JCJC SIMI 9 - JCJC : Sciences de l'information, de la matière et de l'ingénierie : Sciences de l'ingénierie, matériaux, procédés, énergie

Quantitative study of plane Couette flow: turbulent states and transitions – QANCOUET

Submission summary

Turbulence is one of the last fields of “classical” physics that is not to date fully understood in spite of the constant endeavour of scientists and engineers all along the twentieth century to tackle it. The long-term unpredictable behaviour of turbulence and its presence in everyday life experience and in many human activities have motivated numerous studies that have benefited of the interactions of various approaches ranging from mechanical to mathematical concepts that often implies use of dynamical systems, statistical descriptions and even statistical mechanics.

The study of flows is very often motivated by the numerous instabilities likely to develop as the shear of the flow is increased. In this context, the Reynolds number is the natural control parameter (Re=VL/?, V and L are typical velocity and length, ? the cinematic viscosity of the fluid). According to linear stability theory, flows presenting an inflection point in their velocity profile are destabilised via supercritical scenarios and turn turbulent at some finite value of the control parameter. On the other hand, “non-inflectional” flows are usually linearly stable up to large Reynolds number. In spite of this, they often experience complex transitions to turbulence at moderate Re involving the coexistence of laminar and turbulent domains in sub-critical scenarios. Plane Couette flow (pCf) and pipe Poiseuille flow (pPf) belong to this last category and are thus subject to many studies. “Sub-critical shear flows” are of particular interest on an engineering ground (transport of hydrocarbons in pipes, transition in the boundary layer…) but are also widely used to address fundamental issues. These two model shear flows have fed the study of transition to and from turbulence and recently an international controversy has risen on the transitory nature of turbulence in the Poiseuille configuration. If the mechanisms involved in sub-critical transition to turbulence are still not fully understood, in the last years, numerous numerical studies have allowed the discovery of exact coherent states: steady states, travelling waves and periodic orbits. Regarding plane Couette flow, it has to be noted that an active experimental facility is nowadays lacking to balance the increasing numerical interest toward this flow, and this leads to the following questioning:

•Is turbulence of transitory nature in the more extended system of plane Couette flows?
•How experimental work may be associated to the numerical effort made to understand the mechanisms underlying the complex transitions occurring in plane Couette flows between turbulent states?
•How statistical mechanics formalism can help to understand these transitions?

This project aims at implementing an experimental plane Couette flow in order to break into these debates. Even if the previous experimental studies gave a good insight into the transitions and the spatio-temporal behaviour of pCf, quantitative velocity measurements and thorough statistical analysis are nevertheless lacking. Understanding the complex mechanisms involved in the transitions is a strong motivation of this project and requires the obtaining of large statistical sets of observations. We plan to use of a versatile video system allowing high spatial and temporal resolution visualizations and Stereoscopic Particles Imaging Velocimetry (SPIV) to achieve these goals on a carefully designed experiment allowing a good control of the control parameters over long observations.

Project coordination


The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.



Help of the ANR 169,890 euros
Beginning and duration of the scientific project: - 36 Months

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