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Accueil du site > Publications > Publications 2011 > Effective merging dynamics of two and three fluid vortices : Application to two-dimensional decaying turbulence

Effective merging dynamics of two and three fluid vortices : Application to two-dimensional decaying turbulence

Clément Sire, Pierre-Henri Chavanis, and Julien Sopik

par Clément Sire - 17 juin 2010

Preprint arXiv:1006.3206.

We present a kinetic theory of two-dimensional decaying turbulence in the context of two-body and three-body vortex merging processes. By introducing the equations of motion for two or three vortices in the effective noise due to all the other vortices, we demonstrate analytically that a two-body mechanism becomes inefficient at low vortex density n\ll 1. When the more efficient three-body vortex mergings are considered, we show that n\sim t^{-\xi}, with \xi=1. We generalize this argument to three-dimensional geostrophic turbulence, finding \xi=5/4, in excellent agreement with direct Navier-Stokes simulations [J. C. McWilliams et al., J. Fluid Mech. 401, 1 (1999)].