# Streamwise-localized solutions at the onset of turbulence in pipe flow.

@article{Avila2012StreamwiselocalizedSA, title={Streamwise-localized solutions at the onset of turbulence in pipe flow.}, author={Marc Avila and Fernando Mellibovsky and N Roland and Bj{\"o}rn Hof}, journal={Physical review letters}, year={2012}, volume={110 22}, pages={ 224502 } }

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent…

## 113 Citations

### Sustainment of Oscillations in Localized Turbulent Structures in Pipes

- Physics
- 2018

The solution of the Navier–Stokes equations which reproduces some qualitative features of localized turbulent structures developed in circular pipes at transitional Reynolds numbers is numerically…

### Sustainment of Oscillations in Localized Turbulent Structures in Pipes

- PhysicsFluid Dynamics
- 2018

The solution of the Navier–Stokes equations which reproduces some qualitative features of localized turbulent structures developed in circular pipes at transitional Reynolds numbers is numerically…

### Geometry of transient chaos in streamwise-localized pipe flow turbulence

- PhysicsPhysical Review Fluids
- 2019

In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study the…

### NUMERICAL INVESTIGATION OF LOCALIZED EXACT SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN PIPE FLOW

- Physics, Engineering
- 2015

The edge state solution in pipe flow at Re=2200 is calculated numerically. The solution has the form of spatially localized puff-like structure drifting downstream. In the moving frame it is…

### Numerical study of localized turbulent structures in a pipe

- Physics, Engineering
- 2015

A viscous incompressible flow in a circular pipe is studied numerically at the transitional Reynolds number Re = 2200. The limiting solution of the Navier–Stokes equations is investigated, which…

### Numerical study of localized turbulent structures in a pipe

- Physics, EngineeringFluid Dynamics
- 2015

A viscous incompressible flow in a circular pipe is studied numerically at the transitional Reynolds number Re = 2200. The limiting solution of the Navier–Stokes equations is investigated, which…

### 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…

### A mechanism for streamwise localisation of nonlinear waves in shear flows

- PhysicsJournal of Fluid Mechanics
- 2015

We present the complete unfolding of streamwise localisation in a paradigm of extended shear flows, namely two-dimensional plane Poiseuille flow. Exact solutions of the Navier–Stokes equations are…

### 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.

### Analysis and modeling of localized invariant solutions in pipe flow

- Physics
- 2018

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate…

## 17 References

### Recent progress in understanding the transition to turbulence in a pipe

- Engineering
- 2005

The problem of understanding the nature of fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. So far no explanation has been substantiated to…

### On the transient nature of localized pipe flow turbulence

- PhysicsJournal of Fluid Mechanics
- 2010

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…

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

- Physics, EngineeringPhysical review letters
- 2008

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.

### From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

- PhysicsJournal of Fluid Mechanics
- 2012

Abstract We study numerically a succession of transitions in pipe Poiseuille flow that lead from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the…

### Spatially localized structures in dissipative systems: open problems

- Physics
- 2008

Stationary spatially localized structures, sometimes called dissipative solitons, arise in many interesting and important applications, including buckling of slender structures under compression,…

### On a solenoidal Fourier--Chebyshev spectral method for stability analysis of the Hagen--Poiseuille flow

- Mathematics
- 2007

### III. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels

- EducationProceedings of the Royal Society of London
- 1883

1. Objects and Results of the Investigation.—The results of this investigation have both a practical and a philosophical aspect. In their practical aspect they relate to the laws of resistance to the…

### Commun

- Math. Phys. 20, 167 (1971); L. D. Landau and E. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6
- 1987

### Applied Numerical Mathematics 57

- 920
- 2007

### J . Fluid Mech . 217 , 519 ( 1990 ) ; F . Waleffe

- Phys . Rev . Lett .
- 1998