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

TL;DR

This paper models the transition to turbulence in pipe flow as an ecological predator-prey system, revealing the emergence of large-scale zonal flows that suppress turbulence and replicate experimental super-exponential lifetime statistics.

Contribution

It introduces a novel ecological analogy to transitional turbulence, linking fluid dynamics with predator-prey dynamics and the directed percolation universality class.

Findings

Zonal flows emerge at large scales during transition.

Super-exponential lifetime statistics are reproduced.

Turbulence suppression is explained by predator-prey dynamics.

Abstract

The transition to turbulence exhibits remarkable spatio-temporal behavior that continues to defy detailed understanding. Near the onset to turbulence in pipes, transient turbulent regions decay either directly or, at higher Reynolds numbers through splitting, with characteristic time-scales that exhibit a super-exponential dependence on Reynolds number. Here we report 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 reproduces the super-exponential lifetime statistics and phenomenology of pipe flow experiments. Our work demonstrates that a fluid on the edge of turbulence is mathematically analogous to an ecosystem on the edge of extinction, and provides an unbroken link between the equations of fluid dynamics and the directed percolation universality class.