Exact coherent structures and shadowing in turbulent Taylor–Couette flow

Krygier, Michael; Pughe-Sanford, Joshua L.; Grigoriev, Roman O.

doi:10.1017/jfm.2021.522

Cited by 17 publications

(33 citation statements)

References 72 publications

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“…The stability analysis reflected in figure 3 reveals at least two more Hopf bifurcations of the already unstable DRW as is increased beyond the value for the onset of CH-DRW. Solution branches issued from these Hopf points and subsequent bifurcation cascades like the one we report may probably contribute, along with CH-DRW, through global bifurcations involving crises and mergers, to the formation of the strange set that sustains spatiotemporally chaotic dynamics at higher (Krygier, Pughe-Sanford & Grigoriev 2021).…”

Section: Structure and Stability Of Drw And Their Role In The Dynamicsmentioning

confidence: 81%

Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow

et al. 2022

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We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor–Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting–rotating waves (DRW) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circular Couette flow, is determined by the upper and lower branches of DRW solutions originated at saddle-node bifurcations. The mechanism whereby these solutions self-sustain, and the chaotic dynamics they induce, are conspicuously reminiscent of other subcritical shear flows. Remarkably, the flow properties of DRW persist even as the Reynolds number is increased beyond the linear stability threshold of the base flow. Simulations in a narrow parallelogram domain stretched in the azimuthal direction to revolve around the apparatus a full turn confirm that self-sustained vortices eventually concentrate into a localised pattern. The resulting statistical steady state satisfactorily reproduces qualitatively, and to a certain degree also quantitatively, the topology and properties of spiral turbulence as calculated in a large periodic domain of sufficient aspect ratio that is representative of the real system.

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Section: Structure and Stability Of Drw And Their Role In The Dynamicsmentioning

confidence: 81%

Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow

et al. 2022

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“…Moreover, utilizing SRDMD, we extended the Page & Kerswell (2020) DMD-based periodic orbit search method to relative periodic orbits and showed that a guess for a relative periodic orbit can be generated by SRDMD even when turbulence does not follow the relative periodic orbit for a full period, enabling relative periodic orbit searches that would not have been possible via recurrent flow analysis (Chandler & Kerswell 2013). In the light of recent evidence (Krygier, Pughe-Sanford & Grigoriev 2021; Yalnız, Hof & Budanur 2021; Crowley et al. 2022) that the approaches of turbulence to periodic solutions are often not for a full period, we think that SRDMD-based approaches can accelerate relative periodic orbit searches in future studies.…”

Section: Discussionmentioning

confidence: 91%

Symmetry-reduced dynamic mode decomposition of near-wall turbulence

et al. 2022

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Data-driven dimensionality reduction methods such as proper orthogonal decomposition and dynamic mode decomposition have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration, as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for fluid flows in rectangular channels by formulating a continuous symmetry reduction method that eliminates the translations in the streamwise and spanwise directions simultaneously. We demonstrate our method by computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity of the invariant solutions with translation symmetries, i.e. travelling waves and relative periodic orbits, whereas in the latter, our calculations reveal episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion.

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“…In his seminal paper, Taylor explored the Γ 1 limit in which boundary effects of the top and bottom end caps are negligible; in contrast, we investigate the small aspect ratio (Γ = 1) and medium gap (η = 0.71) parameter regime, in which the end effects play a substantial role in driving the fluid motion. Relevant prior studies for this geometry are summarized in [30].…”

Section: Experimental Systemmentioning

confidence: 99%

“…The presence of a continuous (rotational) symmetry in Taylor-Couette flow implies that the most common ECSs will be relative, e.g. traveling waves or RPOs [28,30,32]. RPOs are solutions satisfying…”

Section: Exact Coherent Structures In Tcfmentioning

confidence: 99%

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Observing a dynamical skeleton of turbulence in Taylor–Couette flow experiments

Crowley

Pughe-Sanford

Toler

et al. 2023

Phil. Trans. R. Soc. A.

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Recent work shows that recurrent solutions of the equations governing fluid flow play an important role in structuring the dynamics of turbulence. Here, an improved version of an earlier method (Krygier et al. 2021 J. Fluid. Mech. 923 , A7 and Crowley et al. 2022 Proc. Natl Acad. Sci. USA 119 , e2120665119) is used for detecting and analyzing intervals of time when turbulence ‘shadows’ (spatially and temporally mimics) recurrent solutions in both numerical simulations and laboratory experiments. We find that all the recurrent solutions shadowed in numerics are also shadowed in experiment, and the corresponding statistics of shadowing agree. Our results set the stage for experimentally grounded dynamical descriptions of turbulence in a variety of wall-bounded shear flows, enabling applications to forecasting and control. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.

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Exact coherent structures and shadowing in turbulent Taylor–Couette flow

Abstract: Abstract

Cited by 17 publications

References 72 publications

Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow

Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow

Symmetry-reduced dynamic mode decomposition of near-wall turbulence

Observing a dynamical skeleton of turbulence in Taylor–Couette flow experiments

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