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The long way of a viscous vortex dipole

De Thierry Gallay

Apparaît dans la collection : Mathematics of fluids in motion: Recent results and trends / Fluides en mouvement : résultats récents et perspectives

As a toy model for the viscous interaction of planar vortices, we consider the solution of the two-dimensional Navier-Stokes equation with singular initial data corresponding to a pair of point vortices with opposite circulations. In the large Reynolds number regime, we construct an approximate solution which takes into account the deformation of the stream lines due to vortex interactions, as well as the corrections to the translation speed of the dipole due to finite size effects. Using energy estimates based on Arnold's variational characterization of equilibria for the Euler equation, we then show that our approximation remains valid over a very long time interval, if the viscosity is sufficiently small. This is a joint work with Michele Dolce (Lausanne), which relies on previous studies in collaboration with Vladimir Sverak (Minneapolis).

Informations sur la vidéo

Date de captation 12/11/2024
Date de publication 29/11/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20270203
Citer cette vidéo Gallay, Thierry (12/11/2024). The long way of a viscous vortex dipole. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20270203
URL https://dx.doi.org/10.24350/CIRM.V.20270203

Domaine(s)

Bibliographie

DOLCE, Michele et GALLAY, Thierry. The long way of a viscous vortex dipole. arXiv preprint arXiv:2407.13562, 2024. - https://doi.org/10.48550/arXiv.2407.13562

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