title: Effective merging dynamics of two and three fluid vortices: application to two-dimensional decaying turbulence.
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)].
authors.affiliation: Laboratoire de Physique Théorique-IRSAMC, Université de Toulouse (UPS) and CNRS, Toulouse, France. clement.sire@irsamc.ups-tlse.fr
authors.forename: Clément
authors.initials: C
authors.lastname: Sire
authors.forename: Pierre-Henri
authors.initials: PH
authors.lastname: Chavanis
authors.forename: Julien
authors.initials: J
authors.lastname: Sopik
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D019277:Entropy; D007700:Kinetics; D015233:Models, Statistical; D008962:Models, Theoretical; D016011:Normal Distribution; D010825:Physics / Q000379:methods*; D013269:Stochastic Processes; D013696:Temperature