Critical Point for Bifurcation Cascades and Featureless Turbulence

Canton, Jacopo; Rinaldi, Enrico; Schlatter, Philipp

doi:10.1103/physrevlett.124.014501

Cited by 15 publications

(16 citation statements)

References 41 publications

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“…Furthermore, concomitant scenarios of bypass and classical transition have been observed on longer timescales, and their possibly simultaneous occurrence blurs the long-time output of the edge tracking algorithm. To our knowledge, whereas instances of such a coexistence have been reported in more complicated geometries (Xu et al 2017;Canton et al 2019) this coexistence is reported for the first time that in a simulation of an unforced boundary layer flow. A moving box technique allows for a more efficient usage of the computational domain.…”

Section: Discussionmentioning

confidence: 48%

Edge tracking in spatially developing boundary layer flows

et al. 2019

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Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien-Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.

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Section: Discussionmentioning

confidence: 48%

Edge tracking in spatially developing boundary layer flows

et al. 2019

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“…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%

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

Beneitez

Duguet

Schlatter

et al. 2020

Phys. Rev. Research

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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.

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“…The three canonical cases of curved pipe flow, plane channel flow and the Blasius boundary layer have been assessed numerically in very recent investigations. For curved pipe flow finite curvature leads, above some threshold in the Reynolds number, to an additional instability absent from the straight pipe case [25]. This instability leads to a limit cycle replacing the laminar state.…”

Section: Introductionmentioning

confidence: 97%

A model for the collapse of the edge when two transitions routes compete

Beneitez,

Duguet,

Henningson

2020

Preprint

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The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical systems concept of edge manifold has been suggested in the subcritical case to explain the partition of the state space of the system. This investigation is devoted to the evolution of the edge manifold when a linear stability is added in such subcritical systems, a situation poorly studied despite its prevalence in realistic fluid flows. In particular the fate of the edge state as a mediator of transition is unclear. A deterministic three-dimensional model is suggested, parametrised by the linear instability growth rate. The edge manifold evolves topologically, via a global saddle-loop bifurcation, from the separatrix between two attraction basins to the mediator between two transition routes. For larger instability rates, the stable manifold of the saddle point increases in codimension from 1 to 2 after an additional local saddle node bifurcation, causing the collapse of the edge manifold. As the growth rate is increased, three different regimes of this model are identified, each one associated with a flow case from the recent hydrodynamic literature. A simple nonautonomous generalisation of the model is also suggested in order to capture the complexity of spatially developing flows.

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Critical Point for Bifurcation Cascades and Featureless Turbulence

Cited by 15 publications

References 41 publications

Edge tracking in spatially developing boundary layer flows

Edge tracking in spatially developing boundary layer flows

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

A model for the collapse of the edge when two transitions routes compete

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