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

D. Moxey, D. Barkley

Proc. Nat. Acad. Sci., vol. 107, pp. 8091–8096 (2010)

@article{moxey-2010,
  title = {{Distinct large-scale turbulent-laminar states in transitional pipe flow}},
  author = {Moxey, D. and Barkley, D.},
  journal = pnas,
  volume = {107},
  number = {18},
  pages = {8091--8096},
  year = {2010},
  month = may,
  doi = {10.1073/pnas.0909560107},
  url = {https://davidmoxey.uk/assets/pubs/2010-pnas.pdf},
  abstract = {When fluid flows through a channel, pipe, or duct, there are two basic forms of motion: smooth laminar motion and complex turbulent motion.  The discontinuous transition between these states is a fundamental problem that has been studied for more than 100 years.  What has received far less attention is the large-scale nature of the turbulent flows near transition once they are established.  We have carried out extensive numerical computations in pipes of variable lengths up to 125 diameters to investigate the nature of transitional turbulence in pipe flow.  We show the existence of three fundamentally different turbulent states separated by two distinct Reynolds numbers. Below Re_1 ~ 2300, turbulence takes the form of familiar equilibrium (or long-time transient) puffs that are spatially localized and keep their size independent of pipe length. At Re_1 the flow makes a striking transition to a spatio-temporally intermittent flow that fills the pipe. Irregular alternation of turbulent and laminar regions is inherent and does not result from random disturbances.  The fraction of turbulence increases with Re until Re_2 ~ 2600 where there is a continuous transition to a state of uniform turbulence along the pipe. We relate these observations to directed percolation and argue that Re_1 marks the onset of infinite-lifetime turbulence.},
  month_numeric = {5}
}

Once turbulence near the transition is established, what does it look like at large scales? Simulations in pipes of up to 125 diameters reveal three distinct turbulent states separated by two Reynolds numbers: localised puffs below about 2300, a spatio-temporally intermittent flow filling the pipe above it, and uniform turbulence above about 2600. The alternation of turbulent and laminar regions is inherent to the flow rather than a response to random disturbance.