**Lagrangian investigation of particle dispersion in turbulence:
inhomogeneous seeding and pair dispersion**

The question of particle dispersion in turbulent flows is fundamental to understanding various phenomena in industry and nature, from the emission of pollutants at industrial chimneys to rainfalls or mixing in chemical reactors to volcanic plumes. The characteristics of the considered particles, i.e. size, density, shape, volume fraction, etc., play a crucial role in their dynamics in turbulence. However, even the dynamics of simple tracers, i.e. particles behaving as fluid particles, is still a challenging problem because of the complex nature of turbulence. Particle dispersion, intrinsically Lagrangian, can be well-studied nowadays with the development of high-speed cameras and associated algorithmic methods to track particles in turbulent flows, such as Particle Tracking Velocimetry (PTV).

During my PhD, I used PTV with tracers in a turbulent round jet (see figure 1 left). Particle-based velocimetry requires homogeneous seeding to obtain consistent velocity fields. In this study, we use a specific inhomogeneous seeding only through the nozzle. Based on the inhomogeneously seeded tracers, we measure the mean velocity fields, well-known for a jet. The mean axial velocity is unaffected, while the radial one is strongly modified by the use of a nozzle seeding. We show how this inhomogeneous seeding is responsible for the discrepancy and the compressible nature of the Lagrangian tracer flow. In particular, we find new links between effective compressibility, entrainment, and turbulent diffusion in the jet [1].

I also investigated the problem of pair dispersion in homogeneous isotropic turbulence. This is an old question in turbulence since the seminal work of Richardson in 1926, especially the origin of the cubic super-diffusion. We propose a new formulation of the ballistic cascade phenomenology recently proposed by Bourgoin [2] (see figure 1 right) based on stochastic equations. This stochastic formulation gives a better description of the phenomenon with a more rigorous introduction of the ballistic constant, related to the correlation time of relative velocity. We also compare this model to experimental data of homogeneous isotropic turbulence obtained in the lab with PTV, with experimental measurements of the ballistic constant.

Contact Nathanael Machicoane for more information or to schedule a discussion with the seminar speaker.

[1] T. Basset, B. Viggiano, T. Barois, M. Gibert, N. Mordant, R. B. Cal, R. Volk &

M. Bourgoin, Entrainment, diffusion and effective compressibility in a self-similar

turbulent jet, J. Fluid Mech. 947, A29 (2022).

[2] M. Bourgoin, Turbulent pair dispersion as a ballistic cascade phenomenology, J. Fluid Mech. 772, 678-704 (2015).