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Table of contents
1 Introduction and context
2 Definitions and concepts
2.1 Navier–Stokes equations
2.1.1 Structure functions and intermittency
2.2 Turbulence in two dimensions
2.2.1 Two dimensional Navier–Stokes equations
2.2.2 The double cascade framework
2.2.3 Energy and enstrophy budgets
2.3 Relative dispersion rates of Lagrangian trajectories
2.3.1 Lyapunov exponents
2.3.2 Separation rates
I Turbulent dispersion and mixing
3 Tracers dispersion in two dimensional turbulence
3.1 Introduction
3.1.1 Diffusion at long times
3.1.2 Continuous source
3.2 middling version
3.2.1 Fluid phase integration
3.2.2 Injection mechanism
3.2.3 Removal mechanism
3.3 Results
3.3.1 One point dispersion
3.3.2 Two-point correlation
3.3.3 Phenomenological description
3.4 Brief conclusion
II Inertial particle-laden flows
4 A lattice method for the numerical modelling of inertial particles
4.1 Inertial particles dynamics
4.1.1 Individual particles
4.2 The modelling of dispersed multiphase flows
4.2.1 From microscopic description to macroscopic quantities
4.3 Description of the method
4.4 Application to a one-dimensional random flow
4.4.1 Particle dynamics for d = 1
4.4.2 Lattice-particle simulations
4.5 Application to incompressible two-dimensional flows
4.5.1 Cellular flow
4.5.2 Heavy particles in 2D turbulence
4.6 Conclusions
5 Turbulence modulation by small heavy particles
6 Conclusions and perspectives
6.1 Turbulent transport of particles emitted from a point source
6.2 Modelisation of small inertial particles
6.3 Turbulence modulation by small heavy particles


