Universality at the onset of turbulence in shear flows

TL;DR

This paper investigates the transition to turbulence in shear flows, revealing a universal critical point and phase transition behavior across different geometries, supported by experimental evidence and statistical physics analogy.

Contribution

It uncovers a universal critical point at turbulence onset in shear flows and confirms the phase transition analogy with statistical physics models.

Findings

Identification of a critical point at flow rate transition

Universal critical exponent for turbulence onset

Observation of reverse transition from turbulent to laminar flow

Abstract

The volatile transition from quiescent laminar to strongly fluctuating turbulent dynamics in shear flows remains only poorly understood despite its practical importance and more than a century of intense research. The theoretical understanding of the transition process has been complicated by the lack of a linear instability mechanism and additionally by a catastrophic collapse of turbulence which can occur after extremely long lifetimes. Turbulence close to onset is investigated experimentally in three different geometries: pipe, duct and channel flow. The reverse transition from turbulent to laminar flow is observed to be a general feature of shear flows. A critical point is uncovered at slightly higher flow rates, where the nature of the flow changes abruptly to the generic case of expanding turbulence. The critical exponent associated with this phase transition is found to be universal. This confirms a conjecture made over 20 years ago based on an analogy between fluid turbulence and discrete models in statistical physics.