Streamwise-localized solutions at the onset of turbulence in pipe flow

TL;DR

This paper reports the discovery of spatially localized periodic solutions in pipe flow that serve as building blocks for turbulence, providing insight into the transition to turbulence at the onset.

Contribution

It introduces new localized solutions in pipe flow equations, linking them to the emergence of turbulence, advancing understanding of transitional flow dynamics.

Findings

Localized periodic solutions exist in pipe flow

Turbulence arises from these localized solutions

Solutions are spatially confined and relate to turbulence onset

Abstract

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulence arises from one such solution branch.