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Lagrangian turbulence

This lecture presents the fundamental tools, both theoretical and experimental, of Lagrangian description of turbulence and of the turbulent transport of particles. The Lagrangian approach, where the dynamics and statistics of turbulence are analyzed along particle trajectories, is indeed the natural framework to address numerous problems, as dispersion and transport of particles and substances, which are omni-present in geophysical and environmental applications : transport of sediments, dispersion of pollutants, droplets in clouds, etc.. The last decade has known a renewed interest for the Lagrangian description of turbulence, after almost a century since the first developments by Taylor and Richardson. This revival is both driven by recent experimental technological advances (making of particle tracking one of the most accurate experimental measurements in fluid mechanics) and to the development of stochastic models, offering an interesting alternative to the usual Eulerian description of fluids. In this context, the lecture will focus on two main aspects : (i) the Lagrangian description of turbulence (transport of fluid tracers) and (ii) turbulent transport of material particles :

- Lagrangian turbulence :

  • general motivations
  • single time Lagrangian statistics (velocity and acceleration of fluid particles)
  • two time statistics (increments, spectra and Lagrangian intermittency) ;
  • the single particle dispersion problem ;
  • the pair dispersion problem (the role of turbulent super-diffusivity) ;
  • the role of large scale anisotropy on Lagrangian dynamics ;
  • stochastic models of Lagrangian turbulence
  • experimental Lagrangian techniques ;
- Turbulent transport of material particles :
  • general motivations
  • usual models for particle/turbulence interaction ;
  • inertial effects on single particle Lagrangian statistics (velocity, acceleration, intermittency) ;
  • finite size effects ;
  • collective effects ;
  • role of gravitational effects (settling of heavy particles)

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