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

By Hong-Yan Shih, T. Hsieh, N. Goldenfeld. Nature Physics, 2015

105 citations recorded by the source corpus.

Simulated pipe flow is interpreted using an ecological model in which predatory zonal flow preys on turbulence, and laminar flows emulate nutrients — establishing a link between turbulence and the directed percolation universality class. The mechanisms and universality class underlying the remarkable phenomena at the transition to turbulence remain a puzzle 130 years after their discovery1. Near the onset to turbulence in pipes1, plane Poiseuille flow2 and Taylor–Couette flow3, transient turbulent regions decay either directly4 or through splitting5,6,7,8, with characteristic timescales that exhibit a super-exponential dependence on Reynolds number9,10. The statistical behaviour is thought to be related to directed percolation (DP; refs 6,11,12,13). Attempts to understand transitional turbulence dynamically invoke periodic orbits and streamwise vortices14,15,16,17,18,19, the dynamics of long-lived chaotic transients20, and model equations based on analogies to excitable media21. 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 transition22, 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.

Subfields: Computational Mechanics, Condensed Matter Physics, Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/98cdf9b91ebae4e92726c674ab2edcef8599f2e4

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Citations in the corpus

Stochastic population dynamics in spatially extended predator–prey systems (2017, background): “As a striking example, let us mention the recently uncovered intimate connection of the directed percolation activeabsorbing transition in predator-prey systems with the long-unresolved problem of the onset of turbulence in shear flows [218].”
Theoretical perspective on the route to turbulence in a pipe (2016, background): “Important among these are those by Kaneko (1985), Chaté & Manneville (1987), Sipos & Goldenfeld (2011), Allhoff & Eckhardt (2012), Marschler & Vollmer (2014), and Shih et al. (2016).”
Criticality in the brain: A synthesis of neurobiology, models and cognition. (2017, background): “Chief amongst these is the notion of criticality, an umbrella term that denotes the behaviour of a system perched between order (such as slow, laminar fluid flow) and disorder [such as the turbulence of a fast-flowing fluid, (Shih et al., 2016)].”