Lagrangian Turbulence: From tracers to intermittency and transport

The course focuses on the Lagrangian approach to turbulence and turbulent transport. In the first part, after a brief recap on Eulerian anomalous scaling and the multifractal model, it will be discussed how intermittency manifests in the statistical properties of fluid tracers showing how the multifractal model can be used to rationalize the velocity and acceleration statistics. Moreover, it will be discussed how the non equilibrium character of turbulence and thus its irreversibility can be revealed in the Lagrangian framework. The second part of the course will focus on transport properties by discussing the statistical properties of particle dispersion and then discussing how the Lagrangian approach can be used to understand many aspects of the statistical properties of scalar fields transported by turbulent flows. For instance, it helps in understanding the origin of dissipative anomaly in scalar transport and the anomalous scaling can be traced back to statistical conservation laws along particle trajectories. Examples of passive and active scalar transport will be discussed in the light of Lagrangian approach.

Lecture 1 - Multifractal model

Lecture 2 - Lagrangian Dispersion

Lecture 3 - Passive scalar