Prandtl-Tietjens intermittency in transitional pipe flows

Abstract

In transition pipe flow, when the flow is driven by a constant pressure gradient, it can enter a regime where the Reynolds number varies sinusoidally and the intermittent patches of turbulence appear periodically. Ludwig Prandtl and Oskar Tietjens proposed a qualitative explanation for this phenomenon, but their mechanism has never before been put to a quantitative test. Combining extensive experiments and modeling, we find quantitative agreement between the Prandtl-Tietjens mechanism and experimental observations, and show that this oscillating regime exists for all flows where both the pressure gradient and perturbation are constant.