On the transient nature of localized pipe flow turbulence

TL;DR

This paper investigates whether localized turbulence in pipe flow is transient or sustained, showing that turbulent lifetimes grow super-exponentially with Reynolds number and identifying a lower bound for metastability.

Contribution

It provides extensive numerical simulations and statistical analysis confirming super-exponential growth of turbulent lifetimes and clarifies the conditions for transient versus sustained turbulence.

Findings

Turbulent lifetimes increase super-exponentially with Reynolds number.

Below a certain Reynolds number, turbulence is no longer metastable and relaminarization is memoryless.

Results align quantitatively with recent experimental data.

Abstract

The onset of shear flow turbulence is characterized by turbulent patches bounded by regions of laminar flow. At low Reynolds numbers localized turbulence relaminarises, raising the question of whether it is transient in nature or it becomes sustained at a critical threshold. We present extensive numerical simulations and a detailed statistical analysis of the data, in order to shed light on the sources of the discrepancies present in the literature. The results are in excellent quantitative agreement with recent experiments and show that the turbulent lifetimes increase super-exponentially with Reynolds number. In addition, we provide evidence for a lower bound below which there are no meta-stable characteristics of the transients, i.e. the relaminarisation process is no longer memoryless.