The Onset of Turbulence in Pipe Flow

TLDR

Shear flows transition abruptly from laminar to turbulent as velocity rises, yet the Reynolds number at which pipe flow becomes persistently turbulent remains undetermined. Through extensive experiments and simulations, the authors identified and characterized the processes that sustain turbulence. Turbulence in pipes is transient at low Reynolds numbers but becomes sustained at a distinct critical point, driven by spatial proliferation of chaotic domains rather than increasing temporal complexity.

Abstract

Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or ultimately laminar. We show that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point. Through extensive experiments and computer simulations, we were able to identify and characterize the processes ultimately responsible for sustaining turbulence. In contrast to the classical Landau-Ruelle-Takens view that turbulence arises from an increase in the temporal complexity of fluid motion, here, spatial proliferation of chaotic domains is the decisive process and intrinsic to the nature of fluid turbulence.