Spatiotemporal Intermittency

Chaté, Hugues; Manneville, Paul

doi:10.1007/978-1-4615-2586-8_19

Cited by 15 publications

(14 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to this scenario, called spatiotemporal intermittency (STI) by Kaneko [19], transient chaotic local states of a distributed system may evolve into a sustained turbulent global regime due to spatial coupling. STI has been much studied within the framework of critical phenomena in statistical physics, especially in view of its universality [20]. Coupled map lattices in different spatial dimensions were used to test STI's properties [21,22].…”

mentioning

confidence: 99%

“…Experiments tell us that, in the cases studied so far, it is first-order and thus deprived of any universality (correlation lengths remain finite at threshold). Abstract models considered up to now have been designed on lattices with local couplings and display both kinds of transitions in both one or two dimensions [20][21][22][23]. The problem with this picture -solved by our (semi-)realistic Navier-Sokes modeling of pCf-is that couplings of hydrodynamic origin may have non-local effects linked to pressure, which makes size an important issue.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Manneville

2009

Phys. Rev. E

View full text Add to dashboard Cite

Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent → laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number R low , whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond R low . PACS: 47.20.Ft, 47.27.Cn, 05.45.Jn The transition to turbulence in flows lacking linear instability modes, such as Poiseuille pipe flow driven by a pressure gradient along a circular tube (Ppf) and plane Couette flow driven by two plates moving parallel to each other in opposite directions (pCf), is particularly delicate to understand owing to its abrupt character, without the usual cascade seen in the globally super-critical case, as for e.g. convection. A recent general presentation of the issues is given in [1]. These globally sub-critical flows become turbulent through the nucleation and growth or decay of turbulent domains called puffs (Ppf) or spots (pCf), see, e.g., [2] and [3] for Ppf and pCf, respectively. Most of the work on the transition problem has dealt with special nonlinear solutions (exact coherent structures [4, b]) to the Navier-Stokes equations and their dynamics in the phase space spanned by them. Such solutions, obtained within the so-called Minimal Flow Unit (MFU) assumption [5], have been found at moderate values of the Reynolds number R in Ppf, [6], pCf [4,[7][8][9], and also in plane Poiseuille flow [8,10]. (In pCf, R is defined as Uh/ν where U is the speed of the plates driving the flow, 2h the gap petween the plates, and ν the kinematic viscosity of the fluid.) These solutions are all unstable and, together with their stable and unstable manifolds, they form the skeleton of the turbulent flow at a local scale. The reason why turbulence can be sustained only at much higher values of R (about a factor of two to three higher) is however not clear [2].

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Manneville

2009

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…For example, decay from the sustained turbulent state close to the global stability threshold R g is not well described as a chaotic transient close to a crisis bifurcation point, even though exponential distributions of transient lifetimes are observed near this point [15], because this concept introduced in nonlinear dynamics is not adapted to the account of decay through regression of turbulent patches fluctuating in time and space. On the other hand, the direct connection to statistical physics suggested by Pomeau [40] and underlying the abstract spatio-temporal intermittency approach [41] may seem far-off though it takes spatial extension into account in an analogous way. Extending previous work by one of us [20,22], the approach developed here intends to bridge the gap between low and high dimensional systems in a concrete way and with a semi-quantitative ambition.…”

Section: Resultsmentioning

confidence: 99%

Modeling transitional plane Couette flow

Lagha

Manneville

2007

Eur. Phys. J. B

Self Cite

View full text Add to dashboard Cite

The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it reproduces the globally sub-critical behavior typical of this flow. In particular, the statistics of turbulent transients at decay from turbulent to laminar flow displays striking similarities with experimental findings.

show abstract

“…A vast literature on the mathematical treatment of such bifurcations exists [1] and they have also been studied in natural systems like ecosystems or the climate system, where they are often called regime shifts or tipping points, respectively [30][31][32]. We also do not refer to cases, in which certain parts of a system exhibit a switching of patterns, but the system regarded as a whole remains in a state where different local patterns coexist, such as spatiotemporal intermittency [33], spatiotemporal chaos [34], or moving chimera states [35]. By contrast, several natural systems exhibit intermittent pattern switchings that affect the whole system and cannot be attributed to a parameter change.…”

Section: Introductionmentioning

confidence: 99%

Self-Induced Switchings between Multiple Space-Time Patterns on Complex Networks of Excitable Units

2016

View full text Add to dashboard Cite

We report on self-induced switchings between multiple distinct space-time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly resemble a random process, although the system is deterministic. We show that a chaotic saddle-which contains all the patterns as well as channel-like structures that mediate the transitions between them-is the backbone of such a pattern switching dynamics. Our analyses indicate that essential ingredients for the observed phenomena are that the system behaves like an inhomogeneous oscillatory medium that is capable of self-generating spatially localized excitations and that is dominated by short-range connections but also features long-range connections. With our findings, we present an alternative to the well-known ways to obtain self-induced pattern switching, namely noise-induced attractor hopping, heteroclinic orbits, and adaptation to an external signal. This alternative way can be expected to improve our understanding of pattern switchings in spatially extended natural dynamical systems like the brain and the heart.

show abstract

Spatiotemporal Intermittency

Cited by 15 publications

References 8 publications

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

Modeling transitional plane Couette flow

Self-Induced Switchings between Multiple Space-Time Patterns on Complex Networks of Excitable Units

Contact Info

Product

Resources

About