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Mean field results in fluid mechanics - Lecture 2

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Abstract : 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.

Keywords : stochastic fluid; turbulence; coalescing particles

MSC Codes :
70F99 - None of the above but in this section
 76F25 - Turbulent transport, mixing
 35Q70 - PDEs in connection with mechanics of particles and systems
    Information on the Video

    Language : English
    Available date : 26/01/2024
    Conference Date : 09/01/2024
    Subseries : Research School
    arXiv category : Probability
    Mathematical Area(s) : Analysis and its Applications ; PDE ; Mathematical Physics ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 01:28:05
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-01-09_Flandoli_2.mp4
Information on the Event

Event Title : Stochastic and Deterministic Analysis for Irregular Models / Analyse stochastique et déterministe pour les modèles irréguliers
Dates : 08/01/2024 - 12/01/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/2993.html

Citation Data

DOI : 10.24350/CIRM.V.20122303
Cite this video as: (2024). Mean field results in fluid mechanics - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20122303
URI : http://dx.doi.org/10.24350/CIRM.V.20122303

See Also

Bibliography

  • 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

  • FALKOVICH, Gregory et PUMIR, Alain. Sling effect in collisions of water droplets in turbulent clouds. Journal of the Atmospheric Sciences, 2007, vol. 64, no 12, p. 4497-4505. - https://doi.org/10.1175/2007JAS2371.1

  • 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

  • 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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