Lagrangian analyzes of complex and turbulent flows for advanced flow diagnostics

流体力学是一门有几个世纪历史的科学，其中定义了许多概念来描述流体流动。例如，每个人都知道什么是漩涡，然而，漩涡的确切定义仍然是不可用的，而这可能是流体力学中最常用的概念之一。解释这一观察结果的一个原因是，传统上使用的许多标准并不客观。客观性意味着相对于观察者的独立性，即允许定义独立于参照系的物理量。在旋涡的例子中，龙卷风应该可以从地球或卫星上独立地探测到，而且，它的性质在两个参照系中必须是相同的，这一点并不那么明显。从历史上看，流体力学一直是用欧拉工具来研究的，这意味着信息是在时间上从空间的一个固定点收集的。事实上，这是测量量的最简单或唯一的方法，因为当流体运动时，探针在风洞中总是不动的，或者在飞行中将皮托管固定在飞机上以测量其速度。欧拉量的对应量被称为拉格朗日量。在拉格朗日坐标系中，流体粒子的运动正好相反。这在今天确实成为可能，因为我们可以通过数值模拟或最先进的测量技术轻松获取空间和时间的数据。事实证明，许多拉格朗日量是客观的，这为研究运动中的流体开辟了更广阔的工具领域。

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.