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arXiv · 1006.3206

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

Clément Sire·Pierre-Henri Chavanis·Julien Sopik
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Abstract

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 {(involving vortices of different signs)}, we show that $n\sim t^{-ξ}$, with $ξ=1$. We generalize this argument to three-dimensional geostrophic turbulence, finding $ξ=5/4$, in excellent agreement with direct Navier-Stokes simulations [J.\,C. McWilliams \emph{et al.}, J. Fluid Mech. {\bf 401}, 1 (1999)].

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Clément Sire, Pierre-Henri Chavanis, Julien Sopik. 2011-12-31. Effective merging dynamics of two and three fluid vortices: Application to two-dimensional decaying turbulence. https://doi.org/10.1103/physreve.84.056317

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