Spatiotemporal complexity and universality class of transitional turbulence

Hong-Yan Shih^1*

¹Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Hong-Yan Shih, email:hongyan@gate.sinica.edu.tw

How a laminar flow becomes turbulence has been an unsolved problem for more than a century and is important in various industrial applications. Recently precise measurements in pipe flow experiments showed non-trivial spatiotemporal 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 from the hydrodynamics 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 analogous to an ecosystem on the edge of extinction. This prediction demonstrates that the laminar-turbulent transition is a non-equilibrium phase transition in the directed percolation universality class, and provides a unified picture of transition to turbulence emerging in systems ranging from turbulent convection to magnetohydrodynamics. I will also review recent progress about transitional turbulence.

Keywords: phase transition, turbulence, universality class, pattern formation, non-equilibrium statistical mechanics