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Updated: May 26, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Effective merging dynamics of two and three fluid vortices: application to two-dimensional decaying turbulence
Clément Sire1, Pierre-Henri Chavanis, Julien Sopik
1Laboratoire de Physique Théorique-IRSAMC, Université de Toulouse (UPS) and CNRS, Toulouse, France. clement.sire@irsamc.ups-tlse.fr
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<<1. When the more efficient three-body vortex mergings are considered (involving vortices of different signs), we show that n~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 [McWilliams et al., J. Fluid Mech. 401, 1 (1999)].
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