Directed percolation phase transition to sustained turbulence in Couette flow

Lemoult, Grégoire; Shi, Liang; Jalikop, Shreyas V.; Avila, Kerstin; Hof, Björn

doi:10.1038/nphys3675

Cited by 205 publications

(205 citation statements)

References 34 publications

Supporting

Mentioning

181

Contrasting

Unclassified

Order By: Relevance

“…Moreover, recent direct numerical simulations (DNS) of pipe flow showed the presence of turbulent energy oscillations between small-scale nascent turbulence and a long-wavelength azimuthal flow (a zonal flow), described by a predator-prey-like stochastic model that could be mapped directly into DP near the critical Re (Shih, Hsieh & Goldenfeld 2016) using statistical mechanics techniques. Finally, recent experiments in a high aspect ratio Taylor-Couette system (Lemoult et al 2016) and in channel flow (Sano & Tamai 2016) show scaling behaviour consistent with the DP predictions. Despite these advances, direct and detailed verification that the Navier-Stokes equations generated stochastic solutions in the DP universality class has seemed out of reach due to the huge system sizes needed to observe the predicted effects.…”

Section: Introductionsupporting

confidence: 58%

A statistical mechanical phase transition to turbulence in a model shear flow

Goldenfeld

2017

J. Fluid Mech.

View full text Add to dashboard Cite

It is becoming increasingly clear that the strong spatial and temporal fluctuations observed in a narrow Reynolds number regime around the laminar-turbulent transition in shear flows can best be understood using the concepts and techniques from a seemingly unrelated discipline -statistical mechanics. During the last few years, a consensus has begun to emerge that these phenomena reflect an underlying non-equilibrium phase transition exhibited by a model of interacting particles on a crystalline lattice, directed percolation, that seems very far from fluid mechanics. Now, Chantry et al. (J. Fluid Mech., vol. 824, 2017, R1) have developed a truncated-mode computation of a model shear flow, capable of simulating systems far larger and longer than any previous study and have for the first time generated enough statistical data that a high-precision test of theory is feasible. The results broadly confirm the theory, extending the class of flows for which the directed percolation scenario holds and removing any remaining doubts that non-equilibrium statistical mechanical critical phenomena can be exhibited by the Navier-Stokes equations.

show abstract

Section: Introductionsupporting

confidence: 58%

A statistical mechanical phase transition to turbulence in a model shear flow

Goldenfeld

2017

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…In this model, the decay vs. splitting issue seems to fall into the 1D DP class, strongly suggesting the same property for the experimentally observed transition at R g ≈ 2040 ( §2.1). Sill in a basically 1D configuration, Lemoult et al (2016) considered cylindrical Couette flow (CCF) in a short cell with small curvature and long perimeter and performed a similarly 1D numerical experiment sampling CCF along an appropriately oriented spiral, as a continuation of the work in (Shi et al, 2013). In both cases they found spatially distributed turbulent patches that display exponents compatible with the one-dimensional DP universality class.…”

Section: The Directed Percolation Issue In Spatiotemporally-intermittmentioning

confidence: 99%

“…Joint to the observation that we are now considering extended systems with sizes several orders of magnitude larger than the MFU, this property situates the transition problem within the field of critical phenomena familiar in the statistical physics of many-body systems (Kadanoff et al, 1967;Stanley, 1999). Recent claims for universality (Lemoult et al, 2016;Sano & Tamai, 2016) have to be understood in this framework. Before discussing these claims, let us rewind the movie a little since our current understanding strongly depends on previous perspectives taken.…”

Section: Global Viewpoint On the Transitionmentioning

confidence: 99%

Transition to turbulence in wall-bounded flows: Where do we stand?

Manneville

2016

Mechanical Engineering Reviews

View full text Add to dashboard Cite

In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite range of Reynolds numbers, the transitional range. The archetypical cases of Poiseuille pipe flow and plane Couette flow are first reviewed at the phenomenological level, together with a few other flow configurations. Theoretical approaches are then examined with particular emphasis on the existence of special nontrivial solutions to the Navier-Stokes equations at finite distance from laminar flow. Dynamical systems theory is most appropriate to analyze their role, in particular with respect to the transient character of turbulence in the lower transitional range. The extensions needed to deal with the prominent spatiotemporal features of the transition are then discussed. Turbulence growth/decay in terms of statistical physics of many-body systems and the relevance of directed percolation as a stochastic process able to account for it are next scrutinized. To conclude, we advocate the recourse to well-designed modeling able to provide us with a conceptually coherent picture of the full transitional range and put forward some open issues.

show abstract

“…(See Manneville (2015, 2016 for recent reviews.) Lemoult et al (2016) recently reported a breakthrough in observing universal exponents in an experimental study of Couette flow.…”

Section: Directed Percolationmentioning

confidence: 99%

Theoretical perspective on the route to turbulence in a pipe

2016

View full text Add to dashboard Cite

The route to turbulence in pipe flow is a complex, nonlinear, spatiotemporal process for which an increasingly clear theoretical understanding has emerged. This understanding is explained to the reader in several steps, exploiting analogies to co-existing thermodynamic phases and to excitable and bistable media. In the end, simple equations encapsulating the keys physical properties of pipe turbulence provide a comprehensive picture of all large-scale states and stages of the transition process. Important among these are metastable localized puffs, localized edge states, puff splitting and interactions between puffs, the critical point for the onset of sustained turbulence via spatiotemporal intermittency (directed percolation), and finally the rise of fully turbulent flow in the form of expanding weak and strong turbulent slugs.

show abstract

Directed percolation phase transition to sustained turbulence in Couette flow

Cited by 205 publications

References 34 publications

A statistical mechanical phase transition to turbulence in a model shear flow

A statistical mechanical phase transition to turbulence in a model shear flow

Transition to turbulence in wall-bounded flows: Where do we stand?

Theoretical perspective on the route to turbulence in a pipe

Contact Info

Product

Resources

About