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

• Published in: arXiv.org
• Main Authors: Hong-Yan, Shih, Tsung-Lin Hsieh, Goldenfeld, Nigel
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 31.05.2015
• Subjects: Collapse; Computational fluid dynamics; Computer simulation; Dependence; Fluid flow; Mathematical models; Percolation; Phenomenology; Physics - Chaotic Dynamics; Physics - Fluid Dynamics; Physics - Statistical Mechanics; Pipe flow; Predator-prey simulation; Quantitative Biology - Populations and Evolution; Reynolds number; Traveling waves; Turbulence; Turbulent flow; Variations; Zonal flow (meteorology)
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1505.02807

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.