Dissertation Award in Statistical and Nonlinear Physics Talk: The emergence of collective modes, ecological collapse and directed percolation at the laminar-turbulent transition*

How a laminar flow becomes turbulence has been an unsolved problem for 130 years and is important in various industrial applications. Only since a decade ago, precise measurements in pipe flow experiments showed non-trivial spatio-temporal complexity at the onset of turbulence where lifetime and splitting time of metastable turbulence do not diverge asymptotically as would have been expected in a sharp transition. Based on numerical evidence in the Navier-Stokes equations, we discovered the surprising fact that the fluid behavior at the transition is governed by the emergent predator-prey dynamics of the important long-wavelength mode, leading to the mathematical prediction that the laminar-turbulent transition is a non-equilibrium phase transition in the directed percolation universality class. This prediction explains the universal scaling laws in experimental observations, and provides a unified picture of transition to turbulence emerging in systems ranging from turbulent convection to magnetohydrodynamics.