Statistical model and universality class of transitional turbulence

Hong-Yan Shih^1*

¹Institute of Physics, Academia Sinica, Taipei, Taiwan

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

The onset of turbulence is ubiquitous in daily life and causes energy lost and damages, while how a laminar flow becomes turbulent has remained unsolved for 140 years. Both theory and recent experiments in a quasi-one-dimensional Couette system suggest that the onset of turbulence is a non-equilibrium phase transition in the directed percolation universality class. However, it is not experimentally clear if this universality class applies to pipe flow, where single turbulent puff time scales vary with Reynolds number in a super-exponential way instead of the expected power-law scaling. To see how puff interactions contribute to the critical behavior, we develop stochastic models of puff dynamics by inputting the interaction function measured in pipe experiments, and calculate the phase diagram and critical phenomena. In agreement with renormalization group predictions, we find strong evidence for critical scaling of the turbulent fraction in the directed percolation universality class, with complex crossovers due to finite size effects and the presence of a crystal-like spatiotemporal pattern which results from the repulsion between puffs. I will also show our recent progresses on transitional turbulence, including how an extended ecological model with energy balance successfully recapitulates the spatiotemporal patterns beyond the critical point.

Keywords: phase transition, universality class, turbulence, pattern formation