Turbulence tracks recurrent solutions

Crowley, Catherine; Pughe-Sanford, Joshua L.; Toler, Wesley; Krygier, Michael; Grigoriev, Roman O.; Schatz, Michael F.

doi:10.1073/pnas.2120665119

Cited by 20 publications

(18 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 91%

Symmetry-reduced dynamic mode decomposition of near-wall turbulence

et al. 2022

View full text Add to dashboard Cite

show abstract

“…The experimental TCF apparatus was constructed to be fully transparent to allow for optical access and, therefore, velocimetry measurements anywhere in the flow domain. Time-resolved azimuthal and radial velocity measurements near the horizontal midplane were sufficient in characterizing the dynamics despite the flow having nontrivial structure in the axial direction [31]. Here, the experimental setup and velocimetry techniques are identical to that of [31]; velocity is measured in a horizontal cross-section, as depicted in figure 1.…”

Section: Experimental Systemmentioning

confidence: 99%

“…for some temporal period T and rotation angle Φ. RPOs are time-periodic solutions in a co-moving reference frame of angular speed Φ/T. The numerical turbulent trajectory and recurrent solutions analyzed here are taken from [31], providing us with a library of eight recurrent solutions, (u n , T n , Φ n ) 8 n=1 , that satisfy both the Navier-Stokes equation and equation (3.1) to numerical precision. Their period, azimuthal shift, and stability are summarized in table 1.…”

Section: Exact Coherent Structures In Tcfmentioning

confidence: 99%

See 1 more Smart Citation

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

Crowley

Pughe-Sanford

Toler

et al. 2023

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

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)’.

show abstract

“…An edge state is defined as a weakly-unstable invariant state, whose stable manifold forms part of the basin boundary that separates two distinct long-term dynamical outcomes. Two commonly encountered classes of edge states are saddle equilibria and unstable periodic orbits (UPOs), the latter of which bear a strong significance in modern theories of chaos and turbulence [25][26][27][28][29][30][31] . In fact, Keeler et al 10 employed edge-tracking techniques to reveal the existence of an isolated UPO in the depth-averaged model of our system, emanating from a subcritical Hopf bifurcation.…”

mentioning

confidence: 99%

The unpredictable nature of bubble evolution

Jack

Keeler

Gaillard

et al. 2022

Sci Rep

View full text Add to dashboard Cite

Unpredictable dynamics arising from a sensitivity to initial conditions is commonly associated with chaos. We demonstrate how similar unpredictability manifests in a nonlinear system that possesses a large number of long-term outcomes, namely the propagation of an air bubble within a viscous fluid-filled channel. The system under investigation supports various stable states of single-bubble propagation. In addition, bubbles can readily break up during their propagation. Upon subjecting steadily-propagating bubbles to finite-amplitude perturbations in the form of localised channel constrictions, we identify localised regions of the driving flow rate for which the resulting evolutions are unpredictable. Visibly-indistinguishable bubbles are observed to evolve towards a multitude of long-term outcomes, including each of the stable states available to the initial bubble and various states of permanently-changed bubble topology. By combining high-precision experimental results with simulations of a depth-averaged lubrication model of the system, we determine that this behaviour is driven by a sensitive dependence on initial conditions within the vicinity of an unstable periodic orbit.

show abstract

Turbulence tracks recurrent solutions

Cited by 20 publications

References 52 publications

Symmetry-reduced dynamic mode decomposition of near-wall turbulence

Symmetry-reduced dynamic mode decomposition of near-wall turbulence

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

The unpredictable nature of bubble evolution

Contact Info

Product

Resources

About