Flow Instability: Transition and Non Linearity

In contrast to straight pipes - where the flow is linearly stable at all Reynolds numbers (Re) and turbulence arises only through finite-amplitude perturbations - curved pipes can transition via either a subcritical or a supercritical mechanism (Kühnen et al., JFM, 2015). Indeed, above a critical curvature, the laminar flow becomes linearly unstable and gives way to a travelling wave. As customary for supercritical transition scenarios, subsequent bifurcations render the wavy flow structure chaotic.

Surprisingly, a further increase in Reynolds numbers leads to the intermittent appearance of localized turbulent bursts which resemble puffs, familiar from the subcritical transition in straight pipes. We characterized both their global properties, such as size, frequency, lifetime, birth, and decay rates, as well as their local structure, by measuring their energy content and spectra. With increasing Re, these subcritical structures swiftly take over and erase the wave motions.

Hence, despite the flow’s linear instability and the seemingly simple transition route, the flow is eventually dominated by turbulent motions akin to those in the subcritical straight pipe case.

Funding acknowledgement

Stefano Brizzolara received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant agreement No 101034413.