# 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 } }

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…

## 110 Citations

### Modeling the transition to turbulence in shear flows

- Engineering, Physics
- 2011

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

- Physics
- 2012

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

- Physics, EngineeringJournal 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

- PhysicsNature
- 2015

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

- PhysicsJournal of Fluid Mechanics
- 2017

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

- Physics
- 2015

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.

- PhysicsPhysical review. E
- 2019

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

- Physics
- 2019

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

- Physics, Engineering
- 2014

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

- Physics
- 2011

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…

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