The universality class of the transition to turbulence

TL;DR

This paper demonstrates that the transition to turbulence in shear flows like Couette flow is a second order phase transition belonging to the directed percolation universality class, revealing universal critical behavior.

Contribution

It provides the first evidence that turbulence onset in shear flows is a universal second order phase transition, linking it to directed percolation universality class.

Findings

Transition to turbulence is a second order phase transition.

Turbulent patterns are characterized by universal critical exponents.

Turbulence onset obeys simple collective rules similar to directed percolation.

Abstract

Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature yet characterising the transition that gives rise to it has remained an elusive task. Although in recent studies critical points marking the onset of sustained turbulence have been determined, the physical nature of the transition could not be explained. In extensive experimental and computational studies we show for the example of Couette flow that the onset of turbulence is a second order phase transition and falls into the directed percolation universality class. Consequently the complex laminar-turbulent patterns distinctive for transition in shear flows result from nearest neighbour interactions of turbulent domains and are characterised by universal critical exponents. More generally our study demonstrates that even high dimensional systems far from equilibrium like turbulence exhibit universality at onset and that here the collective dynamics obeys simple rules.