Observation of predator-prey dynamics and the universality class in transitional pipe turbulence

Near the onset to turbulence in pipes, around Re ∼ 1700 − 2000, turbulent puffs decay either directly or, at higher Reynolds numbers through splitting, with characteristic time-scales that exhibit a super-exponential dependence on Reynolds number [3, 1, 7]. The goal of our work [5] is to understand the phenomenology of this transition in terms of standard phase transition concepts, and to calculate the universality class from first principles. Using direct numerical simulations (DNS) of transitional pipe flow, we show that a collective mode, a so-called zonal flow emerges at large scales, activated by anisotropic turbulent fluctuations through an inverse cascade of energy. This zonal flow imposes a shear on the turbulent fluctuations that tends to suppress their anisotropy, leading to stochastic predator-prey dynamics. The effective stochastic theory for the predator-prey modes identified in the DNS reproduces the super-exponential lifetime statistics and phenomenology of pipe flow experiments, correctly predicts the phase diagram of transitional turbulence, and can be mapped exactly to the field theory of directed percolation.