inherently unstable to FF flow instabilities. It is demonstrated that the irreversible bistability exists in other interacting wakes around multiple cylinders. A good understanding of flow bistabilities is pivotal to flow control applications and the interpretation of desynchronised flow features observed at high $Re$ values.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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