Ecological collapse and the emergence of travelling waves at the onset of shear turbulence

Hong Yan Shih, Tsung Lin Hsieh, Nigel Goldenfeld

Research output: Contribution to journalArticlepeer-review


The mechanisms and universality class underlying the remarkable phenomena at the transition to turbulence remain a puzzle 130 years after their discovery. Near the onset to turbulence in pipes, plane Poiseuille flow and Taylor-Couette flow, transient turbulent regions decay either directly or through splitting, with characteristic timescales that exhibit a super-exponential dependence on Reynolds number. The statistical behaviour is thought to be related to directed percolation (DP; refs). Attempts to understand transitional turbulence dynamically invoke periodic orbits and streamwise vortices, the dynamics of long-lived chaotic transients, and model equations based on analogies to excitable media. Here we report direct numerical simulations of transitional pipe flow, showing that a zonal flow emerges at large scales, activated by anisotropic turbulent fluctuations; in turn, the zonal flow suppresses the small-scale turbulence leading to stochastic predator-prey dynamics. We show that this ecological model of transitional turbulence, which is asymptotically equivalent to DP at the transition, reproduces the lifetime statistics and phenomenology of pipe flow experiments. Our work demonstrates that a fluid on the edge of turbulence exhibits the same transitional scaling behaviour as a predator-prey ecosystem on the edge of extinction, and establishes a precise connection with the DP universality class.

Original languageEnglish (US)
Pages (from-to)245-248
Number of pages4
JournalNature Physics
Issue number3
StatePublished - Mar 1 2016

ASJC Scopus subject areas

  • General Physics and Astronomy


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