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… 

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  • O. Reynolds
  • Education
    Proceedings 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