Simplifying the complexity of pipe flow.

@article{Barkley2011SimplifyingTC,
  title={Simplifying the complexity of pipe flow.},
  author={Dwight Barkley},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2011},
  volume={84 1 Pt 2},
  pages={
          016309
        }
}
  • D. Barkley
  • Published 21 January 2011
  • Physics, Engineering
  • Physical review. E, Statistical, nonlinear, and soft matter physics
Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, which additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of… 

Modeling the transition to turbulence in shear flows

One-dimensional models are presented for transitional shear flows. The models have two variables corresponding to turbulence intensity and mean shear. These variables evolve according to simple

Directed percolation model for turbulence transition in shear flows

We analyze a 1 + 1-dimensional directed percolation system as a model for the spatio-temporal aspects of the turbulence transition in pipe flow and other shear flows. Space and time are discrete, and

Theoretical perspective on the route to turbulence in a pipe

  • D. Barkley
  • Physics, Engineering
    Journal of Fluid Mechanics
  • 2016
The route to turbulence in pipe flow is a complex, nonlinear, spatiotemporal process for which an increasingly clear understanding has emerged in recent years. This paper presents a theoretical

The rise of fully turbulent flow

A bifurcation scenario is uncovered that explains the transformation to fully turbulent pipe flow and the front dynamics of the different states encountered in the process and is bridged between understanding of the onset of turbulence and fully turbulent flows.

Universal continuous transition to turbulence in a planar shear flow

We examine the onset of turbulence in Waleffe flow – the planar shear flow between stress-free boundaries driven by a sinusoidal body force. By truncating the wall-normal representation to four

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

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

Periodic solutions and chaos in the Barkley pipe model on a finite domain.

Barkley's bipartite pipe model is a continuous two-state reaction-diffusion system that models the transition to turbulence in pipes, and reproduces many qualitative features of puffs and slugs,

Low-dimensional models of the transition to turbulence

The transition to turbulence in shear flows such as pressure driven pipe flow or plane Couette flow presents an interesting theoretical problem: how do we understand the existence of chaos when the

Direct Numerical Simulation of Transition to Turbulence and Turbulence Control in Pipe Flow

The subject of this thesis is the transition to turbulence and turbulence control in pipe flow. In pipes turbulence arises despite the linear stability of the laminar flow (subcritical transition)

On the decay of turbulence in plane Couette flow

Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold Ret. These bands exist
...

References

SHOWING 1-10 OF 60 REFERENCES

Transition in localized pipe flow turbulence.

Direct numerical simulation of transitional pipe flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates

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

  • P. Manneville
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
By use of 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

The Onset of Turbulence in Pipe Flow

It is shown that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point and is intrinsic to the nature of fluid turbulence.

Turbulence transition and the edge of chaos in pipe flow.

It is shown that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos, formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall.

Distinct large-scale turbulent-laminar states in transitional pipe flow

This work has carried out extensive numerical computations in pipes of variable lengths up to 125 diameters to investigate the nature of transitional turbulence in pipe flow and shows the existence of three fundamentally different turbulent states separated by two distinct Reynolds numbers.

Statistical analysis of the transition to turbulence in plane Couette flow

Abstract:We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical level. We present such a statistical analysis of

Repeller or attractor? Selecting the dynamical model for the onset of turbulence in pipe flow.

Lifetime measurements of turbulence in pipe flow spanning 8 orders of magnitude in time are presented, showing that no critical point exists in this regime and that in contrast to the prevailing view the turbulent state remains transient.

On the transient nature of localized pipe flow turbulence

The onset of shear flow turbulence is characterized by turbulent patches bounded by regions of laminar flow. At low Reynolds numbers localized turbulence relaminarizes, raising the question of

Sensitive dependence on initial conditions in transition to turbulence in pipe flow

The experiments by Darbyshire & Mullin (1995) on the transition to turbulence in pipe flow show that there is no sharp border between initial conditions that trigger turbulence and those that do not.

Decay of turbulence in pipe flow.

A novel experiment has been devised which provides direct evidence for critical point behavior in the longstanding problem of the transition to turbulence in a pipe by reducing the Reynolds number and observing the decay of disordered motion.
...