Transition to Turbulence in Shear Flows

Turbulent flow is ubiquitous in nature and applications: air flows over an airplane or oil flows through pipelines have an irregular spatial structure and are highly time-dependent. For example the flow through the arteries is usually smooth and laminar but some diseases trigger turbulence. Hence, transition from laminar to turbulence flows poses a challenge of great practical and theoretical relevance. For most simple flows (e.g. pipes and channels) the transition point cannot be deduced from the governing equations but once turbulence sets in, it happens abruptly and without precursors. The aim of my research at the Max Planck Research Group Complex Dynamics and Turbulence directed by Björn Hof in Göttingen, was to further our understanding of turbulence in pipe flow close to the transition.

In our first measurements we investigated whether the turbulent state in shear flows is transient or not. We measured lifetime of turbulence in pipe flow spanning eight orders of magnitude in time, drastically extending all previous investigations. We have shown that no critical point exists in this regime and that, in contrast to the prevailing view, the turbulent state remains transient. This means that if you can follow a turbulent patch for long enough it will always decay to the laminar state, although the waiting time can be more than astronomically long. Later computer simulations agree perfectly with our results. We have also proved that lifetimes are independent of the perturbation that generates turbulence. This means that only one turbulent state exists in pipe flow, which can be reached from different perturbations to the flow. Further measurements in duct flow and Poiseuille flow show identical behavior.

At slightly higher flow rates, for which lifetimes can be measured, localized turbulence spreads generating downstream a copy of the localized patch. Although an individual patch will always decay, the competition of decaying and spreading is the key for the understanding of self sustained turbulence. In our group we have performed one million experimental realizations to determine the critical point at which turbulence spreads faster than decays. This point is often quoted in textbooks but curiously it has never been measured before. This solves a 125 years old question, first posted by O. Reynolds.

We also investigated how turbulent patches at moderate Reynolds numbers extract energy from the flow by combining PIV measurements with direct numerical simulations. We uncovered an amplification mechanism that constantly feeds energy from the mean shear into turbulent eddies. At intermediate flow rates, a simple control mechanism suffices to intercept this energy transfer by reducing inflection points in the velocity profile. When activated, an immediate collapse of turbulence is observed, and the flow relaminarizes. This important result was published in Science and also attracted the attention of many international newspapers such as the New York Times.

At the moment I am still involved in some projects. We currently perform experiments with viscoleastic fluids in pipe flow. Our objective is to find the first conclusive evidence for subcritical transition to viscoelastic turbulence in pipe flow, which has been theoretically predicted some years ago. In this case turbulence is not generated by inertia but by elastic forces.