The emergence of collective modes, ecological collapse and directed percolation at the laminar-turbulence transition in pipe flow
Hong-Yan Shih, PhD student at University of Illinois at Urbana-Champaign, willl give a talk on "The emergence of collective modes, ecological collapse and directed percolation at the laminar-turbulence transition in pipe flow".
How do fluids become turbulent as their flow velocity is increased? In recent years, careful experiments in pipes and Taylor-Couette systems have revealed that the lifetime of transient turbulent regions in a fluid appears to diverge with flow velocity just before the onset of turbulence, faster than any power law or exponential function. We show how this superexponential scaling of the turbulent lifetime in pipe flow is related to extreme value statistics, which is a manifestation of a mapping between transitional turbulence and the statistical mechanics model of directed percolation. This mapping itself arises from a further surprising and remarkable connection: laminar and turbulent regions in a fluid behave as a predator-prey ecosystem. 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.