Laboratoire de Physique Théorique
Toulouse - UMR 5152

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 . When the more efficient three-body vortex mergings are considered, we show that , with . We generalize this argument to three-dimensional geostrophic turbulence, finding , in excellent agreement with direct Navier-Stokes simulations [J. C. McWilliams et al., J. Fluid Mech. 401, 1 (1999)].