Lagrangian analyzes of complex and turbulent flows for advanced flow diagnostics

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Fluid mechanics is a centuries old science in which many concepts have been defined to describe fluid flows. For example, everybody knows what is a vortex, however, the very definition of a vortex is still not available, while this is probably one of the most used concept in fluid mechanics. A reason that explains this observation is that many criteria that are traditionally used are not objective. Objectivity means independency with respect to the observer, which namely allows to define physical quantities that are independent of the reference frame. In the example of the vortex, a tornado should be detectable from earth or from a satellite independently of its movement, and moreover, its properties have to be the same in both reference frame, which is not so obvious. Fluid mechanics has been historically approached with Eulerian tools, which means that the information is gathered in time from a fixed point in space. This is in fact the easier or only way to measure a quantity, as a probe is always motionless in a wind-tunnel while the fluid is moving, or a Pitot tube is fixed to an aircraft during a flight to measure its speed. The counterpart of a Eulerian quantity is said to be Lagrangian. In a Lagrangian frame, fluid particles are on the contrary followed in their movement. This is indeed made possible today because we have easily access to data in space and time through numerical simulations or most advanced state-of-the-art measurement techniques. It turns out that many Lagrangian quantities are objective, which opens a broader field of tools to study fluids in motion. The proposed research program aims at exploring what recently developed Lagrangian tools can tell us on fluid flows. For example, the phenomenon of flow separation, which occurs when a layer of fluid separates from a solid surface, inducing for example the aerodynamic stall on an aircraft wing, still can not be detected, and therefore predicted, but a recent Lagrangian theory could solve this problem soon. More generally, the Lagrangian frame provides a perception of many fluid flow mechanisms differing from traditional approaches, which induces new ideas, and allows to solve some challenging problems or to revisit some concepts. A large variety of flows will be examined, coming from both numerical simulations or experimental databases, from simple to most complex flows, such as turbulence. In particular, we will focus on biological flows that are difficult to analyze because of the high three-dimensionality and the temporal pulsation dependence.