Edge tracking in spatially developing boundary layer flows

Beneitez, Miguel; Duguet, Yohann; Schlatter, Philipp; Henningson, Dan S.

doi:10.1017/jfm.2019.763

Cited by 19 publications

(51 citation statements)

References 40 publications

(65 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2001), chaotic edge states (Duguet, Willis & Kerswell 2008; Beneitez et al. 2019) or the minimal seed of turbulence (Pringle & Kerswell 2010; Duguet et al. 2013; Vavaliaris, Beneitez & Henningson 2020) or fully non-autonomous flows dictated by time-dependent external forcing or boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

et al. 2021

Self Cite

View full text Add to dashboard Cite

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

show abstract

Section: Discussionmentioning

confidence: 99%

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…The local edge tracking algorithms do not rely on a Boolean approach, but can be defined as optimizers of a scalar observable. We point out that the identification of local edge properties is not limited to bistable systems, and therefore as future work a revisit of manifold-tracking methods in different situations such as [24,31,73] using this framework is strongly encouraged.…”

Section: Conclusion Discussion and Outlookmentioning

confidence: 99%

“…Global methods can, however, fall short whenever no available global observable can elucidate on which side of the edge the different trajectories evolve [31,73], when one of the attractors undergoes a local bifurcation affecting the values of the bounds [74] or simply when information on the bounds α A,B is not available.…”

Section: A Global Versus Local Methodsmentioning

confidence: 99%

“…For instance, the kinetic energy of the departure from the laminar state is low when the laminar is approached and higher in the turbulent regime itself. Even bounds-based methods, for some flow cases like the Blasius boundary layer flow, have recently shown limitations for the tracking of edge trajectories beyond certain horizon times [31]. Also, even in the general cases the identification of relevant bounds for a well-chosen observable implies a very good knowledge of the system that is not always available.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Edge manifold as a Lagrangian coherent structure in a high-dimensional state space

Beneitez

Duguet

Schlatter

et al. 2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

Dissipative dynamical systems characterized by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a dividing manifold called the edge, which separates trajectories attracted by the laminar state from those reaching the turbulent state. We apply here concepts and tools from Lagrangian data analysis to investigate this edge manifold. This approach is carried out in the state space of autonomous arbitrarily highdimensional dissipative systems, in which the edge manifold is reinterpreted as a Lagrangian coherent structure (LCS). Two different diagnostics, finite-time Lyapunov exponents and Lagrangian descriptors, are used and compared with respect to their ability to identify the edge and their scalability. Their properties are illustrated on several low-order models of subcritical transition of increasing dimension and complexity, as well on wellresolved simulations of the Navier-Stokes equations in the case of plane Couette flow. They allow for a mapping of the global structure of both the state space and the edge manifold based on quantitative information. Both diagnostics can also be used to generate efficient bisection algorithms to approach asymptotic edge states, which outperform classical edge tracking.

show abstract

“…In both cases, however, the two transition scenarios were not known to interact with each other until the present study and one contemporary to it [10]. In spatially developing boundary layers recent work suggests that at high Reynolds numbers the edge of chaos can effectively be interpreted as a manifold dividing classical supercritical and subcritical bypass-type transition [8].…”

mentioning

confidence: 93%

Critical Point for Bifurcation Cascades and Featureless Turbulence

2020

Self Cite

View full text Add to dashboard Cite

In this Letter we show that a bifurcation cascade and fully sustained turbulence can share the phase space of a fluid flow system, resulting in the presence of competing stable attractors. We analyse the toroidal pipe flow, which undergoes subcritical transition to turbulence at low pipe curvatures (pipe-to-torus diameter ratio) and supercritical transition at high curvatures, as was previously documented. We unveil an additional step in the bifurcation cascade and provide evidence that, in a narrow range of intermediate curvatures, its dynamics competes with that of sustained turbulence emerging through subcritical transition mechanisms.

show abstract

Edge tracking in spatially developing boundary layer flows

Cited by 19 publications

References 40 publications

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Edge manifold as a Lagrangian coherent structure in a high-dimensional state space

Critical Point for Bifurcation Cascades and Featureless Turbulence

Contact Info

Product

Resources

About