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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2011

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

Résumé

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 \emph{et al.}, J. Fluid Mech. {\bf 401}, 1 (1999)].

Dates et versions

hal-00493280 , version 1 (18-06-2010)

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Clément Sire, Pierre-Henri Chavanis, Julien Sopik. Effective merging dynamics of two and three fluid vortices: Application to two-dimensional decaying turbulence. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 84, pp.056317. ⟨10.1103/PhysRevE.84.056317⟩. ⟨hal-00493280⟩
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