Bistabilities in two parallel Kármán wakes

Ren, Chengjiao; Cheng, Liang; Xiong, Chengwang; Tong, Feifei; Chen, Tingguo

doi:10.1017/jfm.2021.832

Cited by 10 publications

(21 citation statements)

References 29 publications

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“…In addition, one may find multiple attractors, which is associated to hysteresis, and it seems to be a common feature of many supercritical and subcritical flows, cf. (Subramanian, Sujith & Wahi 2013;Guo et al 2018;Ren et al 2021;Huang et al 2018;Suckale et al 2018). Eventually, for sufficiently large Reynolds numbers, Lorite-Díez & Jiménez-González (2020) and Pier (2013) identified irregular regimes for most rotation rates, which are associated to a T 3 -quasiperiodic attractor.…”

Section: Discussionmentioning

confidence: 98%

Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

et al. 2022

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The wake flow past a streamwise rotating sphere is a canonical model of numerous applications, such as particle-driven flows, sport aerodynamics and freely rising or falling bodies, where the changes in particles’ paths are related to the destabilization of complex flow regimes and associated force distributions. Herein, we examine the spatio-temporal pattern formation, previously investigated by Lorite-Díez & Jiménez-González (J. Fluid Mech., vol. 896, 2020, A18) and Pier (J. Fluids Struct., vol. 41, 2013, pp. 43–50), from a dynamical system perspective. A systematic study of the mode competition between rotating waves, which arise from the linearly unstable modes of the steady-state, exhibits their connection to previously observed helical patterns present within the wake. The organizing centre of the dynamics turns out to be a triple Hopf bifurcation associated with three non-axisymmetric, oscillating modes with respective azimuthal wavenumbers $m=-1,-1$ and $-2$ . The unfolding of the normal form unveils the nonlinear interaction between the rotating waves to engender more complex states. It reveals that for low values of the rotation rate, the flow field exhibits a similar transition to the flow past the static sphere, but accompanied by a rapid variation of the frequencies of the flow with respect to the rotation. The transition from the single helix pattern to the double helix structure within the wake displays several regions with hysteric behaviour. Eventually, the interaction between single and double helix structures within the wake lead towards temporal chaos, which here is attributed to the Ruelle–Takens–Newhouse route. The onset of chaos is detected by the identification of an invariant state of the normal form constituted by three incommensurate frequencies. The evolution of the chaotic attractor is determined using of time-stepping simulations, which were also performed to confirm the existence of bi-stability and to assess the fidelity of the computations performed with the normal form.

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Section: Discussionmentioning

confidence: 98%

Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

et al. 2022

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“…It was found that the flow at low Re undergoes transitions from a single bluff-body wake, via a flip-flop (FF) wake, to coupled-individual wakes such as in-phase (IP) and anti-phase (AP) flows with increasing g * . Other flow modes such as asymmetric single bluff-body vortex shedding flows and bistable flows are also found over the above parameter space (Ren et al 2021a). It is noteworthy that most of those studies are limited to low Re, where the flow was assumed to be two dimensional.…”

Section: Introductionmentioning

confidence: 93%

“…Floquet analysis is employed over one T due to the periodicity of the base flow. The selections of N t,s = 32 and K n = 16 were referred to the validation given by Carmo et al (2008) and Ren et al (2021a).…”

Section: Floquet Stability Analysismentioning

confidence: 99%

“…Rich physics arising from the interaction of wakes behind the cylinders have been revealed at relatively low Re (<∼160) values through stability analysis and direct numerical simulations (DNS); see, e.g. Kang (2003); Carini, Giannetti & Auteri (2014); Ren et al (2021a). It was found that the flow at low Re undergoes transitions from a single bluff-body wake, via a flip-flop (FF) wake, to coupled-individual wakes such as in-phase (IP) and anti-phase (AP) flows with increasing g * .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Three-dimensional wake transitions of steady flow past two side-by-side cylinders

Ren,

Liu,

Cheng

et al. 2023

J. Fluid Mech.

Self Cite

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Three-dimensional (3-D) wake transitions of a steady flow past two side-by-side circular cylinders are investigated through Floquet analysis and direct numerical simulations (DNS) over the gap-to-diameter ratio $g^*$ up to 3.5 and Reynolds number ${\textit {Re}}$ up to 400. When the flows behind two cylinders form in-phase and anti-phase wakes at large $g^*$ , the wake transition is similar to the isolated cylinder counterpart, with the critical ${\textit {Re}}$ for the onset of 3-D transition ( ${\textit {Re}}_{cr-1}$ ) happens at around 180. At small $g^*$ , 3-D transition becomes interestingly complex due to the distinct characteristics formed in base flows. The ${\textit {Re}}_{cr-1}$ suddenly drops to around 60–100 and forms distinct variation trends with $g^*$ . Precisely, the ${\textit {Re}}_{cr-1}$ of the single symmetric wake (SS, $g^*\lessapprox 0.25$ ) is more than half of the isolated cylinder counterpart due to the large length scale of the SS wake. Only mode A is detected in SS. In the asymmetric single wake (ASS, $g^* \approx 0.25\unicode{x2013}0.6$ ) and flip-flop wake (FF, $g^* \approx 0.6\unicode{x2013}1.8$ ), the 3-D transition develops at ${\textit {Re}} \approx 103\unicode{x2013}60$ and 75–60, respectively. The decrease in ${\textit {Re}}_{cr-1}$ with increasing $g^*$ is because of the increased level of wake asymmetry in ASS and irregular vortex shedding in FF. Floquet analysis predicts two new unstable modes, namely mode A $'$ and subharmonic mode C $'$ , of ASS. Both modes are transient features in 3-D DNS and the flow eventually saturates into a new 3-D mode, mode ASS. The gap flow of mode ASS is distinctly characterised by its time-independent spanwise waviness structure that is deflected towards different transverse directions with a long wavelength of about $14$ cylinder diameters. The 3-D mode of the FF is irregular both temporally and spatially. Variations of ${\textit {Re}}_{cr-1}$ with $g^*$ , the characteristics and the physical mechanisms of each 3-D mode are discussed in this study.

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“…Flow past multiple bodies in close configuration is relevant for a range of applications, such as buildings or chimneys in urban and industrial environments, power lines, offshore structures, and heat exchangers. Even at relatively low Reynolds numbers, such flows can exhibit substantially more complexity than flow over a single, isolated body [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

β-Variational autoencoders and transformers for reduced-order modelling of fluid flows

Vinuesa

Solera-Rico

Vila

et al. 2023

Preprint

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Variational autoencoder (VAE) architectures have the potential to develop reduced-order models (ROMs) for chaotic fluid flows. We propose a method for learning compact and near-orthogonal ROMs using a combination of a β-VAE and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The β-VAE is trained to learn a compact latent representation of the flow velocity, and the transformer is trained to predict the temporal dynamics in latent space. Using the β-VAE to learn disentangled representations in latent space, we obtain a more interpretable flow model with features that resemble those observed in the proper orthogonal decomposition, but with a more efficient representation. Using Poincaré maps, the results show that our method can capture the underlying dynamics of the flow outperforming other prediction models. The proposed method has potential applications in other fields such as weather forecasting, structural dynamics or biomedical engineering.

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Bistabilities in two parallel Kármán wakes

Cited by 10 publications

References 29 publications

Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

Three-dimensional wake transitions of steady flow past two side-by-side cylinders

β-Variational autoencoders and transformers for reduced-order modelling of fluid flows

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