Prandtl-Tietjens intermittency in transitional pipe flows

TL;DR

This paper revisits and refines the Prandtl-Tietjens model of intermittency in transitional pipe flows, providing a quantitative framework that aligns with experimental data at higher Reynolds numbers and clarifies the mechanism's intrinsic nature.

Contribution

The authors develop a quantitative model of Prandtl-Tietjens intermittency, demonstrating its validity at higher Reynolds numbers and clarifying its fundamental role in flow transition.

Findings

Model agrees with experimental data at high Reynolds numbers

Prandtl-Tietjens mechanism is intrinsic to flows with constant pressure gradient and perturbations

Refined mechanism explains flow intermittency without flow fluctuations

Abstract

Pipe flow often traverses a regime where laminar and turbulent flow co-exist. Prandtl and Tietjens explained this intermittency as a feedback between the fluctuations of the internal flow resistance and the constant pressure drop driving the flow. However, because the focus has moved towards studying intermittency without flow fluctuations near the universal critical Reynolds number, their explanation has largely disappeared. Here we refine the mechanism, which has never been put to a quantitative test, to develop a model that agrees with experiments at higher Reynolds numbers, enabling us to demonstrate that Prandtl and Tietjens' mechanism is, in fact, intrinsic to flows where both the pressure gradient and perturbation are constant.