Department of Physics, NCU
Statistical mechanics of the laminar-turbulent phase transition and the connection to directed percolation
Speaker
Dr. Hong-Yan Shih
Physics Dept., and Carl R. Woese Institute for Genomic Biology
University of Illinois at Urbana-Champaign
Date 2018.01.17 (Wed)
Time 14:00
Place S4-625
Abstract:In this talk,suitable for non-experts, I describe the recent progress made in understanding the transition between laminar and turbulent flow in pipes and other shear flows. I show that this transition is actually a non-equilibrium phase transition that is in the universality class of directed percolation and reggeon field theory. My work uses direct numerical simulation of pipe flow to show that transitional turbulence is dominated by two collective modes: a longitudinal mode for small-scale turbulent fluctuations whose anisotropy induces an emergent large-scale azimuthal mode (so-called zonal flow) that inhibits anisotropic Reynolds stress [1]. This activation-inhibition interaction leads to stochastic predator-prey-like dynamics, from which it follows that the transition to turbulence belongs to the directed percolation universality class [1]. Finally, I show how predator-prey dynamics arises by deriving phenomenologically an effective field theory of the transition from a coarse-graining of the Reynolds equation. [1] H.-Y. Shih, T.-L. Hsieh and N. Goldenfeld. Nat. Phys. 12, 245 (2016).