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Thierry Gallay; Luis Miguel Rodrigues
Sur le temps de vie de la turbulence bidimensionnelle
Annales de la faculté des sciences de Toulouse Sér. 6, 17 no. 4 (2008), p. 719-733, doi: 10.5802/afst.1199
Article PDF | Reviews MR 2499852 | Zbl 1159.76019

Résumé - Abstract

It is known that all solutions of the two-dimensional Navier-Stokes equation whose vorticity distribution is integrable converge as $t\rightarrow \infty $ to a self-similar flow called Oseen’s vortex. In this article we estimate the time needed for a solution to reach a neighborhood of Oseen’s vortex, starting from arbitrary but well localized initial data. We thus obtain an upper bound on the lifetime of the two-dimensional freely decaying turbulence, depending on the initial Reynolds number. The particular cases where the vorticity distribution is either nonnegative, or sufficiently close to Oseen’s vortex, are studied in more detail.

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