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Bistabilities in two parallel Kármán wakes
Journal article   Peer reviewed

Bistabilities in two parallel Kármán wakes

Chengjiao Ren, Liang Cheng, Chengwang Xiong, Feifei Tong and Tingguo Chen
Journal of Fluid Mechanics, Vol.929, A5
25/12/2021
DOI: https://doi.org/10.1017/jfm.2021.832
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Abstract

JFM Papers
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.

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