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Mean field results in fluid mechanics - Lecture 1

By Franco Flandoli

Appears in collection : Stochastic and Deterministic Analysis for Irregular Models / Analyse stochastique et déterministe pour les modèles irréguliers

Fluid mechanics is rich in mean field results like those of point vortex approximation in 2D. Deviation from the mean field is also a next step of great interest. We illustrate these facts with the example of particle aggregation in a turbulent fluid, a problem of interest for initial rain formation or planet formation in stellar dust disks. The particles have inertia, measured by the so-called Stokes number. When Stokes is large, the mean field theory describes reality well and produces physical laws coherent with experiments. But when Stokes is small, the mean field is not sufficient and a complete solution is still debated. Rigorous elements of the theory and heuristics about the Physics will be given.

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Citation data

  • DOI 10.24350/CIRM.V.20122103
  • Cite this video Flandoli, Franco (08/01/2024). Mean field results in fluid mechanics - Lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20122103
  • URL https://dx.doi.org/10.24350/CIRM.V.20122103



  • ABRAHAMSON, J. Collision rates of small particles in a vigorously turbulent fluid. Chemical Engineering Science, 1975, vol. 30, no 11, p. 1371-1379. - https://doi.org/10.1016/0009-2509(75)85067-6
  • BEC, J., GUSTAVSSON, K., et MEHLIG, B. Statistical models for the dynamics of heavy particles in turbulence. arXiv preprint arXiv:2304.01312, 2023. - https://doi.org/10.48550/arXiv.2304.01312
  • DOU, Zhongwang, BRAGG, Andrew D., HAMMOND, Adam L., et al. Effects of Reynolds number and Stokes number on particle-pair relative velocity in isotropic turbulence: a systematic experimental study. Journal of Fluid Mechanics, 2018, vol. 839, p. 271-292. - https://doi.org/10.1017/jfm.2017.813
  • FLANDOLI, Franco et HUANG, Ruojun. Coagulation dynamics under environmental noise: scaling limit to SPDE. Latin American Journal of Probability and Mathematical Statistics, 2022, vol 19, p. 1241-1292. - https://doi.org/10.30757/ALEA.v19-51
  • HAMMOND, Alan et REZAKHANLOU, Fraydoun. The kinetic limit of a system of coagulating Brownian particles. Archive for rational mechanics and analysis, 2007, vol. 185, no 1, p. 1-67. - http://dx.doi.org/10.1007/s00205-006-0033-5
  • MEHLIG, Bernhard, USKI, Ville, et WILKINSON, Michael. Colliding particles in highly turbulent flows. Physics of Fluids, 2007, vol. 19, no 9. - https://doi.org/10.1063/1.2768931
  • PAPINI, Andrea, et al. Turbulence Enhancement of Coagulating Processes. PhD thesis, Scuola Normale Superiore 2023. - https://hdl.handle.net/11384/137082
  • PAPINI, Andrea, FLANDOLI, Franco, et HUANG, Ruojun. Turbulence enhancement of coagulation: The role of eddy diffusion in velocity. Physica D: Nonlinear Phenomena, 2023, vol. 448, p. 133726. - https://doi.org/10.1016/j.physd.2023.133726
  • PUMIR, Alain et WILKINSON, Michael. Collisional aggregation due to turbulence. Annual Review of Condensed Matter Physics, 2016, vol. 7, p. 141-170. - https://doi.org/10.1146/annurev-conmatphys-031115-011538
  • WILKINSON, Michael, MEHLIG, Bernhard, et BEZUGLYY, Vlad. CaustWILKINSON, Michael, MEHLIG, Bernhard, et BEZUGLYY, Vlad. Caustic activation of rain showers. Physical review letters, 2006, vol. 97, no 4, p. 048501. - http://dx.doi.org/10.1103/PhysRevLett.97.048501

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