Edge of chaos and genesis of turbulence

Chian, Abraham C.‐L.; Muñoz, Pablo R.; Rempel, Erico L.

doi:10.1103/physreve.88.052910

Cited by 11 publications

(2 citation statements)

References 37 publications

(54 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The scenario changes dramatically whenever the basin boundary separating laminar flow from the second attractor has previously undergone a smooth-fractal and, possibly, subsequent fractal-fractal metamorphoses [29]. Then a direct transition from permanent temporal chaos to transient spatio-temporal chaos becomes feasible [30].…”

Section: Bifurcation Mechanisms Behind Saddle Mergermentioning

confidence: 99%

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

2016

View full text Add to dashboard Cite

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier-Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.

show abstract

Section: Bifurcation Mechanisms Behind Saddle Mergermentioning

confidence: 99%

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

2016

View full text Add to dashboard Cite

show abstract

“…Besides such basin boundaries, being invariant sets of the system also supports their own specific dynamics. Some physical situations where the precise dynamics on the basin boundaries matter include climate dynamics [2], endothermic chemical reactions barriers [3], synchronization of phase oscillators [4], the instability of accretion disks [5], laser dynamics in modulated optical cavities [6], magnetic reconnection [7], free fall of objects in a gravity field [8], chaotic plasma devices [9], drift-wave turbulence [10], and many others. However the main illustration for the study of such a mixed-state space comes from hydrodynamics, more particularly the century-old problem of transition from laminar to turbulence [11].…”

Section: Introductionmentioning

confidence: 99%

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

Beneitez

Duguet

Schlatter

et al. 2020

Phys. Rev. Research

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

Nonlinear dynamics in space plasma turbulence: temporal stochastic chaos

Chian

Borotto

Hada

et al. 2022

Rev. Mod. Plasma Phys.

View full text Add to dashboard Cite

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and intermittent magnetic turbulence in coronal mass ejections in the solar corona and solar wind via remote and in situ observations. The signatures of turbulent magnetic reconnection, i.e., bifurcated current sheet, reconnecting jet, parallel/anti-parallel Alfvénic waves, and spiky dynamical pressure pulse, as well as fully developed turbulence, are detected at the leading edge of an interplanetary coronal mass ejection and the interface region of two merging interplanetary magnetic flux ropes. Methods for quantifying the degree of coherence, amplitude–phase synchronization, and multifractality of nonlinear multiscale fluctuations are discussed. The stochastic chaotic nature of Alfvénic intermittent structures driven by magnetic reconnection is determined by a complexity–entropy analysis. Finally, we discuss the relation of nonlinear dynamics and intermittent turbulence in space plasmas to similar phenomena observed in astrophysical and laboratory plasmas, e.g., coronal mass ejections and flares in the stellar-exoplanetary environment and Galactic Center, as well as chaos, magnetic reconnection, and intermittent turbulence in laser-plasma and nuclear fusion experiments.

show abstract

Edge of chaos and genesis of turbulence

Cited by 11 publications

References 37 publications

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

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

Nonlinear dynamics in space plasma turbulence: temporal stochastic chaos

Contact Info

Product

Resources

About