A Universal Transition to Turbulence in Channel Flow

TL;DR

This paper investigates the transition to turbulence in channel flow, revealing a universal critical behavior consistent with directed percolation, and characterizing how turbulent domains spread or decay at critical flow rates.

Contribution

It provides the first experimental evidence that the transition to turbulence in channel flow belongs to the directed percolation universality class, identifying critical exponents and scaling functions.

Findings

Critical behavior observed near transition point.

Turbulent domains either decay or spread depending on flow rate.

Measured critical exponents match directed percolation universality class.

Abstract

Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag properties of fluids, yet when and how turbulence emerges is elusive even for simple flow within pipes and rectangular channels. Unlike the onset of temporal disorder, which is identified as the universal route to chaos in confined flows, characterization of the onset of spatio-temporal disorder has been an outstanding challenge because turbulent domains irregularly decay or spread as they propagate downstream. Here, through extensive experimental investigation of channel flow, we identify a distinctive transition with critical behavior. Turbulent domains continuously injected from an inlet ultimately decayed, or in contrast, spread depending on flow rates. Near a transition point, critical behavior was observed. We investigate both spatial and temporal dynamics of turbulent clusters, measuring four critical exponents, a universal scaling function and a scaling relation, all in agreement with the (2+1)-dimensional directed percolation universality class.