The phase transition to turbulence in spatially extended shear flows

TL;DR

This study experimentally confirms that the transition to turbulence in large-scale cylindrical Couette flow follows the directed percolation universality class, supporting the theory that turbulence onset can be understood through statistical mechanics.

Contribution

The paper provides the first experimental evidence of directed percolation behavior in a shear flow with unprecedented system size, accurately measuring critical exponents near the transition.

Findings

Critical exponents match 2+1D directed percolation predictions.

Transition to turbulence can be described by statistical mechanics.

Large aspect ratio experiments enable precise critical point analysis.

Abstract

Directed percolation(DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however experimental evidence is limited since the largest possible observation times are orders of magnitude shorter than the flows' characteristic time scales. An exception is cylindrical Couette flow where the limit is not temporal but rather the realizable system size. We present experiments in a Couette setup of unprecedented azimuthal and axial aspect ratios. Approaching the critical point to within less than 0.1% we determine five critical exponents, all of which are in excellent agreement with the 2+1D DP-universality class. The complex dynamics encountered at the onset of turbulence can hence be fully rationalized within the framework of statistical mechanics.